The random heat conduction and its associated thermal stress problems were discussed in this report. Several problems were solved by using the theories of heat conduction and elasticity in flat plates, solid spheres and solid cylinders in which the surrounding temperature Ta was varied as a stochastic function of time. For the case where the surrounding temperature Ta followed a weakly stationary process, the autocorrelation function, the mean square and the power spectral density were derived.
As an example, the problem in which the surrounding random temperature is regarded as a white noise process was solved. The form of the autocorrelation function corresponding to white noise was
RTa(τ)=Tsδ(τ)
where δ is Dirac's delta function and Ts is a constant.
The numerical computation was carried out for the mean square of the temperature and thermal stress distribution. The numerical results showed that the large variations of temperature and thermal stress were confined in the thin surface layer and very small or almost zero in the rest. The thickness of the layer was 14 to 15% of the plate thickness or the outer radius of the sphere and cylinder.
