Natural convection in a partially heated porous cavity to Casson fluid

Abstract

Abstract In the present study, the phenomenon of natural convection in a square porous cavity containing Casson fluid is investigated, numerically. The non-Newtonian model of Casson fluid is utilized to obtain the governing equations of a flow problem. The thermal control inside the cavity is managed by partially heating the bottom wall and symmetric cooling of the side walls while the top wall is taken to be adiabatic. The penalty finite element method is used to solve the non-linear coupled equations of the flow problem. The effect of different lengths of heated zone e, Rayleigh number Ra and Darcy number Da has been examined on flow velocity and temperature distribution inside the cavity. The impact of effective viscosity of the fluid by varying Casson fluid parameter γ on the flow of fluid and heat transport has also been investigated. The results are demonstrated by plotting streamlines, isotherms and average Nusselt number over wide ranges of governing parameters. The obtained results show that with an increase in Casson fluid parameter γ and Darcy number Da, heat transfer and flow circulation increases. It is also observed that the conduction dominant heat transfer takes place for low Darcy number over a wide range of the Rayleigh number (102 ≤ Ra ≤ 106).