Derive equations for the temperature in a slab if the thermal conductivity

(a) is constant,

(b) varies linearly as \(k(T)=k_{0}+a\left(T-T_{0}\right)\), and

(c) varies as a quadratic function \(k(T)=\) \(k_{0}+a\left(T-T_{0}\right)+b\left(T-T_{0}\right)^{2}\).

State how the heat flow should be calculated for each of these cases. How should the "mean" temperature on which to base the mean conductivity be defined for each of these cases?