(i) Derive an expression for the relation between heat loss and temperature difference across the inner and outer surfaces of a hollow sphere, the conductivity of which varies with temperature in manner given by k=k0 [1+a(T-T0)] , where T0 is a reference temperature.
(ii) Find the corresponding result for for a hollow cylinder.
(iii) Compare the expressions derived for parts (i) and (ii) for the special case of the outside radius becoming infinite. Explain the different values obtained.