Invoking a nonlinear density-temperature relation [NDT] and assuming the Darcy flow model, a simple mathematical theory is proposed for the analysis of the transient buoyancy driven thermal convection around a point heat source of thermal energy embedded in an unbounded porous medium of low permeability. Making use of a regular perturbation analysis, analytical solutions for both the flow and temperature fields have been obtained in the form of series expansions in terms of a thermal Rayleigh number which is based on the strength ofthesourceandthemedium permeability. The resultsareexemplified by drawing the streamlines at two different times and are delineated by comparing them with that of the linear Boussinesq model. The significance of the NDT variations has been highlighted and the solutionforthefreeconvectionflowofwater at 4°C has been deduced.

porous medium, free convection, point heat source, nonlinear Boussinesq model.