Question

(10 points) The diagram on the left below shows a configuration in which there is uniform heat generation in the material labeled \"A\". This material is insulated on the left side. Material \"B\" has no generation. The thermal conductivity of \"B\" is less than that of \"A\". An engineer at your company has modeled the problem and has presented you with a temperature profile they have calculated on the right. Since you know heat transfer well, you find several errors with their solution. List three errors that this engineer has made in this temperature graph and explain why they are incorrect. These are conceptual. Insulated L h Tfluid = 20 °C KA ?gen KB < KA X Temperature, °C Temperature vs Position 250 200 150 100 50 0 0 L Position, x 2L Here are some formulas for heat generation that you might find helpful. Plane wall with generation, asymmetric: $T(x) = \frac{\dot{e}_{gen}L^2}{2k} \left(1 - \frac{x^2}{L^2}\right) + \frac{T_2 + T_1}{2} + \frac{T_1 + T_2}{2}$ Symmetrical boundary conditions, planar wall: $T(x) = \frac{\dot{e}_{gen}L^2}{2k} \left(1 - \frac{x^2}{L^2}\right) + T_1$ $T_s, \text{ plane wall} = T_{\infty} + \frac{\dot{e}_{gen}L}{h}$ parabolic

          (10 points)
The diagram on the left below shows a configuration in which there is uniform heat
generation in the material labeled \"A\". This material is insulated on the left side.
Material \"B\" has no generation. The thermal conductivity of \"B\" is less than that of
\"A\". An engineer at your company has modeled the problem and has presented
you with a temperature profile they have calculated on the right. Since you know
heat transfer well, you find several errors with their solution.
List three errors that this engineer has made in this temperature graph and
explain why they are incorrect. These are conceptual.
Insulated
L
h
Tfluid = 20 °C
KA
?gen
KB < KA
X
Temperature, °C
Temperature vs Position
250
200
150
100
50
0
0
L
Position, x
2L
Here are some formulas for heat generation that you might find helpful.
Plane wall with generation, asymmetric: $T(x) = \frac{\dot{e}_{gen}L^2}{2k} \left(1 - \frac{x^2}{L^2}\right) + \frac{T_2 + T_1}{2} + \frac{T_1 + T_2}{2}$
Symmetrical boundary conditions, planar wall: $T(x) = \frac{\dot{e}_{gen}L^2}{2k} \left(1 - \frac{x^2}{L^2}\right) + T_1$
$T_s, \text{ plane wall} = T_{\infty} + \frac{\dot{e}_{gen}L}{h}$
parabolic

Added by Helen J.

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