Further observations on a problem of constant surface heating of a variable-conductivity halfspace

A solution to the problem of constant surface heating of an initially constant-temperature, $T_0^*$, halfspace where the material in question has a temperature-dependent thermal conductivity is obtained. The thermal conductivity, ${k^ * }$, is specifically given by ${k^ * } = k_0^ * \exp \left [ {\lambda \left ( {{T^ * } - T_0^ * } \right )/T_0^ * } \right ]$. The solution is valid for both heating and cooling of the material where $\lambda$ and $k_0^ *$ are arbitrary in magnitude, and $\lambda$ can be either positive or negative in sign.