A theoretical study is made of the surface temperature of a
front heated slab in the presence of small holes drilled to
within a fraction of a centimeter of the heated surface. In
addition, equations and calculations are presented which yield
an estimate of the error incurred when the surface temperature
is measured by a transducer located at the end of such a hole.
In the absence of a practical exact solution to the problem, the
method of attack chosen here leads to an upper bound on the
additional surface temperature or hot spot caused by a cavity.
The upper bound is justified because it is a close upper bound
and, for cavity dimensions in the range of interest, the
resulting hot spot is quite small. It is shown, for instance,
that a ☒‐mm hole drilled to within 1 mm of the exposed surface
will cause a time variant surface hot spot that is no more than
1.5% of the surface temperature. If the hole depth is reduced to
☒ mm, then the hot spot is less than 5.5% of the surface
temperature. An additional finding i