PERIODIC TEMPERATURE-VARIATIONS IN AN INHOMOGENEOUS SOIL - A COMPARISON OF APPROXIMATE AND EXACT ANALYTICAL EXPRESSIONS

Comparisons (of the first harmonic) between exact and two approximate analytical solutions to the one-dimensional heat conduction equation f or an inhomogeneous soil show that the approximate analytical solution s are potentially more useful for profiles of soil thermal properties that exhibit positive or zero concavity than for those that exhibit ne gative concavity. Comparisons between the two approximate analytical s olutions also suggest that one solution provides a much easier method for estimating profiles of soil thermal properties from soil temperatu re profiles than does the other. A brief summary of three analytical s olutions to the one-dimensional heat conduction equation is also given . Furthermore, some of these extent analytical solutions are unique to the present study and employ relatively simple and easily implemented algorithms for their evaluation. For many applications involving peri odic variations in soil temperature, these algorithms are likely to pr ovide more realistic results than can be obtained by assuming homogene ous soil properties with their associated ''exponentially decaying'' s olution for soil temperatures. It is further suggested that the soluti ons presented in this work could be used to verify more complex numeri cal models of soil heat flow.