Background: The present paper is focused on the numerical investigation of the effects of
temperature dependent viscosity and temperature-dependent thermal conductivity on steady, free convection
flow of a viscous incompressible fluid in a vertical rectangular duct.
Objectives: The purpose of this study was to provide an overview of the flow field if one assumes that
viscosity and thermal conductivity parameters are not constant but they depend on the temperature.
Methods: Finite difference scheme of second order accuracy was applied to solve the two dimensional
coupled nonlinear equations. Validity of the obtained results was justified with the literature.
Results: The effects of the non-dimensional parameters such as variable viscosity, variable thermal
conductivity, Grashof number, Brinkman number and aspect ratio on the velocity, temperature, shear
stress, volumetric flow rate and heat transfer rate were evaluated and depicted pictorially and also in the
form of tables. It was observed that the effects of variable viscosity and thermal conductivity on the
velocity and temperature fields were significant.
Conclusion: It has been concluded that for positive values of the viscosity and conductivity variation
parameters, the viscous fluid flows in the upward direction and for negative values, the fluid flows in
the downward direction of the duct. Increase in the viscosity variation parameter, the thermal conductivity
variation parameter, Grashof number, Brinkman number and the aspect ratio resulted in the
improvement of the volumetric flow rate.