DOI: 10.1615/JPorMedia.v14.i4.50

pages 329-343

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CONVECTION AND HEAT TRANSFER IN LAYERED SLOPING,WARM-WATER AQUIFERS

Robert McKibbin
Institute of Information and Mathematical Sciences, Massey University at Albany, Auckland, New Zealand

Nicholas Hale
Oxford Centre for Collaborative Applied Mathematics, Mathematical Institute, Oxford, OX1 3LB, United Kingdom

Robert W. Style
Oxford Centre for Collaborative Applied Mathematics, Mathematical Institute, Oxford, OX1 3LB, United Kingdom

Nicole Walters
School of Mathematics, Statistics and Operations Research, Victoria University of Wellington, New Zealand

ABSTRACT

What convective flow is induced if a geologically-stratified groundwater aquifer is subject to a vertical temperature gradient? How strong is the flow? What is the net heat transfer? Is the flow stable? How does the convection affect the subsequent species distribution if a pollutant finds its way into the aquifer? This paper begins to address such questions. Quantitative models for buoyancy-driven fluid flow in long, sloping warm-water aquifers with both smoothly- and discretely-layered structures are formulated. The steady-state profiles are calculated for the temperature and for the fluid specific volume flux (Darcy velocity) parallel to the boundaries in a sloping system subjected to a perpendicular temperature gradient, at low Rayleigh numbers. The conducted and advected heat fluxes are compared and it is shown that the system acts somewhat like a heat pipe. The maximum possible ratio of naturally advected-to-conducted heat transfer is determined, together with the corresponding permeability and thermal conductivity profiles.

Keywords: warm water, aquifers, convection, layered systems, mass transfer, heat transfer