Abstract Free convection over a vertical rectangular duct filled with porous matrix with variable viscosity and variable thermal conductivity is studied in this paper. We consider the two-dimensional steady laminar flow and Brinkmanâ€“Forchheimer extended Darcy model to define the porous medium. Using the appropriate variables the basic governing equations are transformed to non-dimensional governing equations. The fluid viscosity is assumed to vary exponentially with temperature whereas the thermal conductivity is assumed to vary linearly with temperature. One of the vertical walls of the duct is cooled with constant temperature while the other wall is heated to constant but different temperature. The governing coupled nonlinear momentum and energy equations are solved numerically using finite difference method. The effect of pertinent parameters such as variable viscosity, variable thermal conductivity, Darcy number, inertial parameter, Grashof number, Brinkman number and aspect ratio on the velocity, temperature, volumetric flow rate, shear stress and heat transfer are discussed.

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