Numerical Study of Natural Convection Flow in a Square Porous Enclosure Filled with Casson Viscoelastic Fluid

Abstract

The present simulation, a numerical investigation of natural convection of Casson viscoelastic fluid in a porous square enclosure has been reported. Darcy-Boussinesq approximation mathematical model has been considered. The enclosure has been uniformly heated from the left wall and uniformly cooled from right side wall. The developed partial differential equations of the present computational domain are employed by using stream function approach along with finite difference scheme. The house-computational numerical algorithm has been validated against with the previous work and the computational results have been registered a good correlation. All the important results as shown by streamlines, isotherms, and local Nusselt numbers, the impact of Casson fluid parameter (β), Rayleigh number (Ra) is examined. It has been observed that with the increase in Casson fluid parameter (β), the buoyancy induced fluid circulation and convection effect decreases inside the enclosure. For each Rayleigh number, there correspond a critical Casson fluid parameter (β), for which the heat transfer inside the enclosure takes place solely by conduction mode. It has been also observed that at high Casson viscoelastic fluid the effect of increase in Rayleigh number on average Nusselt number is lesser compared to the effect of increasing Rayleigh number at low Casson viscoelastic fluid.