Consider a large plane wall of thickness L and constant thermal conductivity k The left side of the wall (x 0) is maintained at a constant temperature T 0 , while the right surface at x L is insulated Heat is generated in the wall at the rate of e gen ax 2 Btu h ft 3 Assuming steady one dimensional...

The Answer is in the image, click to view ...

Consider a large plane wall of thickness L and constant thermal conductivity k. The left side of

Question:

Consider a large plane wall of thickness L and constant thermal conductivity k. The left side of the wall (x = 0) is maintained at a constant temperature T₀, while the right surface at x = L is insulated. Heat is generated in the wall at the rate of ė_gen = ax² Btu/h · ft³. Assuming steady one-dimensional heat transfer,

(a) Express the differential equation and the boundary conditions for heat conduction through the wall,

(b) By solving the differential equation, obtain a relation for the variation of temperature in the wall T(x) in terms of x, L, k, a, and T₀, and
(c) What is the highest temperature (ºC) in the plane wall when: L = 1 ft, k = 5 Btu/h · ft · ºF, a = 1200 Btu/h · ft⁵, and T₀ = 700ºF.