Hawaii Geothermal Project : similarity solutions for free convection about a dike

Abstract

An analysis is made for steady free convection of groundwater about a hot dike trapped in an aquifer of infinite extent. Within the framework of boundary layer approximations, similarity solutions are obtained for a class of problems where wall temperature varies as xλ, i.e., a power function of distance from the origin where wall temperature begins to deviate from that of the surrounding groundwater. The uniform heat flux solution emerged as a special case with λ = 1/3. It is found that vertical velocity and the temperature profiles are of the same shape, and that the boundary layer thickness is proportional to the square root of the distance from the leading edge. Analytical expressions are obtained for boundary layer thickness, local and overall surface heat flux, as well as the local and average heat transfer coefficients. Some representative velocity and temperature profiles around a dike are also presented.