thermal management analysis of a li-ion battery cell using phase

8/17/2019 Thermal Management Analysis of a Li-ion Battery Cell Using Phase

1/18

See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/292994606

Thermal management analysis of a Li-ionbattery cell using phase change material loaded

with carbon fibers

Article in Energy · February 2016

Impact Factor: 4.84 · DOI: 10.1016/j.energy.2015.12.064

CITATIONS

2

READS

22

5 authors, including:

M. Azizi

University of Texas at Arlington

4 PUBLICATIONS 9 CITATIONS

SEE PROFILE

Fereshteh Samimi

Shiraz University


SEE PROFILE

Gholamreza Karimi

Shiraz University


SEE PROFILE

All in-text references underlined in blue are linked to publications on ResearchGate,

letting you access and read them immediately.

Available from: Gholamreza Karimi

Retrieved on: 13 May 2016

https://www.researchgate.net/profile/Gholamreza_Karimi4?enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg%3D%3D&el=1_x_4https://www.researchgate.net/profile/Gholamreza_Karimi4?enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg%3D%3D&el=1_x_4https://www.researchgate.net/profile/Gholamreza_Karimi4?enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg%3D%3D&el=1_x_5https://www.researchgate.net/profile/Gholamreza_Karimi4?enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg%3D%3D&el=1_x_5https://www.researchgate.net/profile/M_Azizi2?enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg%3D%3D&el=1_x_4https://www.researchgate.net/profile/M_Azizi2?enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg%3D%3D&el=1_x_4https://www.researchgate.net/profile/Fereshteh_Samimi?enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg%3D%3D&el=1_x_4https://www.researchgate.net/profile/Fereshteh_Samimi?enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg%3D%3D&el=1_x_4https://www.researchgate.net/publication/292994606_Thermal_management_analysis_of_a_Li-ion_battery_cell_using_phase_change_material_loaded_with_carbon_fibers?enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg%3D%3D&el=1_x_3https://www.researchgate.net/publication/292994606_Thermal_management_analysis_of_a_Li-ion_battery_cell_using_phase_change_material_loaded_with_carbon_fibers?enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg%3D%3D&el=1_x_3https://www.researchgate.net/publication/292994606_Thermal_management_analysis_of_a_Li-ion_battery_cell_using_phase_change_material_loaded_with_carbon_fibers?enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg%3D%3D&el=1_x_3https://www.researchgate.net/publication/292994606_Thermal_management_analysis_of_a_Li-ion_battery_cell_using_phase_change_material_loaded_with_carbon_fibers?enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg%3D%3D&el=1_x_3https://www.researchgate.net/publication/292994606_Thermal_management_analysis_of_a_Li-ion_battery_cell_using_phase_change_material_loaded_with_carbon_fibers?enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg%3D%3D&el=1_x_3https://www.researchgate.net/publication/292994606_Thermal_management_analysis_of_a_Li-ion_battery_cell_using_phase_change_material_loaded_with_carbon_fibers?enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg%3D%3D&el=1_x_3https://www.researchgate.net/publication/292994606_Thermal_management_analysis_of_a_Li-ion_battery_cell_using_phase_change_material_loaded_with_carbon_fibers?enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg%3D%3D&el=1_x_3https://www.researchgate.net/publication/292994606_Thermal_management_analysis_of_a_Li-ion_battery_cell_using_phase_change_material_loaded_with_carbon_fibers?enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg%3D%3D&el=1_x_3https://www.researchgate.net/publication/292994606_Thermal_management_analysis_of_a_Li-ion_battery_cell_using_phase_change_material_loaded_with_carbon_fibers?enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg%3D%3D&el=1_x_3https://www.researchgate.net/?enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg%3D%3D&el=1_x_1https://www.researchgate.net/profile/Gholamreza_Karimi4?enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg%3D%3D&el=1_x_7https://www.researchgate.net/institution/Shiraz_University?enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg%3D%3D&el=1_x_6https://www.researchgate.net/profile/Gholamreza_Karimi4?enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg%3D%3D&el=1_x_5https://www.researchgate.net/profile/Gholamreza_Karimi4?enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg%3D%3D&el=1_x_4https://www.researchgate.net/profile/Fereshteh_Samimi?enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg%3D%3D&el=1_x_7https://www.researchgate.net/institution/Shiraz_University?enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg%3D%3D&el=1_x_6https://www.researchgate.net/profile/Fereshteh_Samimi?enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg%3D%3D&el=1_x_5https://www.researchgate.net/profile/Fereshteh_Samimi?enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg%3D%3D&el=1_x_4https://www.researchgate.net/profile/M_Azizi2?enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg%3D%3D&el=1_x_7https://www.researchgate.net/institution/University_of_Texas_at_Arlington?enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg%3D%3D&el=1_x_6https://www.researchgate.net/profile/M_Azizi2?enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg%3D%3D&el=1_x_5https://www.researchgate.net/profile/M_Azizi2?enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg%3D%3D&el=1_x_4https://www.researchgate.net/?enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg%3D%3D&el=1_x_1https://www.researchgate.net/publication/292994606_Thermal_management_analysis_of_a_Li-ion_battery_cell_using_phase_change_material_loaded_with_carbon_fibers?enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg%3D%3D&el=1_x_3https://www.researchgate.net/publication/292994606_Thermal_management_analysis_of_a_Li-ion_battery_cell_using_phase_change_material_loaded_with_carbon_fibers?enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg%3D%3D&el=1_x_2


2/18

Thermal management analysis of a Li-ion battery cell using phase

change material loaded with carbon bers

Fereshteh Samimi a, b, Aziz Babapoor b , Mohammadmehdi Azizi b , Gholamreza Karimi b, *

a Department of Chemical Engineering, Shiraz Branch, Islamic Azad University, Shiraz, Iranb Department of Chemical Engineering, Shiraz University, Shiraz 7134851154, Iran

a r t i c l e i n f o

Article history:

Received 26 May 2015

Received in revised form

14 December 2015

Accepted 16 December 2015

Available online xxx

Keywords:

Li-ion battery

PCMs (phase change materials)

Carbon ber

Simulation

Thermal energy management

a b s t r a c t

High latent heat of PCMs (phase change materials) has made them as one of the most important ma-

terials for thermal management purposes. However, PCMs’ low thermal diffusivities could limit their use

in applications which require fast thermal response. The goal of this study is to simulate thermal per-

formance of a lithium ion battery cell in the presence of carbon ber-PCM composites. The effect of

carbon ber loading within the PCM on thermal performance is studied and the results are compared

with the experimental data. The results showed that the presence of carbon bers increases the effective

thermal conductivity of PCM and hence inuences temperature distribution within the cell. PCM com-

posites containing higher percentages of carbon bers present a more uniform temperature distribution.

The results showed that the minimum and maximum thermal conductivity enhancement of 85% and

155% respectively (105% on average). A reasonable agreement is obtained between the simulation results

and the experimental data.

© 2015 Elsevier Ltd. All rights reserved.

1. Introduction

Robust, reliable and ef cient storage units are required as an

integral part of renewable energy systems due to their output

unpredictability [1]. Energy storage makes the systems more cost

effective by reducing the wastage of energy and also enhances the

performance and reliability of energy systems. The energy storage

can also solve the imbalance between the energy supply and con-

sumption of energy that normally exist in the most systems and

thereby helps in saving of capital costs. It is also desirable for more

effective and environmentally benign energy use [2,3].

Thermal energy might be stored in the form of sensible heat

(energy stored by raising the temperature of the storage materialsolid or liquid) or latent heat (energy stored by either melting or

freezing when a substance changes from one phase to another).

When the reverse process occurs, this energy becomes available. It

has been generally accepted that latent heat thermal energystorage

technique is a good engineering option primarily because higher

energy storage density can be obtained with lower temperature

difference between storage and retrieval [1e5]. Phase change

materials are capable of storing and releasing thermal energy at a

nearly xed temperature by taking advantage of their latent heat

(heat of fusion) during phase change. They change from solid to

liquid (liquid to solid) at the melting (solidication) point, reacting

by means of external temperature changes. The melting tempera-

ture varies over a wide range for different PCMs (phase change

materials), e.g., paraf ns, fatty acids, sugar alcohols, salt hydrates,

etc. [1,5,6].

Amongst the various kinds of PCMs, paraf n wax presents

applicable characteristics such as large latent heat of fusion,

negligible supercooling, low vapor pressure during melting,

chemical stability, and total recyclability. Therefore paraf n wax is

being normally considered as one of the most prospective candi-dates in energy systems. However, the relatively low thermal

conductivity associated with paraf n wax leads to lower heat

transfer rates during melting/solidication processes [1,2]. To

overcome this problem, the introduction of highly conductive

materials to form a composite of PCM and thermal conductivity

promoter have been recently proposed; using different types of ns

on the metal wall, and adding metal foam matrix and carbon-based

materials to the PCM are the common promoters used to enlarge

the thermal conductivity of paraf n wax [6e12]. Although, metal

foams have an ultralight porous structure with high strength-to-

density ratio and relatively high thermal conductivity [12], carbon* Corresponding author. Tel.: þ98 71 36473170.E-mail addresses: [email protected], [email protected] (G. Karimi).

Contents lists available at ScienceDirect

Energy

j o u r n a l h o m e p a g e : w w w . e l s e v i e r . co m / l o c a t e / e n e r g y

http://dx.doi.org/10.1016/j.energy.2015.12.064

0360-5442/©

2015 Elsevier Ltd. All rights reserved.

Energy 96 (2016) 355e371

http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-https://www.researchgate.net/publication/227421332_Thermal_Conductivity_Enhancement_of_Phase_Change_Materials_for_Thermal_Energy_Storage_A_Review?el=1_x_8&enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg==https://www.researchgate.net/publication/223277538_Phase_transition_temperature_ranges_and_storage_density_of_paraffin_wax_phase_change_materials?el=1_x_8&enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg==https://www.researchgate.net/publication/262975374_Heat_transfer_characteristics_of_thermal_energy_storage_of_a_composite_phase_change_materials_Numerical_and_experimental_investigations?el=1_x_8&enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg==http://-/?-http://-/?-https://www.researchgate.net/publication/227421332_Thermal_Conductivity_Enhancement_of_Phase_Change_Materials_for_Thermal_Energy_Storage_A_Review?el=1_x_8&enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg==https://www.researchgate.net/publication/223525511_Heat_transfer_characteristics_of_thermal_energy_storage_system_using_PCM_capsules_a_review_Renew_Sustain_Energy_Rev?el=1_x_8&enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg==https://www.researchgate.net/publication/257375359_Development_of_PCMcarbon-based_composite_materials?el=1_x_8&enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg==https://www.researchgate.net/publication/227421332_Thermal_Conductivity_Enhancement_of_Phase_Change_Materials_for_Thermal_Energy_Storage_A_Review?el=1_x_8&enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg==https://www.researchgate.net/publication/223277538_Phase_transition_temperature_ranges_and_storage_density_of_paraffin_wax_phase_change_materials?el=1_x_8&enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg==http://-/?-http://-/?-https://www.researchgate.net/publication/251581825_A_numerical_investigation_of_heat_transfer_in_phase_change_materials_PCMs_embedded_in_porous_metals?el=1_x_8&enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg==mailto:[email protected]:[email protected]://www.sciencedirect.com/science/journal/03605442http://www.elsevier.com/locate/energyhttp://dx.doi.org/10.1016/j.energy.2015.12.064http://dx.doi.org/10.1016/j.energy.2015.12.064http://dx.doi.org/10.1016/j.energy.2015.12.064https://www.researchgate.net/publication/223525511_Heat_transfer_characteristics_of_thermal_energy_storage_system_using_PCM_capsules_a_review_Renew_Sustain_Energy_Rev?el=1_x_8&enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg==https://www.researchgate.net/publication/257375359_Development_of_PCMcarbon-based_composite_materials?el=1_x_8&enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg==https://www.researchgate.net/publication/223277538_Phase_transition_temperature_ranges_and_storage_density_of_paraffin_wax_phase_change_materials?el=1_x_8&enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg==https://www.researchgate.net/publication/223277538_Phase_transition_temperature_ranges_and_storage_density_of_paraffin_wax_phase_change_materials?el=1_x_8&enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg==https://www.researchgate.net/publication/262975374_Heat_transfer_characteristics_of_thermal_energy_storage_of_a_composite_phase_change_materials_Numerical_and_experimental_investigations?el=1_x_8&enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg==https://www.researchgate.net/publication/251581825_A_numerical_investigation_of_heat_transfer_in_phase_change_materials_PCMs_embedded_in_porous_metals?el=1_x_8&enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg==https://www.researchgate.net/publication/227421332_Thermal_Conductivity_Enhancement_of_Phase_Change_Materials_for_Thermal_Energy_Storage_A_Review?el=1_x_8&enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg==https://www.researchgate.net/publication/227421332_Thermal_Conductivity_Enhancement_of_Phase_Change_Materials_for_Thermal_Energy_Storage_A_Review?el=1_x_8&enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg==https://www.researchgate.net/publication/227421332_Thermal_Conductivity_Enhancement_of_Phase_Change_Materials_for_Thermal_Energy_Storage_A_Review?el=1_x_8&enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg==http://dx.doi.org/10.1016/j.energy.2015.12.064http://dx.doi.org/10.1016/j.energy.2015.12.064http://dx.doi.org/10.1016/j.energy.2015.12.064http://www.elsevier.com/locate/energyhttp://www.sciencedirect.com/science/journal/03605442http://crossmark.crossref.org/dialog/?doi=10.1016/j.energy.2015.12.064&domain=pdfmailto:[email protected]:[email protected]://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-


3/18

materials are more proper candidates for thermal and electrical

conductive llers because of their superior thermal and electrical

properties, prominent chemical stability as well as larger specic

surface area and lower density than those of metals [10].

Lithium-ion (Li-ion) cells have shown excellent performance for

high energy storage density and competitive cost [13,14]. Devel-

opment of Li-ion batteries enabled progress in mobile communi-

cations, consumer electronics, automotive and aerospace

industries. However, Li-ion batteries suffers from temperature rise

beyond their normal operating range resulting in a fast aging and

accelerated capacity fade. Therefore, thermal management of Li-ion

batteries has an effective role in large power applications in

addressing the thermal safety apart from enhancing the perfor-

mance and extending the cycle life. Utilization of PCM is a commonapproach for thermal management of Li-ion battery packs. The PCM

introduced in the cell and/or battery supplies a compact and simple

design for controlling battery temperature in Li-ion technology

[14e19].

There are several studies conducted on thermal management of

batteries. In one review by Al-Hallaj et al. [20], it was shown that

the technology base for such a PCM integrated in the battery

module is available in a relatively simple design, and thereby

providing appreciable cost reduction compared to active cooling

systems. Tong et al. [21] demonstrated that safety issues raised

from a lithium-ion battery during operation can be attributed to the

variation of its temperature. Smith et al. [22] showed that proper

comprehending of heat generation and design of heat dissipation

paths are essential for assuring the safety of lithium ion modulesduring abuse events such as external shorts. Abdalla et al. [23]

provided blocks for Li-ion battery thermal management. Thermal

properties of PCM-EG (phase change material-expanded graphite)

composites have been veried. The results indicated that the PCM/

EG composites are strongly affected by their ambient temperatures.

When the percentage of paraf n wax increases in the composite

material, the thermal conductivity was improved at low operating

temperatures while reverse behaviors was observed at relatively

high operating temperature. Frusteri et al. [24] evaluated the in-

uence of carbon bers loading on thermal conductivity

enhancement of an inorganic PCM. Fibers of different lengths were

randomly distributed in an eutectic mixture of Mg (NO3)26H2OeMgCl2 6H2OeNH4NO3 (as a PCM) and thermal conductivity

measurements of the obtained composite were accomplished byhot-wire method. It was shown that the homogeneity grade of the

composite (PCM and ber) plays a signicant role in the improve-

ment of heat diffusion [25]. Recently, Javani et al. [26] have applied

a nite volume based numerical model to investigate thermal

Table 2

Thermo-physical properties of carbon

ber.

Name Thermal conductivity (W/m K) Density (kg/m3) Specic heat capacity (J/kg K)

Carbon ber 50 2000 500

Table 1

Thermo-physical properties of paraf n mixture.

Melting point temperature (C) Density (liquid phase) (kg/m3) Density (solid phase) (kg/m3) Thermal conductivity of solid phase (W/m K) Latent heat of fusion (kJ/kg)

42e49 768 912 0.21 242

Table 3

Labels of samples (ber length ¼ 1 mm).

Sample label Mass fraction of ber [%]

W0 0

W1 0.32

W2 0.46

W3 0.56

W4 0.69

Fig. 1. Experimental setup and the data acquisition system (1-power source 2-container 3-battery module 4-thermocouples 5-temperature indicator 6-data acquisition system)

[26].

F. Samimi et al. / Energy 96 (2016) 355e 371356

https://www.researchgate.net/publication/257176628_Thermal_and_electrical_conductivity_enhancement_of_graphite_nanoplatelets_on_form-stable_polyethylene_glycolpolymethyl_methacrylate_composite_phase_change_materials?el=1_x_8&enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg==https://www.researchgate.net/publication/245105599_Simulation_of_passive_thermal_management_system_for_lithium-ion_battery_packs?el=1_x_8&enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg==https://www.researchgate.net/publication/229318954_Passive_control_of_temperature_excursion_and_uniformity_in_high-energy_Li-ion_battery_packs_at_high_current_and_ambient_temperature?el=1_x_8&enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg==http://-/?-http://-/?-https://www.researchgate.net/publication/223586534_Thermal_modeling_of_secondary_lithium_batteries_for_electric_vehicle_hybrid_electric_vehicle_application?el=1_x_8&enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg==https://www.researchgate.net/publication/272384457_Correlating_uncertainties_of_a_lithium-ion_battery_-_A_Monte_Carlo_simulation?el=1_x_8&enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg==https://www.researchgate.net/publication/229642145_Thermalelectrical_modeling_for_abuse-tolerant_design_of_lithium_ion_modules?el=1_x_8&enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg==https://www.researchgate.net/publication/248254014_Thermomechanical_behaviors_of_the_expanded_graphite-phase_change_material_matrix_used_for_thermal_management_of_Li-ion_battery_packs?el=1_x_8&enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg==https://www.researchgate.net/publication/257525087_Thermal_conductivity_measurement_of_a_PCM_based_storage_system_containing_carbon_fibers?el=1_x_8&enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg==https://www.researchgate.net/publication/229294657_Numerical_approach_to_describe_the_phase_change_of_an_inorganic_PCM_containing_carbon_fibres?el=1_x_8&enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg==https://www.researchgate.net/publication/276121117_Numerical_Modeling_of_Sub-module_Heat_Transfer_with_PCM_for_Thermal_Management_of_Electric_Vehicle_Battery_Packs?el=1_x_8&enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg==http://-/?-https://www.researchgate.net/publication/276121117_Numerical_Modeling_of_Sub-module_Heat_Transfer_with_PCM_for_Thermal_Management_of_Electric_Vehicle_Battery_Packs?el=1_x_8&enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg==https://www.researchgate.net/publication/229294657_Numerical_approach_to_describe_the_phase_change_of_an_inorganic_PCM_containing_carbon_fibres?el=1_x_8&enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg==https://www.researchgate.net/publication/248254014_Thermomechanical_behaviors_of_the_expanded_graphite-phase_change_material_matrix_used_for_thermal_management_of_Li-ion_battery_packs?el=1_x_8&enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg==https://www.researchgate.net/publication/257525087_Thermal_conductivity_measurement_of_a_PCM_based_storage_system_containing_carbon_fibers?el=1_x_8&enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg==https://www.researchgate.net/publication/229642145_Thermalelectrical_modeling_for_abuse-tolerant_design_of_lithium_ion_modules?el=1_x_8&enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg==https://www.researchgate.net/publication/257176628_Thermal_and_electrical_conductivity_enhancement_of_graphite_nanoplatelets_on_form-stable_polyethylene_glycolpolymethyl_methacrylate_composite_phase_change_materials?el=1_x_8&enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg==https://www.researchgate.net/publication/272384457_Correlating_uncertainties_of_a_lithium-ion_battery_-_A_Monte_Carlo_simulation?el=1_x_8&enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg==https://www.researchgate.net/publication/223586534_Thermal_modeling_of_secondary_lithium_batteries_for_electric_vehicle_hybrid_electric_vehicle_application?el=1_x_8&enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg==https://www.researchgate.net/publication/245105599_Simulation_of_passive_thermal_management_system_for_lithium-ion_battery_packs?el=1_x_8&enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg==https://www.researchgate.net/publication/229318954_Passive_control_of_temperature_excursion_and_uniformity_in_high-energy_Li-ion_battery_packs_at_high_current_and_ambient_temperature?el=1_x_8&enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg==http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-


4/18

management of an electric vehicle battery pack using PCM. The

effects of different operating conditions were compared for the

submodule in the presence and the absence of PCM. A more uni-

form temperature distribution was observed when the PCM was

employed.

Despite a large number of investigations have been conducted

for thermal management of Li-ion batteries, there is a funda-

mental lack of information on the optimum condition of PCM

composites, especially those which involve carbon bers. There-

fore the objective of the present work is to examine the heat

transfer enhancement due to presence of carbon ber in a PCM in

a more detail. To this end, thermal management of a discharging

lithium ion battery is simulated in the presence of various cooling

media (a) air, (b) PCM and (c) PCM loaded with carbon bers using

CFD (computational uid dynamic) technique. The simulation

results are compared with the experimental data available in the

literature [27] to verify the composite effectiveness for thermal

management purposes. A very good agreement was observed

between experimental and simulation results for thermal con-

ductivity which is the most signicant parameter in thermal

management. The numerical and experimental results can be

used as a guideline for designing BTMS (battery thermal man-

agement system).

2. Experimentations

Battery discharge is a highly exothermic process. This may

lead to accumulation of heat inside the battery if the generated

heat cannot be removed ef ciently [20,28]. This accumulation of

heat becomes more severe if the battery is operated under

insulating conditions or in a hot environment. Under such con-

ditions, a signicant temperature rise can develop within the

battery and consequently, risking thermal runaway [28]. Having

large amount of latent energy at small temperature changes,

PCMs can be used to absorb and store the heat generated by the

batteries while minimizing the temperature variation in the

battery pack [13,28].In this work, a mixture of paraf ns provided from Merck was

used as the continuous phase change medium with the desired

melting point temperature. Thermo-physical properties of paraf n

mixture are listed in Table 1. Carbon bers were provided from

Zoltex Corporation. The mixture of carbon bers and melted

paraf n was agitated for 2 h at a temperature above its melting

point to ensure that a perfect mixture is obtained. Thermo-physical

properties of carbon ber are listed in Table 2.

Various composites having different mass fraction of carbon -

ber were produced and utilized in a series of experiments to study

the effects of carbon ber loading on the heat transfer rate. Table 3

displays the specications of each experiment.

In practice, the amount of heat dissipation in a Li-ion battery is a

function of state of charge, rate of discharge (or charge) and the

operating temperature. For a regular AA Li-ion battery (e.g.

14500AA), this amount is reported to be approximately 2 W on

average [29,30]. In this work, a cylindrical battery simulator

(14.5 mm in diameter and 50.5 mm in length) was used to simulate

an operating battery during discharge. Fig. 1 shows the experi-

mental setup and the data acquisition system. The battery like

Fig. 2. Variation of temperature of the battery cell, (a): t ¼

0 and (b): t ¼

60 (min).

Fig. 3. Time variations of battery surface temperature in the presence of air (natural

convection).

F. Samimi et al. / Energy 96 (2016) 355e 371 357

https://www.researchgate.net/publication/274096038_Thermal_management_of_a_Li-ion_battery_using_carbon_fiber-PCM_composites?el=1_x_8&enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg==https://www.researchgate.net/publication/223586534_Thermal_modeling_of_secondary_lithium_batteries_for_electric_vehicle_hybrid_electric_vehicle_application?el=1_x_8&enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg==https://www.researchgate.net/publication/223354629_Thermal_modeling_and_design_considerations_of_lithium-ion_batteries?el=1_x_8&enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg==http://-/?-https://www.researchgate.net/publication/223354629_Thermal_modeling_and_design_considerations_of_lithium-ion_batteries?el=1_x_8&enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg==http://-/?-https://www.researchgate.net/publication/245105599_Simulation_of_passive_thermal_management_system_for_lithium-ion_battery_packs?el=1_x_8&enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg==https://www.researchgate.net/publication/223354629_Thermal_modeling_and_design_considerations_of_lithium-ion_batteries?el=1_x_8&enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg==http://-/?-http://-/?-http://-/?-http://-/?-https://www.researchgate.net/publication/251670543_A_review_of_power_battery_thermal_energy_management?el=1_x_8&enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg==https://www.researchgate.net/publication/229382558_Heat_transfer_in_phase_change_materials_for_thermal_management_of_electric_vehicle_battery_modules?el=1_x_8&enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg==http://-/?-https://www.researchgate.net/publication/274096038_Thermal_management_of_a_Li-ion_battery_using_carbon_fiber-PCM_composites?el=1_x_8&enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg==https://www.researchgate.net/publication/229382558_Heat_transfer_in_phase_change_materials_for_thermal_management_of_electric_vehicle_battery_modules?el=1_x_8&enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg==https://www.researchgate.net/publication/251670543_A_review_of_power_battery_thermal_energy_management?el=1_x_8&enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg==https://www.researchgate.net/publication/223354629_Thermal_modeling_and_design_considerations_of_lithium-ion_batteries?el=1_x_8&enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg==https://www.researchgate.net/publication/223354629_Thermal_modeling_and_design_considerations_of_lithium-ion_batteries?el=1_x_8&enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg==https://www.researchgate.net/publication/223354629_Thermal_modeling_and_design_considerations_of_lithium-ion_batteries?el=1_x_8&enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg==https://www.researchgate.net/publication/223586534_Thermal_modeling_of_secondary_lithium_batteries_for_electric_vehicle_hybrid_electric_vehicle_application?el=1_x_8&enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg==https://www.researchgate.net/publication/245105599_Simulation_of_passive_thermal_management_system_for_lithium-ion_battery_packs?el=1_x_8&enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg==http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-


5/18

simulator dissipates heat at a constant heat ux set at of 870 W/m2

equivalent to 2 W. The battery simulatoris mounted in the center of

a 6 mm-thick rectangular container lled with PCM or PCM

composites.

Babapoor et al. [27] have recently showed that the presence of

carbon ber in the paraf n mixture can signicantly improve the

effective thermal conductivity of the cooling medium and hence

carbon ber loaded PCM can be very suitable for thermal man-agement of battery cells in a module or stack.

3. Mathematical modeling

Fig. 1 displays the problem. A cylindrical battery is situated in

the center of a rectangular container lled with the PCM composite

to simulate the experimental setup. Heat is generated within the

battery and dissipated intothe PCM as the cooling medium. As time

elapses, the PCM is heated and the melting starts at the battery-

PCM interface. The melting zone extends towards the container

boundaries. For the axisymmetric cylindrical system considered,

the governing equations for continuity, momentum and energy are

as follows [31e

33]:

Fig. 4. Variations of temperature distributions within the battery cell in the presence of PCM at (a): t ¼ 0, (b): t ¼ 30, (c): t ¼ 60, (d): t ¼ 90 (min).

Fig. 5. Time variations of battery surface temperature in the presence of PCM.


https://www.researchgate.net/publication/274096038_Thermal_management_of_a_Li-ion_battery_using_carbon_fiber-PCM_composites?el=1_x_8&enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg==http://-/?-http://-/?-http://-/?-https://www.researchgate.net/publication/274096038_Thermal_management_of_a_Li-ion_battery_using_carbon_fiber-PCM_composites?el=1_x_8&enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg==http://-/?-http://-/?-http://-/?-http://-/?-


6/18

Fig. 6. Variations of temperature distributions within the battery cell in the presence of carbon ber loaded PCM (W4) (a): t ¼ 0, (b): t ¼ 30, (c): t ¼ 60, (d): t ¼ 90.

Fig. 7. Variation of battery surface temperature in the presence of carbon ber loaded

PCM (W4).

Fig. 8. Variation of battery surface temperature versus time for various carbon ber

loadings.



7/18

Continuity equation:

vr

vt þ

1

r

v

vr ðrr yr Þ þ

v

v z ðry z Þ ¼ 0 (1)

Momentum equations:

rvu

vt

þ rðu:VÞu ¼ VP þ r g !þ V:tþ F

!(2)

where F !

(volume force) is dened as below:

F r ¼ 0 (3)

F z ¼ r g b

T T ref

(4)

where T ref is the reference temperature and is equal to 293.15 K and

b is volumetric thermal expansion coef cient (1/K).

The initial conditions are:

At t ¼ 0 : ur ¼ u z ¼ 0 (5)

At t ¼ 0 : P ¼ r g ðhbatt z Þ (6)

where hbatt is the height of the battery.

Energy equation:

rC pvT

vt þ rC pu:VT ¼ V:ðkVT Þ þ Q (7)

The initial and boundary conditions are:

At t ¼ 0 T ¼ 298:15K (8)

At boundaries : n:ð kVT Þ ¼ hðT ∞ T Þ (9)

where T ∞

is the ambient temperature and equals to 298.15 K.

The battery heat equation can be written as:

rC pvT

vt ¼ Q (10)

where Q , as the heat generated is equal to 236.4 (kW/m3) equiva-

lent to 2 W per battery.

The energy equation for the cooling medium (air, PCM, carbonber-PCM composite), is as follows:

rC pvT

vt þ rC pu:VT ¼ V:ðkVT Þ (11)

The thermal conductivity, specic heat and density of the PCM

are calculated as bellow:

k pcm ¼ qk phase1 þ ð1 qÞk phase2 (12)

C p

pcm ¼ q

C p

phase1þ ð1 qÞ

C p

phase2 (13)

r pcm ¼

qr phase1C p phase1

þ ð1 qÞr phase2C p phase2

q

C p phase1 þ ð1 qÞ

C p phase2

(14)

where q is the liquid fraction. For carbon ber-PCM composite the

latent heat content can be expressed as a function of the latent heat

of the PCM (L), PCM composite mass fraction (f) and liquid fraction

(q) as indicated in Eq. (15).

Lcomp ¼ L4q (15)

The liquid fraction is described as the mass ratio of melted PCM

to the total mass of PCM in the uid. The PCM melting temperature

ranges from T solidus to T liquidus.

Density, specic heat capacity, latent heat and viscosity of the

carbon ber loaded PCM are dened as follows [33e39]:

rcomp ¼ 4rc þ ð1 4Þr pcm (16)

C p

comp ¼4

rC p

c þ ð1 4Þ

rC p

pcm

rcomp(17)

Lcomp ¼ð1 4ÞðrLÞ pcm

rcomp(18)

mcomp ¼ 0:983eð12:959fÞm pcm (19)

The effective thermal conductivity of carbon ber-PCM com-

posite which includes the effects of

ber mass fractions,

Fig. 9. Variation of the battery surface temperature in z-direction for various carbon

ber loadings.

Fig. 10. Variation of cell temperature in r-direction for various carbon ber loadings.


http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-


8/18

Fig. 11. Simulation results for thermal conductivity enhancement factor of composites.

Fig. 12. Experimentally measured thermal conductivity enhancement factor for various PCM composites.



9/18

temperature dependence as well as properties of the base PCM and

bers subject to Brownian motion is given by Refs. [33e39].

K comp ¼K c þ 2K pcm 2

K pcm K c

4

K c þ 2K pcm þ

K pcm K c 4

K pcm

þ 5 104bkx4r pcmC p pcm ffiffiffiffiffiffiffiffiffi

BT

rc dc

s f ðT ;4Þ

(20)

whereB is Boltzmann constant, 1.381 1023 J/K and

bk ¼ 8:4407ð1004Þ1:07304 (21)

f ðT ;4Þ ¼

2:8217 1024þ 3:917 103 T

T ref

þ 3:0669 1024 0:00391123

(22)

where T ref is the reference temperature (298 K). Also, x is a

correction factor in Brownian motion term, because there is no

Brownian motion in solid phase. Its value is dened as the same as

for liquid fraction (q).

4. Numerical method

The numerical technique based onnite-volume method is used

for solving the governing momentum and energy equations [32].

SIMPLER algorithm is used to couple the temperature and velocity

equations and since the governing equations are nonlinear, suc-

cessive over-underrelaxation methodis used to solve the equations

[33].

5. Results and discussion

5.1. Thermal behavior

Figs. 2 and 3 depict the simulation results for natural convection.

The results show that during the rst 60 min, the battery body

temperatures experiences a dramatic rise, up to 70 C (343 K),

which is more than the maximum allowable operating temperature

for Li-ion batteries (45e55 C) [20,27,40e42], and after that time,

the variation of temperature is very small. As expected, naturally

convection air is not an appropriate coolant for thermal manage-

ment purposes.

Therefore, other thermal management system should be used to

control the battery temperature. This can be achieved without

excessive complexity by using a passive cooling system that in-

corporates PCMs as coolant [42]. The temperature results are dis-

played in Figs. 4 and 5.

It is seen from Figs. 4 and 5 that the battery surface temperature

rises up to 57 C (330 K) after 120 min which is approximately 15 C(25%) lower than that of natural convection. In fact, the PCM would

act as a heat sink for the generated heat during the battery

discharge.

Figs.6 and 7 represent the results of simulation for carbon ber-

PCM composite. Here, the mass concentration of carbon bers is

0.69%, the same as experimental study [27].

It is observed that the presence of carbon bers affects the

distribution of temperature within the thermal management sys-

tem. The effectof various carbonberloadings on time variations of

battery surface temperature is shown in Fig. 8. In Fig. 8, the

maximum temperature of composite W4 is 1 K less than blank

which is 329.7 K. The effect of carbon ber loadings on the varia-tions of battery surface temperature along the height is shown in

Fig. 9. Here, a temperature difference between W4 and blank of

1.1 K can be seen along the battery simulator. The maximum tem-

perature reaches to 325.5 K in composite W4. The effect of carbon

berloadings on radial temperature variations is shown in Fig.10. It

is seen from this gure that the temperature difference between

the composite W4 and blank is reduced at larger radii. It should be

mentioned that blank is the sample made of pure paraf n without

carbon bers.

From thesegures, it can be concluded that adding carbonbers

to the PCM affect the temperature distributions within the cell and

Table 4

A comparison between the numerical and experimental thermal conductivity

enhancement factors at various times.

Time (min) hmodel hexperiment Error (deviation)

W110 1.1 0.542857143 0.557142857

20 1.052632 0.80952381 0.24310819

30 1.209524 0.580952381 0.628571619

40 1.222222 0.942857143 0.27936485750 1.035714 0.904761905 0.130952095

60 0.883333 1.076190476 0.192857476

70 0.859155 0.885714286 0.026559286

80 1.060606 0.885714286 0.174891714

90 1.057971 1.068571429 0.010600429

100 1.074627 1.068571429 0.006055571

110 1.089552 1.114285714 0.024733714

120 1.057971 1 0.057971

W210 1.181593 0.855639098 0.325953902

20 1.22199 0.936507937 0.285482063

30 1.552194 0.869950739 0.682243261

40 1.48532 0.980408163 0.504911837

50 1.283714 0.953667954 0.330046046

60 1.263067 1.039183673 0.223883327

70 1.10117 0.942857143 0.158312857

80 1.223644 0.965714286 0.257929714

90 1.10365 1.025087108 0.078562892

100 1.103638 1.022857143 0.080780857

110 1.103959 1.040816327 0.063142673

120 1.203648 1 0.203648

W310 1.001275 0.982072829 0.019202171

20 1.002514 0.99031477 0.01219923

30 1.002832 0.982539683 0.020292317

40 1.004388 0.997178131 0.007209869

50 1.002478 0.993115318 0.009362682

60 1.001838 1.005079365 0.003241365

70 1.000253 0.992626728 0.007626272

80 1.002422 0.995428571 0.006993429

90 1.00304 1.003428571 0.000388571

100 1.002725 1.003428571 0.000703571

110 1.00335 1.005772006 0.002422006

120 1.002729 1 0.002729

W410 1.001116 0.956462585 0.044653415

20 1.00157 0.980295567 0.021274433

30 1.003467 0.960714286 0.042752714

40 1.003457 0.993073593 0.010383407

50 1.001554 0.985714286 0.015839714

60 0.99874 1.011149826 0.012409826

70 0.999338 0.984415584 0.014922416

80 1.001812 0.990062112 0.011749888

90 1.00243 1.007453416 0.005023416

100 1.00242 1.007619048 0.005199048

110 1.003046 1.01242236 0.00937636

120 1.002121 1 0.002121


http://-/?-http://-/?-https://www.researchgate.net/publication/264959862_Computational_Methods_for_Fluid_Dynamics?el=1_x_8&enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg==https://www.researchgate.net/publication/284859680_Numerical_Heat_Transfer_and_Fluid_Flow?el=1_x_8&enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg==http://-/?-http://-/?-http://-/?-https://www.researchgate.net/publication/234876619_A_Novel_Thermal_Management_System_for_Electric_Vehicle_Batteries_Using_Phase-Change_Material?el=1_x_8&enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg==http://-/?-http://-/?-http://-/?-https://www.researchgate.net/publication/274096038_Thermal_management_of_a_Li-ion_battery_using_carbon_fiber-PCM_composites?el=1_x_8&enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg==http://-/?-http://-/?-http://-/?-http://-/?-https://www.researchgate.net/publication/264959862_Computational_Methods_for_Fluid_Dynamics?el=1_x_8&enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg==https://www.researchgate.net/publication/284859680_Numerical_Heat_Transfer_and_Fluid_Flow?el=1_x_8&enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg==https://www.researchgate.net/publication/234876619_A_Novel_Thermal_Management_System_for_Electric_Vehicle_Batteries_Using_Phase-Change_Material?el=1_x_8&enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg==https://www.researchgate.net/publication/274096038_Thermal_management_of_a_Li-ion_battery_using_carbon_fiber-PCM_composites?el=1_x_8&enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg==http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-


10/18

Fig. 13. Velocity distribution in air at (a) t ¼ 30 and (b) t ¼ 90 (min), in carbon ber-free PCM at (c) t ¼ 30 and (d) t ¼ 90 (min) and in carbon ber loaded PCM (W4) at (e) t ¼ 30 and

(f) t ¼ 90 (min).



11/18

the composites made of larger percentages of carbonbers can lead

to more uniform temperature distributions.

5.2. Thermal conductivity enhancement

It is evident that the effective thermal conductivity of PCM

composite is crucial in thermal management perspective. The

presence of a heat transfer promoter (e.g. nanoparticles, metal

matrix) in PCM can provide better heat transfer paths through the

cooling medium.

With known thermal conductivity for the blank PCM, a thermal

conductivity enhancement factor (h), can be dened as [27].

h ¼keff ;c keff ;b

keff ;b(23)

In this equation, keff,c and keff,b denote effective thermal con-

ductivity of composite and blank, respectively.

Fig. 11 shows the simulation results for the thermal conductivity

enhancement factor of various PCM composites versus time.

According to the denition given in Eq. (23), the enhancement

factor (h) for a ber-free PCM (blank) is zero. The presence of car-

bon bers in the PCM improves the effective thermal conductivity

considerably, however; this parameter depends on the mass frac-

tion of the carbonbers used. In addition, PCMs with higher carbon

ber loadings (e.g. W3 and W4) have a steadier trend and their

thermal conductivity enhancement factors remain approximately

constant. On the other hand, samples with smaller carbon ber

loadings (W1 and W2) show unsteady performance owing to small

and unsteady variation of temperature difference (not tempera-

ture) of this samples. In other words, samples containing small

amounts of carbon bers have a performance similar to the blank

Fig. 14. Density of PCM at (a) t ¼ 30 and (b) t ¼ 90 (min) and of composite sample W4 at (c) t ¼ 30 and (d) t ¼ 90 (min).


https://www.researchgate.net/publication/274096038_Thermal_management_of_a_Li-ion_battery_using_carbon_fiber-PCM_composites?el=1_x_8&enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg==http://-/?-http://-/?-https://www.researchgate.net/publication/274096038_Thermal_management_of_a_Li-ion_battery_using_carbon_fiber-PCM_composites?el=1_x_8&enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg==http://-/?-http://-/?-http://-/?-


12/18

and that is why thermal conductivity enhancement factor of these

samples is unsteady.

5.3. Model assessment

Fig. 12 displays the experimental results [27] for thermal con-

ductivity enhancement factor of various PCM composites versus

time. From Figs.11 and 12 and Table 4, there exist a good agreement

between thermal conductivity enhancement factor obtained

experimentally [27] and those predicted by simulation.The melting rate is an important factor in latent heat thermal

energy storage systems such as battery thermal management sys-

tems. At high melting rates, more liquied PCM is available in the

system for natural convection and therefore the velocity of liquid

increases.

5.4. Velocity distribution

Fig. 13(aef) represents the velocity distribution for natural

convection, PCM and carbon ber-PCM composite. As it can be

observed from Fig. 13(a, b), the velocity increases up to 10 mm/s

after 90 min for air cooling system. This change is approximately

dramatic for natural convection which affects the battery body

temperature. These changes in velocity roots from the changein the

density of air.

Fig. 13(c, d) depicts the velocity distribution in the PCM at 30

and 90 min. Under such conditions, the veriations of velocity

within the cell is very small (e.g. between zero to 0.41 mm/s after

90 min) due to parran's larger density and viscosity with

respect to air. Fig. 13(e, f) shows the velocity distribution in the

carbon

ber-PCM composite with 0.69wt.% of carbon

berloading. In this condition, the maximum velocity of carbon ber-

PCM composite in the cell shows 15% decrease compared with

that of the pure paraf n which was predictable because of the

presence of carbon bers which seriously mitigates the motion of

liquied paraf ns.

The maximum amount of energy stored by PCM composite can

be reduced by the presence of carbon bers due to its lower heat

capacity hence, the rate of melting increases. On the other hand, by

increasing carbon ber loading, the velocity of melted composite

decreases owing to resistance of bers against natural convection.

According to the results of simulation, the effect of bers resistant

Fig. 15. Kinematic viscosity of PCM at (a) t ¼ 30 and (b) t ¼ 90 (min) and of composite sample W4 at (c) t ¼ 30 and (d) t ¼ 90 (min).


http://-/?-https://www.researchgate.net/publication/274096038_Thermal_management_of_a_Li-ion_battery_using_carbon_fiber-PCM_composites?el=1_x_8&enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg==http://-/?-http://-/?-https://www.researchgate.net/publication/274096038_Thermal_management_of_a_Li-ion_battery_using_carbon_fiber-PCM_composites?el=1_x_8&enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg==http://-/?-http://-/?-http://-/?-http://-/?-https://www.researchgate.net/publication/274096038_Thermal_management_of_a_Li-ion_battery_using_carbon_fiber-PCM_composites?el=1_x_8&enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg==https://www.researchgate.net/publication/274096038_Thermal_management_of_a_Li-ion_battery_using_carbon_fiber-PCM_composites?el=1_x_8&enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg==http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-


13/18

against motion is dominant which can root from the drop in

buoyancy force caused by added bers.

5.5. Thermo-physical properties

The physical state of PCM has a key role in assessment of the

effectiveness of thermal behavior of carbon ber-PCM composites.

Figs. 14 and 15 show typical changes in density and kinematic

viscosity of PCM and carbonber-PCM composite within the cell at

two different time intervals e.g. 30 and 90 min after cell operation.

The time intervals 30 and 90 min are selected because the changes

in density and kinematic viscosity aresignicant. From Fig.14(ced),

it is obvious that adding carbon bers to the composite increases

the composite density by 8.28% after 90 min. This is due to the

larger density of bers compared to the PCM. Adding bers to the

PCM affects its thermal performance and because density is a

function of temperature, the variation of density occurs. Motion of

particles in melted PCM composite affects its thermal performance

and therefore its density too.

Fig. 16 shows the effect of carbon ber loading on density of

carbon ber-PCM composite.

Changes in density are demonstrated for samples containing

0.32 and 0.46 wt.% carbon bers after 60 min which represent an

increase of about 1.5% by increasing the fraction of carbon ber.

Fig. 17(aed) shows the specic heat capacity distribution of PCM

and PCM composite with 0.69wt.% of carbon ber loading at times

30 and 90 min.

5.6. Phase change state

In PCMs, the changes in phase condition (here solid to liquid)

substantially affect other parameters such as velocity and temper-

ature distributions. Therefore, in this research phase condition is

investigated for both PCM and carbonber-PCM composite and the

results are compared to each other. Figs. 18 and 19 show the phase

transition for PCM carbon ber-loaded PCM composite with 0.69%

wt. at various time intervals.

It is seen from these gures that as time passes, heat is dissi-pated into the PCM (or PCM composite), paraf n is melted and the

melting zone expands. It is observed that a majority of paraf n

(more than 90%) is liqueed after 90 min. The solideliquid

interface which is at at the early stage of melting becomes more

and more distorted as the uid motion is intensied. The solid-

eliquid interface is more progressed near the regions where the

heated ow is upward, while at the zones where the uid motion

is downward, the interface moves more slowly. During the

melting process, natural convection of the liquid phase is devel-

oped, which causes ascending of hot liqueed P CM and

descending of cold liquid PCM. The shapes of the interface for

different carbon ber loadings are basically the same (Figs. 18 and

19). However, the extent of melting region decreases as the mass

fraction of carbon ber increases.

The melting rate is an important factor in latent heat thermal

energy storage systems such as battery thermal management sys-

tems. At high melting rates, more liquid is available in the system

for natural convection and therefore the velocity of liquid phase

increases.

6. Conclusions

Thermal performance of a Li-ion battery was simulated when

dissipating heat into a phase change material loaded with carbon

bers. The effect of carbon ber mass fraction on heat transfer was

studied. From the simulation results, the following conclusions can

be drawn: (a) the presence of carbon bers has a signicant in-uence on thermos-physical properties of PCM e.g. 11% increase in

density of sample W2 compared with the blank, (b) the solideliquid

interface is more progressed near the regions where the heated

ow is upward, while at regions where the uid motion is down-

ward, the interface moves more slowly, (c) the more melting rate,

the more liquied PCM is available in the cell for natural convection

and therefore the velocity of the liquid increases, (d) while PCMs

can control the battery temperature much betterthan air by natural

convection, they suffer from their low thermal conductivities.

Carbon ber-loaded PCM composites can be a good replacement to

solve this issue. (e) the presence of carbon bers in the PCM results

in signicantly improvement of effective thermal conductivity and

consequently, this makes the medium very suitable for thermal

management of battery cells in a module or stack.

Fig. 16. Density of sample at t ¼ 60 (min), (a): W1, (b): W2.


http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-


14/18

Fig. 17. Specic heat capacity of PCM at (a) t ¼ 30, (b) t ¼ 60, and of composite sample W4 at (c) t ¼ 30 and (d) t ¼ 90 (min).



15/18

Fig. 18. Phase transition for sample W0, (a): t ¼ 0, (b): t ¼ 30, (c): t ¼ 60 and (d): t ¼ 90 (min) (phase 1 is the solid phase.).



16/18

Fig. 19. Phase transition for sample W4, (a): t ¼ 0, (b): t ¼ 30, (c): t ¼ 60 and (d): t ¼ 90 (min) (phase 1 is the solid phase.).



17/18

Nomenclature

B Boltzmann constant, 1.381 1023 J/K

Cp specic heat capacity (J/mol K)

D carbon ber diameter (m)

F volume force (N)

G acceleration of gravity (m/s2)

H heat transfer coef cient (W m2 K1)

L latent heat of the PCM (J/kg)

K thermal conductivity (W m1 K1)

P pressure (Pa)

DP pressure changes (Pa)

Q volumetric heat source (W m3)

r radial distance (mm)

T temperature (C)

t time (s)

w carbon ber mass fraction

z axial distance (mm)

Greek letters

q liquid fraction

m viscosity (Pa. s)

r density (kg/m3)n velocity (m/s)

4 carbon ber mass fraction

t shear stress (Pa)

x correction factor in Brownian motion term

b volumetric thermal expansion coef cient (K1)

h thermal conductivity enhancement factor

Superscripts and subscripts

b blank

batt battery

c carbon ber

comp carbon ber-PCM composite

eff effective

ref reference state

Abbreviations

CFD computational uid dynamic

Li-ion lithium-ion

PCM phase change material

PCM-EG phase change materialeexpanded graphite

References

[1] Fan L, Khodadadi JM. Thermal conductivity enhancement of phase changematerials for thermal energy storage: a reviews. Renew Sustain Energy Rev2011;15:24e46.

[2] He B, Martin V, S etterwall F. Phase transition temperature ranges and storagedensity of paraf n wax phase change materials. Energy 2004;29:1785e804.

[3] Aadmi M, Karkri M, Hammouti M. Heat transfer characteristics of thermalenergy storage of a composite phase change materials: numerical andexperimental investigations. Energy 2014;72:381e92.

[4] Cao L, Tang Y, Fang G. Preparation and properties of shape-stabilized phasechange materials based on fatty acid eutectics and cellulose composites forthermal energy storage. Energy 2015;80:98e103.

[5] Felix Regin A, Solanki SC, Saini JS. Heat transfer characteristics of thermalenergy storage system using PCM capsules: a review. Renew Sustain EnergyRev 2008;12:2438e58.

[6] Gilart PM, Martınez AY, Barriuso MG, Martınez CM. Development of PCM/carbon-based composite materials. Sol Energy Mater Sol Cells 2012;107:205e11.

[7] Liu Z-H, Zheng B-C, Wang Q, Li S-S. Study on the thermal storage performanceof a gravity assisted heat pipe thermal storage unit with granular high-temperature phase change materials. Energy 2015;81:754e65.

[8] Chandrasekaran P, Cheralathan M, Kumaresan V, Velraj R. Enhanced heattransfer characteristics of water based copper oxide nanouid PCM (phase

change material) in a spherical capsule during solidication for energy ef -cient cool thermal storage system. Energy 2014;72:636e42.

[9] Li WQ, Qu ZG, Zhang BL, Zhao K, Tao WQ. Thermal behavior of porousstainless-steel ber felt saturated with phase change material. Energy2013;55:846e52.

[10] Zhang L, Zhu J, Zhou W, Wang J, Wang Y. Thermal and electrical conductivityenhancement of graphite nanoplatelets on form-stable polyethylene glycol/polymethyl methacrylate composite phase change materials. Energy 2012;39:294e302.

[11] Xu B, Li Z. Paraf n/diatomite/multi-wall carbon nanotubes composite phase

change material tailor-made for thermal energy storage cement-based com-posites. Energy 2014;72:371e80.

[12] Tian Y, Zhao CY. A numerical investigation of heat transfer in phase changematerials (PCMs) embedded in porous metals. Energy 2011;36:5539e46.

[13] Mills A, Al-Hallaj S. Simulation of passive thermal management system forlithium-ion battery packs. J Power Sources 2005;141:307e15.

[14] Kizilel R, Lateef A, Sabbah R, Farid MM, Selman JR, Al-Hallaj S. Passive controlof temperature excursion and uniformity in high-energy Li-ion battery packsat high current and ambient temperature. J Power Sources 2008;183:370e5.

[15] Goli P, Legedza S, Dhar A, Salgado R, Renteria J, Balandin AA. Graphene-enhanced hybrid phase change materials for thermal management of Li-ionbatteries. J Power Sources 2014;248:37e43.

[16] Khateeb SA, Amiruddin S, Farid M, Selman JR, Al-Hallaj S. Thermal manage-ment of Li-ion battery with phase change material for electric scooters:experimental validation. J Power Sources 2005;142:345e53.

[17] Zhang S, Zhao R, Liu J, Gu J. Investigation on a hydrogel based passive thermalmanagement system for lithium ion batteries. Energy 2014;68:854e61.

[18] Hu X, Li SE, Jia Z, Egardt B. Enhanced sample entropy-based health manage-ment of Li-ion battery for electried vehicles. Energy 2014;64:953e60.

[19] Kizilel R, Sabbah R, Selman JR, Al-Hallaj S. An alternative cooling system toenhance the safety of Li-ion battery packs. J Power Sources 2009;194:1105e12.

[20] Al-Hallaj S, Selman JR. Thermal modeling of secondary lithium batteries forelectric vehicle/hybrid electric vehicle applications. J Power Sources2002;110:341e8.

[21] Tong W, Koh WQ, Birgersson E, Mujumdar AS, Yap C. Correlating uncertaintiesof a lithium-ion battery e a Monte Carlo simulation. Int J Energy Res 2015;39:778e88.

[22] Smith K, Kim G-H, Darcy E, Pesaran A. Thermal/electrical modeling for abuse-tolerant design of lithium ion modules. Int J Energy Res 2010;34:204e15.

[23] Alrashdan A, Mayyas AT, Al-Hallaj S. Thermo-mechanical behaviors of theexpanded graphite-phase change material matrix used for thermal manage-ment of Li-ion battery packs. J Mater Process Technol 2010;210:174e9.

[24] Frusteri F, Leonardi V, Vasta S, Restuccia G. Thermal conductivity measure-ment of a PCM based storage system containing carbon bers. Appl ThermEng 2005;25:1623e33.

[25] Frusteri F, Leonardi V,Maggio G. Numerical approach to describe the phase

change of an inorganic PCM containing carbon bers. Appl Therm Eng2006;26:1883e92.[26] Javani N, Dincer I, Naterer GF. Numerical modeling of submodule heat transfer

with phase change material for thermal management of electric vehicle bat-tery packs. J Therm Sci Eng Appl 2015;7. http://dx.doi.org/10.1115/1.4029053.

[27] Babapoor A, Azizi M, Karimi G. Thermal management of a Li-ion battery usingcarbon ber-PCM composites. Appl Therm Eng 2015;82:281e90.

[28] Al-Hallaj S, Maleki H, Hong JS, Selman JR. Thermal modeling and designconsiderations of lithium-ion batteries. J Power Sources 1999;83:1e8.

[29] Rao Z, Wang S. A review of power battery thermal energy management.Renew Sustain Energy Rev 2011;15:4554e71.

[30] Duan X, Naterer GF. Heat transfer in phase change materials for thermalmanagement of electric vehicle battery modules. Int J Heat Mass Transf 2010;53:5176e82.

[31] Valan Arasu A, Mujumdar AS. Numerical study on melting of paraf n waxwith Al2O3 in a square enclosure. Int Commun Heat Mass Transf 2012;39:8e16.

[32] Ferziger J, Peric M. Computational method for uid dynamics. Berlin:Springer-Verlag; 1996.

[33] Patankar SV. Numerical heat transfer and uid ow. Washington: HemispherePub Co; 1980.

[34] Chow LC, Zhong JK. Thermal conductivity enhancement for phase changestorage media. Int Commun Heat Mass Transf 1996;23:91e100.

[35] Vajjha RS, Das DK, Namburu PK. Numerical study of uid dynamic and heattransfer performance of Al2O3 and CuO nanouids in the at tubes of aradiator. Int J Heat Fluid Flow 2010;31:613e21.

[36] Kandasamy R, Wang XQ, Mujumdar AS. Transient cooling of electronics usingphase change material (PCM)-based heat sinks. Appl Therm Eng 2008;28:1047e57.

[37] Sasmito AP, Kurnia JC, Mujumdar AS. Numerical evaluation of laminar heattransfer enhancement in nanouid ow in coiled square tubes. Nanoscale ResLett 2011;6:376e90.

[38] Rao Y, Frank D, Peter S. Convective heat transfer characteristics of micro-encapsulated phase change material suspensions in mini channels. J HeatMass Transf 2007;44:175e86.


https://www.researchgate.net/publication/227421332_Thermal_Conductivity_Enhancement_of_Phase_Change_Materials_for_Thermal_Energy_Storage_A_Review?el=1_x_8&enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg==https://www.researchgate.net/publication/227421332_Thermal_Conductivity_Enhancement_of_Phase_Change_Materials_for_Thermal_Energy_Storage_A_Review?el=1_x_8&enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg==https://www.researchgate.net/publication/227421332_Thermal_Conductivity_Enhancement_of_Phase_Change_Materials_for_Thermal_Energy_Storage_A_Review?el=1_x_8&enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg==https://www.researchgate.net/publication/227421332_Thermal_Conductivity_Enhancement_of_Phase_Change_Materials_for_Thermal_Energy_Storage_A_Review?el=1_x_8&enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg==https://www.researchgate.net/publication/227421332_Thermal_Conductivity_Enhancement_of_Phase_Change_Materials_for_Thermal_Energy_Storage_A_Review?el=1_x_8&enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg==https://www.researchgate.net/publication/227421332_Thermal_Conductivity_Enhancement_of_Phase_Change_Materials_for_Thermal_Energy_Storage_A_Review?el=1_x_8&enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg==https://www.researchgate.net/publication/223277538_Phase_transition_temperature_ranges_and_storage_density_of_paraffin_wax_phase_change_materials?el=1_x_8&enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg==https://www.researchgate.net/publication/223277538_Phase_transition_temperature_ranges_and_storage_density_of_paraffin_wax_phase_change_materials?el=1_x_8&enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg==https://www.researchgate.net/publication/223277538_Phase_transition_temperature_ranges_and_storage_density_of_paraffin_wax_phase_change_materials?el=1_x_8&enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg==https://www.researchgate.net/publication/223277538_Phase_transition_temperature_ranges_and_storage_density_of_paraffin_wax_phase_change_materials?el=1_x_8&enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg==https://www.researchgate.net/publication/223277538_Phase_transition_temperature_ranges_and_storage_density_of_paraffin_wax_phase_change_materials?el=1_x_8&enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg==https://www.researchgate.net/publication/223277538_Phase_transition_temperature_ranges_and_storage_density_of_paraffin_wax_phase_change_materials?el=1_x_8&enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg==https://www.researchgate.net/publication/223277538_Phase_transition_temperature_ranges_and_storage_density_of_paraffin_wax_phase_change_materials?el=1_x_8&enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg==https://www.researchgate.net/publication/262975374_Heat_transfer_characteristics_of_thermal_energy_storage_of_a_composite_phase_change_materials_Numerical_and_experimental_investigations?el=1_x_8&enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg==https://www.researchgate.net/publication/262975374_Heat_transfer_characteristics_of_thermal_energy_storage_of_a_composite_phase_change_materials_Numerical_and_experimental_investigations?el=1_x_8&enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg==https://www.researchgate.net/publication/262975374_Heat_transfer_characteristics_of_thermal_energy_storage_of_a_composite_phase_change_materials_Numerical_and_experimental_investigations?el=1_x_8&enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg==https://www.researchgate.net/publication/262975374_Heat_transfer_characteristics_of_thermal_energy_storage_of_a_composite_phase_change_materials_Numerical_and_experimental_investigations?el=1_x_8&enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg==https://www.researchgate.net/publication/262975374_Heat_transfer_characteristics_of_thermal_energy_storage_of_a_composite_phase_change_materials_Numerical_and_experimental_investigations?el=1_x_8&enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg==https://www.researchgate.net/publication/262975374_Heat_transfer_characteristics_of_thermal_energy_storage_of_a_composite_phase_change_materials_Numerical_and_experimental_investigations?el=1_x_8&enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg==https://www.researchgate.net/publication/272381562_Preparation_and_properties_of_shape-stabilized_phase_change_materials_based_on_fatty_acid_eutectics_and_cellulose_composites_for_thermal_energy_storage?el=1_x_8&enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg==https://www.researchgate.net/publication/272381562_Preparation_and_properties_of_shape-stabilized_phase_change_materials_based_on_fatty_acid_eutectics_and_cellulose_composites_for_thermal_energy_storage?el=1_x_8&enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg==https://www.researchgate.net/publication/272381562_Preparation_and_properties_of_shape-stabilized_phase_change_materials_based_on_fatty_acid_eutectics_and_cellulose_composites_for_thermal_energy_storage?el=1_x_8&enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg==https://www.researchgate.net/publication/272381562_Preparation_and_properties_of_shape-stabilized_phase_change_materials_based_on_fatty_acid_eutectics_and_cellulose_composites_for_thermal_energy_storage?el=1_x_8&enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg==https://www.researchgate.net/publication/272381562_Preparation_and_properties_of_shape-stabilized_phase_change_materials_based_on_fatty_acid_eutectics_and_cellulose_composites_for_thermal_energy_storage?el=1_x_8&enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg==https://www.researchgate.net/publication/272381562_Preparation_and_properties_of_shape-stabilized_phase_change_materials_based_on_fatty_acid_eutectics_and_cellulose_composites_for_thermal_energy_storage?el=1_x_8&enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg==https://www.researchgate.net/publication/223525511_Heat_transfer_characteristics_of_thermal_energy_storage_system_using_PCM_capsules_a_review_Renew_Sustain_Energy_Rev?el=1_x_8&enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg==https://www.researchgate.net/publication/223525511_Heat_transfer_characteristics_of_thermal_energy_storage_system_using_PCM_capsules_a_review_Renew_Sustain_Energy_Rev?el=1_x_8&enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg==https://www.researchgate.net/publication/223525511_Heat_transfer_characteristics_of_thermal_energy_storage_system_using_PCM_capsules_a_review_Renew_Sustain_Energy_Rev?el=1_x_8&enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg==https://www.researchgate.net/publication/223525511_Heat_transfer_characteristics_of_thermal_energy_storage_system_using_PCM_capsules_a_review_Renew_Sustain_Energy_Rev?el=1_x_8&enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg==https://www.researchgate.net/publication/223525511_Heat_transfer_characteristics_of_thermal_energy_storage_system_using_PCM_capsules_a_review_Renew_Sustain_Energy_Rev?el=1_x_8&enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg==https://www.researchgate.net/publication/223525511_Heat_transfer_characteristics_of_thermal_energy_storage_system_using_PCM_capsules_a_review_Renew_Sustain_Energy_Rev?el=1_x_8&enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg==https://www.researchgate.net/publication/257375359_Development_of_PCMcarbon-based_composite_materials?el=1_x_8&enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg==https://www.researchgate.net/publication/257375359_Development_of_PCMcarbon-based_composite_materials?el=1_x_8&enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg==https://www.researchgate.net/publication/257375359_Development_of_PCMcarbon-based_composite_materials?el=1_x_8&enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg==https://www.researchgate.net/publication/257375359_Development_of_PCMcarbon-based_composite_materials?el=1_x_8&enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg==https://www.researchgate.net/publication/257375359_Development_of_PCMcarbon-based_composite_materials?el=1_x_8&enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg==https://www.researchgate.net/publication/257375359_Development_of_PCMcarbon-based_composite_materials?el=1_x_8&enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg==https://www.researchgate.net/publication/257375359_Development_of_PCMcarbon-based_composite_materials?el=1_x_8&enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg==https://www.researchgate.net/publication/257375359_Development_of_PCMcarbon-based_composite_materials?el=1_x_8&enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg==https://www.researchgate.net/publication/257375359_Development_of_PCMcarbon-based_composite_materials?el=1_x_8&enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg==https://www.researchgate.net/publication/257375359_Development_of_PCMcarbon-based_composite_materials?el=1_x_8&enrichId=rgreq-dd5d9349-beaa-48bd-91a8-f41dcdcedc8c&enrichSource=Y292ZXJQYWdlOzI5Mjk5NDYwNjtBUzozNDE1OTMyMjQ2OTU4MTJAMTQ1ODQ1MzU3OTM5Mg==https://www.researchgate.net/publication/276301692_Study_on_the_thermal_storage_performance_of_a_gravity-assisted_heat-pipe_thermal_storage_unit_with_granular_high-temperature_phase-change_materials?el=1_x_8&enrichId=

thermal management analysis of a li-ion battery cell using phase

Documents