A finite difference model for undefined end boundary to analyse the heat transfer in dry sands

Accurate prediction of thermal regime (i.e. the variation of soil temperature, θ, and heat flux, (Formula presented.)) to investigate the migration of thermal energy in soil mass, poses challenge to the geoenvironmental engineers while dealing with various thermo-active structures. In this context, several numerical approaches have been attempted to solve the heat transfer equation (HTE) for conduction to predict the thermal regime. However, most of them need accurate boundary condition defined and involve complicated numerical approach which is inconvenient for the practising engineers. Hence, an attempt has been made in the present study to develop a simplified, but numerically efficient, approach based on the finite difference method (FDM) to analyse one dimensional heat transfer in dry sands when the end boundary is not defined. Furthermore, a time-dependent initial boundary condition has been applied to this model to simulate similar experimental condition and results have been compared vis-à-vis those obtained from the experiment and COMSOL Multiphysics® to validate the proposed approach.