Free convection in a square cavity filled with a Casson fluid under the effects of thermal radiation and viscous dissipation

Abstract

Purpose

The main purpose of this numerical work is to study free convection of Casson fluid in a square differentially heated cavity taking into account the effects of thermal radiation and viscous dissipation.

Design/methodology/approach

The cavity is heated from the left vertical wall and cooled from the right vertical wall while horizontal walls are insulated. The governing partial differential equations invoking Rosseland approximation for thermal radiation with corresponding boundary conditions have been solved by finite difference method of the second-order accuracy using dimensionless variables stream function, vorticity and temperature. The governing parameters are Rayleigh number (Ra = 10⁵), Prandtl number (Pr = 0.1, 0.7, 7.0), Casson parameter (γ = 0.1-5.0), radiation parameter (R_d = 0-10), Eckert number (Ec = 0-1.0).

Findings

It is found that an increase in Casson parameter leads to the heat transfer enhancement and fluid flow intensification. While a growth of Eckert number illustrates the heat transfer suppression.

Originality/value

The originality of this work is to analyze for the first-time natural convective fluid flow and heat transfer of a Casson fluid within a differentially heated square cavity under the effects of thermal radiation and viscous dissipation. The results would benefit scientists and engineers to become familiar with the flow behavior of such non-Newtonian fluids, and the way to predict the properties of this flow for possibility of using this specific fluid in various engineering and industrial processes, such as chyme movement in intestine, blood flows, lubrication processes with grease and heavy oils, glass blowing, electronic chips, food stuff, slurries, etc.

Citation

Pop, I. and Sheremet, M. (2017), "Free convection in a square cavity filled with a Casson fluid under the effects of thermal radiation and viscous dissipation", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 27 No. 10, pp. 2318-2332. https://doi.org/10.1108/HFF-09-2016-0352