Reconsider Prob. 2–88. Using the relation given for the heat generation in the wall, plot the heat generation as a function of the distance x in the range of x = 0 to x = L, and discuss the results. Use the EES (or other) software.

Data From Problem 88

Consider a large plane wall of thickness L = 0.05 m. The wall surface at x = 0 is insulated, while the surface at x = L is maintained at a temperature of 30°C. The thermal conductivity of the wall is k = 30 W/m · K, and heat is generated in the wall at a rate of ė_gen = ė₀e-^0.5x/L W/m³ where ė₀ = 8 × 10⁶ W/m³. Assuming steady one-dimensional heat transfer,

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

(b) Obtain a relation for the variation of temperature in the wall by solving the differential equation,

(c) Determine the temperature of the insulated surface of the wall.