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 is that the magnitude of the hot spot is nearly independent of the temporal shape of the surface heat pulse for a large variance in the latter.