A plane wall of thickness L=4cm has a thermal conductivity of k=20 W/mK. A chemical reaction takes place inside the wall resulting in a uniform heat generation at a rate of 10^5w/m^3. Sandwiched between the wall and an insulating layer is a film heater of negligible thickness that generates a heat flux q=16kW/m^2. The opposite sode of the wall is in contact with water at temperature T=40C. A thermocouple mounted on the surface of the wall in contact with water reads T=90C.
Determine the convection coefficient between the wall and water. Also show that the steady state temperature distribution has form T(x) = ax^2 + bx + c.