Transient Heat Transfer from a Circular Cylinder with Constant Heat Flux in a Saturated Porous Layer

Application to Groundwater Velocimetry

Abstract

Transient heat transfer from a cylindrical object placed in a saturated porous layer, which is simulating a heat-generating probe vertically placed in an aquifer, has been studied both analytically and numerically. When constant heat flux is specified on the eylinder surface, it is shown that the surface temperature rise with time and the elapsed time to reach steady state can determine the effective thermal conductivity of the saturated porous layer, as well as the groundwater velocity running through it. A present study reveals two distinctive regimes existing during the transient process. For small times, the heat transfer is dominated by conduction, while for large times conduction is balanced with convection. Recognizing these characteristics enables us to develop approximate solutions valid for respective regimes. Complete two dimensional solutions are generated numerically in order to demonstrate the accuracy of the approximate solutions. An application to groundwater velocimetry has been suggested.