We present an analysis of fluid flow and heat transfer through a single horizontal channel with permeable walls which are at different temperatures. The problem is set in the context of hot dry rock geothermal energy extraction where water, introduced through an injection well, passes through a horizontal fracture by which transfer of heat is facilitated through advection of the fluid flowing toward the recovery well. We consider the walls of the fracture to have properties of a permeable medium and we study the effect of slip boundary conditions on velocity and temperature profiles for low Reynolds number (< 7) based on a similarity solution and perturbation expansion. We show that the velocity and heat transfer profiles are altered with the channel width, the permeability and a slip coefficient α, which is a dimensionless constant related to the inherent properties of the channel.

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