© 1961 by Oxford University Press
TWO PROBLEMS OF UNSTEADY HEAT CONDUCTION WITH SHOCK TUBE APPLICATIONS
( Royal Aircraft Establishment Farnborough )
In the first part of the paper, the temperature at all points of a semi-infinite solid heated at a rate Q(y, t) over a strip h < y < h of its surface z = 0 is obtained from the analysis of Lowan (1). It is shown that with a constant heating rate, the ratio of the mean temperature at the surface strip to that when the same heating rate is applied to the whole surface – 
< y < is 1–(l/2h)
(Kt/
) (k = thermal diffusivity, t = time), provided the diffusion depth 2(kt) is moderately small. This permits one to estimate the error introduced by edge effects in the calibration by short-duration Joule heating of thin film resistance thermometers for use in shock tubes.
The remainder of the paper deals with the variation of the surface temperature T{t) at the stagnation point of a bluff body in a shock tube. It is noted that the heating rate Q(t) may be written
where A1; A2, Tlv Tt and (pkc)i are constants, and t0 is the time that elapses between the passage of the shock wave and that of the interface between test and driving gases. The exact solution for T(t) in these circumstances is found by operational methods in section 4, and expanded to give a simple approximation for small values of (t—to).