Conduction heat transfer with varying cross section

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SUMMARY

The discussion focuses on calculating conduction heat transfer (Q) between two stadium-shaped sections with differing thicknesses and temperatures. The first section has a thickness of 5 mm and a temperature of 1020°C, while the second section has a thickness of 0.9 mm and a temperature of 20°C. The heat conduction equations for each section are defined as Q1 = (-K*A1*(1020-T))/d1 and Q2 = (-K*A2*(T-20))/d2, where K is the thermal conductivity, A1 and A2 are the cross-sectional areas, and d1 and d2 are the thicknesses. The goal is to eliminate T to find a single expression for Q.

PREREQUISITES
  • Understanding of conduction heat transfer principles
  • Familiarity with thermal conductivity (K) and its significance
  • Knowledge of geometry related to heat transfer calculations
  • Ability to manipulate algebraic equations for thermal analysis
NEXT STEPS
  • Study the derivation of heat conduction equations in varying geometries
  • Learn about thermal conductivity values for different materials
  • Explore numerical methods for solving heat transfer problems
  • Investigate the impact of cross-sectional area on heat transfer rates
USEFUL FOR

Mechanical engineers, thermal analysts, and students studying heat transfer principles will benefit from this discussion, particularly those working with complex geometries in thermal systems.

imselva
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Conduction_Case_12.jpg

How to modify this Formula? and arrive at the solution.
Q = -K(Th-Tc)A/thickness
 
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I don't understand the geometry you are trying to specify.
 
The geomentry consists of two parts in complete contact with each other.
The first part is a Stadium shape with 5 mm thickness and a height of 39.4mm.
The second part is also Stadium shape with 0.9mm thickness and a height of 64.8mm.

The Bottom of the first part is at 1020°C and the top for the second part is 20°C.
I want to calculate the conduction heat Transfer between the two different temperatures. How to find Q?
 
View attachment Unbenannt.PNGThe temperature T1 at the top Surface is 1020°C and T2 at the Bottom Surface is 20°C and K is the thermal conductivity of the material.

What is the conduction heat Transfer Q. ?
 
Let T be the temperature at the junction between the two parts. Q is going to be the same through each of the two parts. In terms of T, what are the two heat conduction equations for each of the two parts?
 
Q1 = (-K*A1*(1020-T))/d1
Q2 = (-K*A2*(T-20))/d2
 
imselva said:
Q1 = (-K*A1*(1020-T))/d1
Q2 = (-K*A2*(T-20))/d2
Q1 and Q2 are both Q. Eliminate T between the two equations.
 

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