Home / Questions / A spherical container of inner radius r1 2 m outer radius r2 21 m and thermal conductivity
A spherical container of inner radius r_{1} = 2 m, outer radius r_{2} = 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/m^{2} ·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, and
(c) evaluate the rate of heat gain to the iced water.
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