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. (C) 1997 Elsevier Science Ltd.