A hemispherical chunk of fat has radius a=2 cm. The flat side of the hemisphere sits at height z=0. At t=0 the temperature of the fat is T0=300 K. At this time, the stove is turned on and the surface at z=0 heats according to T=T0+(T1-T0)tanh(t/60), where T1=400 K, and times are in seconds. Assuming that the rest of the fat surface exposed to the air has an insulating boundary condition, and the fat has the thermal properties of water, find T(r,theta,t).

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