Dimensionless characterization of the problem of heat transfer in soils with horizontal, underground and permeable thin layer: Direct and inverse problems

Abstract

From the dimensionless mathematical model of a scenario 2D, in which heat is transferred from a fluid flow within a thin, horizontal underground layer to the surrounding soil, the dimensionless groups that ruled the solutions are derived. The dependencies of the main unknowns of interest on the parameters of the problem are deduced after the introduction of a characteristic length and time, also assumed as unknowns, for which a constant temperature profile is developed. These dependencies are verified and depicted by universal curves and abacus than can be used in an easy way for the solution of the direct problem in any scenario. The number of dimensionless groups that appear in the solutions are reduced and some of them are collected in the characteristic length and time. In addition, two protocols are proposed for the estimations of flow velocity in the permeable layer from the measurements of experimental temperature profiles, one for the steady state and other for the transient profiles. An illustrative standard application shows the efficiency of such protocols.