One-dimensional, steady-state conduction with uniform internal energy generation occurs in a plane wall with a thickness of 50 mm and a constant thermal conductivity of 5 W/mK . For these conditions, the temperature distribution has the form T(x) = a + bx + cx2. The surface at x = 0 has a temperature of To = 120 oC and experiences convection with a fluid at 20 oC and h = 460 W/m2K . The surface at x = L is well insulated. .

(a) Applying an overall energy balance to the wall, calculate the volumetric energy generation rate.
(b) Determine the coefficients a, b, and c by applying the boundary conditions to the prescribed temperature distribution. Use the results to calculate and plot the temperature distribution.