A solution to the problem of constant surface heating of an initially constant-temperature,
T
0
∗
T_0^*
, halfspace where the material in question has a temperature-dependent thermal conductivity is obtained. The thermal conductivity,
k
∗
{k^ * }
, is specifically given by
k
∗
=
k
0
∗
exp
[
λ
(
T
∗
−
T
0
∗
)
/
T
0
∗
]
{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
λ
\lambda
and
k
0
∗
k_0^ *
are arbitrary in magnitude, and
λ
\lambda
can be either positive or negative in sign.