In a food processing facility, a spherical container of inner radius r = 43 cm, outer radius r2= 45 cm, and thermal conductivity k= 2.5 W/m°C is used to store hot water and to keep it at 100°C at all times. To accomplish this, the outer surface of the container is wrapped with a 550 W electric strip heater and then insulated. The temperature of the inner surface of the container is observed to be nearly 100°C at all times. Assuming 15 percent of the heat generated in the heater is lost through the insulation. (a) Express the differential equation and the boundary conditions for steady one-dimensional heat conduction through the container, (b) Obtain a relation for the variation of temperature in the container material by solving the differential equation, (c) Evaluate the outer surface temperature of the container, (d) Also determine how much water at 100°C this tank can supply steadily if the cold water enters at 35°C. sulation -Electric heater Ro waler Spherical container Fig. 2 – Spherical container

Consider a stainless steel spoon ( k = 8.7 Btu/hrft°F) partially immersed in boiling water at 200 deg * F in a kitchen at 75°F. The handle of the spoon has a cross section of 0.08in * 0.5in and extends 7 inches into the air from the free surface of the water. If the heat transfer coefficient at the exposed surfaces of the spoon handle is 3 Btu/hrft²°F, determine the temperature of the tip of the spoon handle. Assume that the heat loss from the tip of the spoon is negligible.

Consider the base plate of a 750-W household iron with a thickness of L=0.6 cm, base area of A=170 cm2, and thermal conductivity of k=22 W/m.oC. The inner surface of the base plate is subjected to uniform heat flux generated by the resistance heaters inside. When steady operating conditions are reached, the outer surface temperature of the plate is measured to be 85 oC. Disregarding any heat loss through the upper part of the iron, (a) express the differential equation and the boundary conditions for steady one-dimensional heat conduction through the plate, (b) obtain a relation for the variation of temperature in the base plate by solving the differential equation, and (c) evaluate the inner surface temperature.

A glass window with an area of 0.625 m² is installed in the wooden outside wall of a room. The wall dimensions are 25 x 3.05 m. The wood has a k of 0.151W/m.K and is 3.05 cm thick. The glass has a k of 0.692W/m.K and is 5.0 mm thick. The temperature of the inside room is 27°C and outside air temperature is 268K. (1)What is the heat loss through wooden wall and glass window q(W) ? (2) What are the total heat loss?