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
5W/m K. For these conditions, the temperature distribution
has the form T(x)= a + bx + cx2. The surface at
x =0 has a temperature of T(0) = To = 120C and experiences
convection with a fluid for which T =20C and h= 500 W/m2 *K. 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.
(c) Consider conditions for which the convection coefficient is halved, but the volumetric energy generation
rate remains unchanged. Determine the new values of a, b, and c, and use the results to plot the
temperature distribution. Hint: recognize that T(0) is no longer 120C.
(d) Under conditions for which the volumetric energy generation rate is doubled, and the convection coefficient
remains unchanged (h =500 W/m2 K), determine the new values of a, b, and c and plot the corresponding temperature distribution.