# Conduction heat transfer with varying cross section

• I

## Summary:

The thickness of the 39.4mm part is 5mm and the thickness of 64.8 mm part is.
The temperature on the top cross sectional Surface is 1020°C and 20°C on the Bottom cross sectional surface.
If K is the thermal conductivity of the material. T1 and T2 are hot and Cold temp. A1 and A2 are the cross sectional Areas. What is the conduction heat Transfer Q?

How to modify this Formula? and arrive at the solution.
Q = -K(Th-Tc)A/thickness

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Chestermiller
Mentor
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. ?

Chestermiller
Mentor
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

Chestermiller
Mentor
Q1 = (-K*A1*(1020-T))/d1
Q2 = (-K*A2*(T-20))/d2
Q1 and Q2 are both Q. Eliminate T between the two equations.