A study of variations of the soil temperature via heat equation

Abstract

In this article, firstly will be presented a review of the problem that relates the temperature of the soil surface to its temperature at a given depth, i. e. , through periodic variation of temperature at the soil surface, will be wanted to verify the influence caused by this a certain depth, ignoring influences of the radioactive processes of the interior of the Earth, that represent ideal conditions. In the modeling of the problem in question, the known Heat Equation is used, making an analogy to the problem of conducting heat in a semi-infinite bar, thermally isolated on its sides. Mathematical details of the solution of the heat equation will be presented. The soil temperature variation in relation to the surface on a summer day and on a winter day in the city of São Paulo will be used as a case study with the data provided by the meteorological station of the Institute of Astronomy, Geophysics and Atmospheric Sciences (IAG) of USP.

Keywords: Fourier Series; Partial Diferencial Equations; Boundary value problem; Heat conduction through a semi-infinity bar