In recent analyses of the hot-water system at Wairakei, New Zealand (Mercer, Pinder, and Donaldson, 1975) and the vapor-dominated system at Larderello, Italy (Petracco and Squarci, 1975), it has been suggested that large quantities of cold water are entering the reservoir by flowing down from the surface and then horizontally into the reservoir because of decreased reservoir pressures. It is also suggested that decreased reservoir pressures should increase these downward flows above their preexploitation levels. In order to estimate the effects of vertical flows on the temperature distribution, two idealized problems are analyzed in this paper. In both problems, the initial condition is a linear temperature increase with depth, and the flow starts at time equal to zero. In the first problem, the flow is through a semi-confining layer with the temperature fixed at the top and bottom of the layer. In the second problem, the flow is into a half-space with the surface temperature fixed.

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