Problem #4:Consider a long solid cylinder of radius ro = 4 cm and thermal conductivity k = 25 W/m C. Heat is generated in the cylinder uniformly at a rate of go = 35 W/cm3. The side surface of the cylinder is maintained at a constant temperature of T, = 80C. The variation of temperature in the cylinder is given by T() ** [-(0)7. )*] +7 1 + Based on this relation, determine (a) if the heat conduction is steady or transient, (b) if it is one-, two-, or three-dimensional, and (c) the value of heat flux on the side surface of the cylinder at r = ro. 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 T=80C while the right side loses heat by convection to the surrounding air at T = 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 #6: Consider a steam pipe of length L = 30 ft, inner radius ri= 2 in, outer radius r2 = 2.4 in, and thermal conductivity k = 7.2 Btu/h.ft 'F. Steam is flowing through the pipe at an average temperature of 300F, and the average convection heat transfer coefficient on the inner surface is given to be h= 12.5 Btu/hft?.OF. If the average temperature on the outer surfaces of the pipe is T2 = 175F, (a) express the differential equation and the boundary conditions for steady one-dimensional heat conduction through the pipe, (b) obtain a relation for the variation of temperature in the pipe by solving the differential equation, and (c) evaluate the rate of heat loss from the steam through the pipe 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