Problem #5: Consider a large plane wall of thickness L = 0.4 m, thermal conductivity k=2.3 W/m. C, and surface area A = 20 m. The left side of the wall is maintained at a constant temperature of T1=80C while the right side loses heat by convection to the surrounding air at Tr. = 15C with a heat transfer coefficient of h = 24 W/m2.C. Assuming constant thermal conductivity and no heat generation in the wall, (a) express the differential equation and the boundary conditions for steady one-dimensional heat conduction through the wall, (b) obtain a relation for the variation of temperature in the wall by solving the differential equation, and (c) evaluate the rate of heat transfer through the wall. Problem # 7: A 2-kW resistance heater wire with thermal conductivity of k = 20 W/mC, a diameter of D = 5 mm, and a length of L = 0.7 m is used to boil water. If the outer surface temperature of the resistance wire is Ts= 110C, determine the temperature at the center of the wire. a