Modelling the effects of temperature on the flow of fluid through loamy soil with spatial dependent thermo-physical property

Abstract

The modelling of effects of temperature on the flow of fluid through loamy soil with spatial dependent thermo-physical property was studied. Navier-Stoke equations were modified with Boussinesq’s approximation under necessary conditions for the flow of the fluid through the porous medium considered (loamy soil). These set of equations formed the governing equations for the flow in dimensional form. After reducing the equations into non-dimensional form employing some relevant dimensionless parameters, they were converted to ordinary differential equations and solved analytically which formed the desired model. Data retrieved concerning specific information about the loamy soil were imputed into the model and Matlab R2009b was then used to display the results on graphs. The effects of relevant physical parameters were examined on the velocity of the fluid. Increasing thermal Grashof number (Gr), Internal heat (Q) and solar radiation enhance the velocity of the fluid while the Prandtl number reduces the rate of the flow.