Contemporary Engineering Sciences, Vol. 11, 2018, no. 61, 3013 - 3020

HIKARI Ltd, www.m-hikari.com

https://doi.org/10.12988/ces.2018.87308

Comparative Analysis of Fin Heat Transfer

Using Simulation Software

Jose Di Filippo Buitrago, Álvaro Garzón Campo

and Guillermo Valencia Ochoa

Research Group on Energy Efficient Management - kaí, Faculty of Engineering

University of Atlántico, km 7 Antigua via Puerto Colombia

Copyright © 2018 Jose Di Filippo Buitrago, Álvaro Garzón Campo and Guillermo Valencia

Ochoa. This article is distributed under the Creative Commons Attribution License, which permits

unrestricted use, distribution, and reproduction in any medium, provided the original work is

properly cited.

Abstract

Engineering education software has become a key factor in completing the

objectives of an education program and achieving a student's results. This article

presents the validation of the Profiles Fins program by comparing it with the

results obtained by the already known Solidworks® that allows to determine the

temperature distribution, heat transfer coefficient, efficiency and effectiveness of

the different types of fins. The variation of these values with respect to their

change in fin geometry was analyzed to give as results which present the best heat

dissipation percentages.

Keywords: heat transfer fins, simulation software, Profile Fins, comparative

analysis

1. Introduction

Because of the size reduction, performance improvement and cost minimization in

fin fabrication, the industry and its researchers are continually striving to find the

optimal structure and design. [1] that maximizes the rate of heat dissipation.

Ghasemi and others.[2] They used the differential transformation method to solve

the nonlinear heat transfer equation [3] in the longitudinal fin with temperature-

dependent internal heat generation and thermal conductivity [4]. Campo y

Celentano[5] briefly evaluated the maximum heat transfer attributes of the

optimum straight ends with the quarter-circle profile proposed by Isachenko and

others. In terms of three descriptive parameters: the thermal conductivity k, the

3014 Jose Di Filippo Buitrago et al.

average coefficient of convection h ~, and the semi-thickness at the base R. Dogan

et al. [6] numerically researched the natural convection in a stationary state and

the radiation heat transfer of various thin sets of fins onto a horizontal baseplate.

Kundu and Wongwises [7] performed a complete thermal analysis on a

rectangular fin [8] with its primary surface taking into consideration the heat

exchange (radiation) with the environment together with the convective mode of

heat transfer. Yaici and Ghorab [9] presented the results of three-dimensional

computational fluid dynamics (CFD) simulations to investigate the effect of poor

distribution of incoming airflow on the thermohydraulic performance of fin heat

exchangers and plate tubes. Moitsheki and Bradshaw-Hajek [10] They considered

a heat conduction model that emerges in transient heat transfer through

longitudinal fins of a heterogeneous (functionally classified) material. In this case,

the thermal conductivity depends on the spatial variable. The heat transfer

coefficient is temperature dependent and is given by the power law function. The

resulting nonlinear partial differential equation is analyzed using both classical

and non-classical symmetry techniques. Ndlovu and Moitsheki [19] derived

approximate analytical solutions (series) for temperature distribution in

rectangular and convex longitudinal parabolic fins with temperature-dependent

thermal conductivity and heat transfer coefficient. The transitory heat conduction

problem is solved for the first time using the two-dimensional differential

transformation method (DTM 2D). Senapati and others[20] found that with the

addition of fins to the heated isothermal surface of a tube, heat transfer increases

for laminar flow and turbulent flow, heat transfer first increases and achieves a

maximum value, then begins to decrease.

A software will be used to simulate the heat transference present in fins by

varying their geometry, to validate the Profile Fins software and idealize the fin

geometry supported in SolidWorks and the results it produces.

2. Methodology

2.1.Fundamental equations

Depending on the specific geometry of each fin, its heat transfer capacity is

defined.

�̇�𝑐𝑜𝑛𝑑, 𝑥 = �̇�𝑐𝑜𝑛𝑑, 𝑥 + ∆𝑥 + �̇�𝑐𝑜𝑛𝑣 (1)

In the special case of a constant cross-section and constant thermal conductivity,

𝑑2𝜃

𝑑𝑥2 − 𝑎2𝜃 = 0 where 𝑎2 =ℎ𝑝

𝑘𝐴𝑐 (2)

At the tip of the fin there are several boundary conditions, including specific

temperature, negligible heat loss, convection or convection and combined

radiation.

Comparative analysis of fin heat transfer using simulation software 3015

For a fin of sufficiently long and uniform cross section (Ac = constante) CF flipper tip: 𝜃(𝐿) = 𝑇(𝐿) − 𝑇∞ when L → ∞

�̇�𝑙𝑜𝑛𝑔 𝑓𝑖𝑛 − 𝑘𝐴𝑐𝑑𝑇

𝑑𝑥|

𝑥=0= √ℎ𝑝𝑘𝐴𝑐 (𝑇𝑏 − 𝑇∞) (3)

Negligible heat loss from the tip of the fin (isolated fin tip),

�̇�𝑖𝑛𝑠𝑢𝑙𝑎𝑡𝑒𝑑 𝑓𝑖𝑛 𝑡𝑖𝑝 = 0

CF flipper tip: 𝑑𝜃

𝑑𝑥|

𝑥=𝐿= 0

�̇�𝑖𝑛𝑠𝑢𝑙𝑎𝑡𝑒𝑑 𝑓𝑖𝑛 𝑡𝑖𝑝= −𝑘𝐴𝑐

𝑑𝑇

𝑑𝑥|

𝑥=0= √ℎ𝑝𝑘𝐴𝑐(𝑇𝑏 − 𝑇∞) (4)

Convection (combined convection and radiation) from the tip of the fin

Corrected fin length

𝐿𝑐 = 𝐿 +𝐴𝑐

𝑝 (5)

𝐿𝐶,𝑟𝑒𝑐𝑡𝑎𝑛𝑔𝑢𝑙𝑎𝑟 𝑓𝑖𝑛 = 𝐿 + 𝑡

2 Y 𝐿𝑐,𝑐𝑦𝑙𝑖𝑛𝑑𝑒𝑟 𝑓𝑖𝑛 = 𝐿 +

𝐷

4 (6)

Fin Efficiency To consider the effect of this decrease in temperature on heat

transfer, a fin efficiency is defined as,

𝑛𝑓𝑖𝑛 =�̇�𝑓𝑖𝑛

�̇�𝑓𝑖𝑛,𝑚á𝑥

(7)

2.2.Fin design and analysis with simulation software

The fins were designed with the help of Solidworks simulation software in 2D and

3D plane, using commands such as lines, midpoint lines, arc, circumference, 3D

extrusion, etc. The fins were designed with the following specifications: length

l=100 mm, width b=60 mm and thickness y=20 mm. The specifications of each

fin is shown in Error! Reference source not found..

3016 Jose Di Filippo Buitrago et al.

Error! Reference source not found.studied in the software

After the design is created, the next step is to analyze the fin for heat transfer

using Solidworks Simulation software. The type of analysis was first selected as

thermal analysis for the stationary heat transfer process. The material of the piece

was assigned, then the thermal load was applied, in this case, temperature through

the plate and convective properties of the environment, the unit system was used

as customization length in mm, temperature in k and thermal energy in J.

Now from the adjustment of the 3D mesh was established a mesh size of 60% to

fine. The design mesh was generated as shown in Error! Reference source not

found.a. In this assignment the material has thermal conductivity, heat transfer

convection coefficient for fluid, surface temperature and ambient temperature as:

Thermal conductivity, k = 200 W / m. k, Convection coefficient of heat transfer, h

= 40 W / m2. K, Temperature of the surface of the wall to which the fin was

attached to 328, 15 K, and ambient temperature to 303,15 K. With the help of the

Profile Fins simulation software, the respective simulations were carried out under

the same conditions that were used in the Solidworks software for both material

and environment. Error! Reference source not found. 2a and Error! Reference

source not found.2b displays the software Profile Fins.

Type of fin Efficiency Fin Area

rectangular straight

𝑛𝑓𝑖𝑛 =tanh 𝑚𝐿𝑐

𝑚𝐿𝑐

𝑚 = 2ℎ/𝑘𝑡

𝐿𝑐 = 𝐿 +𝑡

2

𝐴𝑓𝑖𝑛 = 2𝑤𝐿𝑐

Straight triangular

𝑛𝑓𝑖𝑛 =1

𝑚𝐿

𝑙1(2𝑚𝐿)

𝑙0(2𝑚𝐿)

𝑚 = 2ℎ/𝑘𝑡

𝐴𝑓𝑖𝑛 = 2𝑤 𝐿2 + (𝑡/2)2

Rectangular profile circular

𝑛𝑓𝑖𝑛

= 𝑐2

𝑘1(𝑚𝑟1)𝐼1(𝑚𝑟1)𝐼1 𝑚𝑟1 𝑘1(𝑚𝑟2𝑐)

𝑙0 𝑚𝑟1 𝑘1 𝑚𝑟2𝑐 + 𝑘0(𝑚𝑟1)𝐼1(𝑚𝑟2𝑐)

𝑚 = 2ℎ/𝑘𝑡

𝑟2𝑐 = 𝑟2 +𝑡

2

𝐴𝑓𝑖𝑛 = 2𝜋(𝑟22𝑐 − 𝑟2

1)

Straight parabolic

𝑛𝑓𝑖𝑛 =2

1 + (2𝑚𝐿)2 + 1

𝑚 = 2ℎ/𝑘𝑡

𝐴𝑓𝑖𝑛 = 𝑤𝐿[𝐶1 + (𝐿/𝑡)ln(𝑡

/𝐿) + 𝐶1)]

𝐶1 = 1 + (𝑡/𝐿)2

Rectangular profile

herringbone

𝑛𝑓𝑖𝑛 =tanh 𝑚𝐿𝑐

𝑚𝐿𝑐

𝑚 = 4ℎ/𝑘𝐷

𝐿𝑐 = 𝐿 +𝐷

4

𝐴𝑓𝑖𝑛 = 𝜋𝐷𝐿𝑐

Comparative analysis of fin heat transfer using simulation software 3017

a) b)

Error! Reference source not found., b) Rectangular fin interface.

3. Results and discussion

There are infinite parameters, variables and factors that influence the way in

which each fin dissipates heat. Using software simulation (Profile Fins and

Solidworks) the temperature distribution was found in each geometric variation

and compared when it changed its border condition. Error! Reference source not

found.a shows how SW shows the heat on the fin surface and how it is conducted

from the heat source outwards.

Error! Reference source not found., b) Cylindrical fin.

By varying the surface fin geometry and under the same conditions, Error!

Reference source not found. 3b shows that heat is dissipated at a slightly lower

temperature in a cylindrical fin. Profile Fins, being a specialized software for this

type of simulation, shows us a more realistic result that does not differ from the

one shown in Solidworks but shows the temperature distribution as a function of

the distance from the base of the fin to the tip. In Error! Reference source not

found.4 it is clearly seen that applying the border condition C. F. Mechanisms

combined has a greater heat dissipation, however, it is observed that there is a

similarity between the graph corresponding to Solidworks and the

3018 Jose Di Filippo Buitrago et al.

border condition of insulated tip used in Profile Fins. Error! Reference source

not found.4b shows that for parabolic geometry fins, contradictory results were

found between the two softwares, due to the configuration of the profile Fins

software.

a) b)

Error! Reference source not found., b) Parabolic fin.

Conclusion

The ProfileFins tool was successfully introduced in the mechanical engineering

classes where its analysis capability was validated depending on the geometry of

each fin. Three different extended geometries were studied with the help of the

two programs and the surface area equations, the heat distribution was observed

observing and concluding that there is a greater heat dissipation with rectangular

fins, the operation of the ProfileFins software is validated, noting that it has an

adequate behavior to the comparison made with Solidworks, besides being much

more specific offering more detailed information of the heat distribution behavior.

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Received: July 19, 2018; Published: August 8, 2018