In a food processing facility, a spherical container of inner radius r1 = 40 cm, outer radius r2 = 41 cm, and thermal conductivity k = 1.5 W/m·K 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 800-W electric strip heater and then insulated. The temperature of the inner surface of the container is observed to be nearly 120°C at all times.

Assume 10 percent of the heat generated in the heater is lost through the insulation, express the differential equation and the boundary conditions for steady one-dimensional heat conduction through the container.