Similarity solutions for convection of groundwater adjacent to horizontal impermeable surfaces with axisymmetric temperature distribution : Technical report No. 14

Abstract

The axisymmetric buoyancy-induced groundwater flow adjacent to horizontal impermeable surfaces with wall temperature being a power function of radius is discussed in this paper. With the boundary layer simplifications, the governing non-linear partial differential equations can be transformed into a coupled pair of non-linear ordinary differential equations with two-point boundary conditions that can be integrated numerically by established techniques. Simple algebraic expressions for boundary layer thickness and heat transfer rate are obtained. Applications to free convective flow in a liquid-dominated geothermal system at high Rayleigh number are discussed.