The temperature distribution across a wall 0.3 m thick at a certain instant of time is T(x) = a + bx + cx2, where T is in degrees Celsius and x is in meters, a = 200°C, b = -200°C/m, and c = 30°C/m2. The wall has a ther- mal conductivity of 1 W/m · K.
(a) On a unit surface area basis, determine the rate of heat transfer into and out of the wall and the rate of change of energy stored by the wall.
(b) If the cold surface is exposed to a fluid at 100°C, what is the convection coefficient?