Three-dimensional heat conduction in permafrost beneath heated buildings

The general Green's function solution has been integrated for the case of heat conduction in a homogeneous semi-infinite medium in which the temperature at the surface varies sinusoidally with time but the mean temperature and amplitude of the variation are different within and outside an arbitrarily shaped region at the surface. The amplitude and mean temperature can be treated as functions of position within the arbitrary surface region. For certain simple surface regions the results can be expressed in terms of tabulated functions. Numerical results for the general case can be obtained by simple graphical procedures. The results can be applied to the study of disturbances in ground temperature caused by the presence of bodies of water or by engineering surface modifications such as those produced by erecting a heated building. The primary application of such studies is in high-latitude regions where much of the undisturbed ground is perennially frozen. In such areas, a method of predicting the extent of thawing induced by various modifications of the temperature of the ground surface is important in problems of engineering design and logistics.