A Wall with Various Sets of Boundary Conditions
Consider steady one-dimensional heat conduction in a large plane wall of thickness L and constant thermal conductivity k with no heat generation. Obtain expressions for the variation of temperature within the wall for the following pairs of boundary conditions (Fig):
(a) - k \frac{d T(0)}{d x} = q_{0} = 40 W / cm ^{2} \quad \text { and } \quad T(0) = T_{0} = 15^{\circ} C
(b) - k \frac{d T(0)}{d x} = \dot{q}_{0} = 40 W / cm ^{2} \quad \text { and } \quad - k \frac{d T(L)}{d x} = \dot{q}_{L} = - 25 W / cm ^{2}
(c) - k \frac{d T(0)}{d x} = q_{0} = 40 W / cm ^{2} \quad \text { and } \quad - k \frac{d T(L)}{d x} = q_{0} = 40 W / cm ^{2}