Analytical approach for inverse problems theory applications towards determination of thermophysical characteristics of soil

Abstract

Current paper presents analytical expressions received for investigation of determination of thermophysical characteristics of soil applying the theory of inverse problems. There was considered experimental design with exact measurements and constructed mathematical model for considered case. The analytical expression for transient one-dimensional temperature field was received by Laplace transform. Additional data, such as the heat flux at inlet domain received by conducting numerical simulation of the heat source via computational model. Presented analytical expression for heat transfer parameter allows to determine the soil thermal property without loss of precision, which is crucial in agricultural field. Paper discusses posed peculiarities considered for the inverse problem methodology along with derivation stages of analytical expression. The analytical expression for proposed model is presented both in the frequency and real time domain by applied direct and inverse Laplace transform. The measured outlet input data is interpolated further by the 8-th order polynomial and presented with approximation residuals.