Heat flow through composite material

[gfd43tg]

Homework Statement

The cross section of a 20 cm thick, 3 m wide, and 1 m high composite wall is shown. The conductivities of materials A, B and C are 1.0, 0.1, and 0.05 W m-1 K-1, respectively. One side is exposed to air at 295 K with a heat transfer coefficient of 4 W m-2 K-1, and the other side is exposed to air at 260 K with a heat transfer coefficient of 16 W m-2 K-1. Estimate the heat flow through the wall. Carefully discuss any assumptions you make.

Homework Equations

The Attempt at a Solution

For this problem, my biggest concern is if I did my thermal circuit correctly. Also, is the area just the area of each composite material perpendicular to the direction of heat flow?

The reason I got 5 sections of A,B, and C is because the width is given as 3 meters, and a divide by 40+20 = 60 cm to get 5 sections, so there is a lot of parallel heat flow happening here.

 

[Chestermiller]

You have the circuit set up correctly. But, I don't like this problem. Why? Because if you assume 1D heat flow, the temperature profile through the A's will be different from the temperature profile through the BC's. Just calculate the temperature at the center of A, and also calculate the temperature at the boundary between B and C. You will get different numbers. In order to solve this as a 1D heat conduction problem, you need to assume that there is insulation at the boundaries between the A's and the BC's. Otherwise the heat flow will be 2D.

Chet

 

[gfd43tg]

Doesn't surprise me that my professor doesn't know what she is doing, I got that impression from the get-go!