4. (35 pts). A plane wall of thickness L = 0.25 m is subjected to a constant heat flux on one face and convection on the other as shown in

the figure below. The heat flux on the face @ x = 0 is q" = -350 W/m^2 and the convection coefficient is h = 20 W/m2.°C @ x = L. There is internal generation of q = 4 kW/m^3 within the wall, and the thermal conductivity is k = 15 W/m-°C. The temperature distribution is of the form T(x)= ax^2 + bx + c, where a, b, and c are constant coefficients. a)Conduct a first law analysis, draw a system and derive the heat differential equation for this wall. b)Solve the differential equation and apply appropriate boundary conditions to determine temperature distribution coefficients a, b, and c. Leave in symbolic form in terms of q, qo", h, k, L and To as appropriate. c)Calculate the wall temperature T(x) at x = 0 and x = L. d)Calculate the wall heat flux qL" at x = L. e)Calculate the maximum wall temperature and its location. f)Sketch the wall temperature distribution.