  We present numerical studies of electrical breakdown in disordered materials
using a two-dimensional thermal fuse model with heat diffusion. A conducting
fuse is heated locally by a Joule heating term. Heat diffuses to neighbouring
fuses by a diffusion term. When the temperature reaches a given threshold, the
fuse breaks and turns into an insulator. The time dynamics is governed by the
time scales related to the two terms, in the presence of quenched disorder in
the conductances of the fuses. For the two limiting domains, when one time
scale is much smaller than the other, we find that the global breakdown time
$t_r$ follows $t_r\sim I^2$ and $t_r\sim L^2$, where $I$ is the applied
current, and $L$ is the system size. However, such power law does not apply in
the intermediate domain where the competition between the two terms produces a
subtle behaviour.
