A plane wall is made of two layers of material, layers A and B as shown in the figure. Layer A has a thermal conductivity depending strongly on the temperature: k = aT3

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A plane wall is made of two layers of material, layers A and B as shown in the figure. Layer A has a thermal conductivity depending strongly on the temperature: k = aT3 , where a is a known constant, and ˙q is zero. Layer B has a chemical reaction causing an internal heat generation in this layer that has a constant value, ˙q = b (b is a known constant). The conductivity k is constant in layer B. Both walls have thickness L and all quantities are constant over the surfaces of the layers. The right-hand-side of layer B is insulated, while the left-hand-side of layer A is exposed to constant temperature T1. Find the temperature distribution in both layers, assuming steady state.

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