Polytechnic University of Puerto RicoChemical Engineering Department

Winter 2016

Ashley M. Ramirez Quiles Stephanie P. Rivera Ares Edgared M. Troche Muñiz Jorge Sepulveda November 29, 2016 CHE 3321- 22 Prof. Pablo Traverso

Heat Transfer Linear Conductivity Effect

AgendaObjectives

Theory

Equipment

Procedure

Data

Calculations

Security

References

Objectives

Determine thermal conductivity and temperature difference in stainless steel, brass, aluminum and isolators for a steady state conduction.

Contact resistance effect in the interphase and thermal paste

Conduct analysis and comparison of the resistance effects

TheoryConduction Heat Transfer

Energy is transferred as heat due to a temperature potential difference in a body, or between bodies in contact with each other.

Figure 1. Representation of heat flow [1]

Theory

Thermal proportionality constant :

; Heat transfer rate is proportional to the temperature gradient.

; Fourier’s Law

Wiedemann-Franz Law:

, and

Figure 2. One-dimensional steady state heat transfer, temperature gradients. [2]

TheoryEnergy Balance:

+

For constant Thermal Conductivity:

+;

Figure 2. Volume element for one dimensional heat-conduction. [2]

T1>T2

Theory Under steady state conditions, the

temperature distribution is linear, and the temperature gradient may be expressed as:

Fourier’s Rate Equation;

Experimental

Figure 3. Linear direction of heat flow. [3]

TheoryHeat Flow:

Figure 4. One-dimensional heat transfer through a composite wall, and its equivalent electrical analog. [3]

;

(𝐴∗𝑅𝑡 h)=𝑅𝑣𝑎𝑙𝑢𝑒=∆𝑇𝑞𝐴

=∆𝑥𝑘

Theory

Overall Heat-Transfer Coefficient (U)

In a composite wall we can state that;

Figure 5. Composite wall. [4]

TheoryReduced cross-sectional area of heat transfer between thermocouples:

From Fourier’s Law;

Rearranging the equation;

;

Figure 6. Composite wall with reduced area. [5]

TheoryThermal Contact Resistance:

From the energy balance equation;

Figure 8. Joint-roughness model for the analysis of hc . [3]

𝑞=𝑇 2𝐴−𝑇2 𝐵

𝐿𝑔

2𝑘𝐴 𝐴𝑐+

𝐿𝑔

2𝑘𝐵 𝐴𝑐

+𝑘 𝑓 𝐴𝑣𝑇 2 𝐴−𝑇 2𝐵

𝐿𝑔=𝑇 2 𝐴−𝑇 2𝐵

1h𝑐 𝐴

h𝑐=1𝐿𝑔

( 𝐴𝑐

𝐴2𝑘𝐴𝑘𝐵

𝑘𝐴+𝑘𝐵+𝐴𝑣

𝐴 𝑘 𝑓 );Figure 7. Illustration of the thermal contact resistance effect, temperature profile. [5]

Figure 9. Ideal and actual thermal contact. [2]

Theory

Figure 11. Effect of metallic coatings on thermal contact surfaces. [2]

Figure 10. Contact conductance of typical surfaces. [3]

MaterialThermal

Conductivity - k - 

W/(m K)

Temp.(oC)

Air, atmosphere (gas) 0.024 25

Aluminum 205 25

Aluminum Brass 121 25

Beef, lean (78.9% moisture) 0.43 - 0.48 25

Brass 109 25

GM280 (Si, thermal

paste)1.2 -45

Stainless Steel 16 25

Water 0.58 25

Figure 12. Thermal conductivities of various materials. [6][7]

Equipment

Equipment

Procedure Measure the temperature distribution for

the steady state conduction of energy through a uniform flat wall and demonstrate the effect of a change in the heat flow.

Understand the use of the Fourier Frequency equation to determine the rate of heat flux through solid materials for one-dimensional heat flow.

Measure the temperature distribution for steady-state energy conduction through a composite flat wall and determine the global heat transfer coefficient for a heat flow through a combination of different materials in series.

Determine the thermal conductivity (k) of a sample of metal.

Procedure Show that the temperature gradient is

inversely proportional to the cross-sectional area for one-dimensional heat flow in a solid material of constant thermal conductivity.

Demonstrate the effect of contact resistance on thermal conduction between adjacent materials.

Understand the application of poor conductors (insulators) and determine the thermal conductivity k (the proportionality constant) of an insulation.

Observe the conduction of the heat in an unstable state (qualitative only with a graphic recorder or a connected PC).

Data

Heater Voltage (V)Heater current (Amps)

Heated Section Temperature (°C)Cooled Section Temperature (°C)

Cooling Water Flowrate (L/min)Heat Flow (Watts)

V I T1, T2, T3 T6, T7, T8 Fw Q=VI

• As the electrical supply to the heater is Direct Current the power supplied to the heater is simply obtained from the product of the Voltage and Current, i.e. [5]

Heater Power (Q) = Voltage (V) x Current (I)

Calculations Steady-State Heat

Conduction:

The Fourier Rate Equation:

(m2 , cross sectional area of bar)

The Overall Heat Transfer Coefficient:

(m2 ) cross sectional area

(∘C)

Temperature difference across composite wall

Calculations Thermal Conductivity:

(Constant of Proportionality)

Inverse Proportionality of Temperature Gradient to Area:

Effect of Contact Resistance on Thermal Conduction:

Calculations Thermal Conductivity and

Application of Insulators: Unsteady State Conduction

of Heat:

Safety

References

[1] http://philschatz.com/physics-book/contents/m42228.html

[2] Dr. Balku, Ş. (2015). STEADY HEAT TRANSFER AND THERMAL RESISTANCE NETWORKS. Retrieve from http://slideplayer.com/slide/6638492/

[3] J P Holman, S. B. (2011). HEAT TRANSFER (In SI Units). (10). (M.-H. G. Holdings, Ed.) New York, United States.

[4] http://www.engr.iupui.edu/~mrnalim/me314lab/lab02.htm

[5] Manual Lab.

[6] http://hyperphysics.phy-astr.gsu.edu/hbase/Tables/thrcn.html

[7] http://www.engineeringtoolbox.com/thermal-conductivity-d_429.html

ANY QUESTIONS?