A plane wall of thickness L = 4 cm has a thermal conductivity of k = 20 W/m · K. A chemica...

A plane wall of thickness L = 4 cm has a thermal conductivity of k = 20 W/m · K. A chemical reaction takes place inside the wall resulting in a uniform heat generation at a rate of ėgen = 105W/m3  Sandwiched between the wall and aninsulating layer is a film heater of negligible thickness that generates a heat flux qs= 16kW/m2  The opposite side of the wall is in contact with water at temperature T∞ = 40°C. Athermocouple mounted on the surface of the wall in contact with the water reads Ts= 90°C.

(a)   Determine the convection coefficient between the wall and water.

(b) Show that the steady-state temperature distribution has the form T(x) = ax2 + bx + c, and determine the values and units of a, b, and c. The origin of x is shown in the figure.

(c) Determine the location and value of the maximum temperature in the wall. Could this location be found with-out knowing a, b, and c, but knowing that T(x) is a quadratic function? Explain.