Abstract

In this study we investigate the three-dimensional (3-D) mixed convection fluid flow within a horizontal duct, the walls of which are assumed to be maintained at specified constant temperatures. The fluid flowing through the duct is assumed to be steady and laminar and the results presented are mainly concentrated on those obtained when using parameter values that are typically found in hydraulic fractures, a technique used in the oil industry to enhance the production rate of an oil well. The full 3-D governing equations are non-dimensionalized and simplified using a narrow gap type approximation and the resulting two-dimensional (2-D) governing equations are found to be parabolic in the streamwise direction. A stream function is introduced into the solution procedure, which consists of marching streamwise along the duct using a finite-difference technique. Results are found for Newtonian and power-law fluids, as well as Newtonian fluids with a temperature dependent viscosity.

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