A spherical container of inner radius r₁ = 2 m, outer radius r₂ = 2.1 m, and thermal conductivity k = 30 W/m · K is filled with iced water at 0°C. The container is gaining heat by convection from the surrounding air at T∞ = 25°C with a heat transfer coefficient of h = 18 W/m² · K. Assuming the inner surface temperature of the container to be 0°C,

(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 by solving the differential equation,

(c) Evaluate the rate of heat gain to the iced water.