Simulation of unsteady natural convection flow of a Casson viscoplastic fluid in a square enclosure utilizing a MAC algorithm

Non‐Newtonian fluids are increasingly being deployed in energy systems and materials processing. Motivated by these developments, in the current study, a numerical simulation is performed on two‐dimensional, unsteady buoyancy‐driven flow in a square cavity filled with non‐Newtonian fluid (Casson liquid). The enclosure geometry features vertical isothermal walls (with one at higher temperature than the other) and thermally insulated horizontal walls. The conservation equations for mass, momentum, and energy are normalized via appropriate transformations and the resulting dimensionless partial differential boundary value problem is solved computationally with a marker and cell algorithm, which features a finite difference scheme along with a staggered grid system. The projection method is employed to evaluate the pressure term. Extensive visualizations of the impact of emerging physical parameters (Rayleigh number and Casson viscoplastic parameter) on streamline and isotherm distributions in the cavity are presented for fixed Prandtl number. Nusselt number, that is, heat transfer rate, is increased with rising values of the Casson viscoplastic fluid parameter for any value of Rayleigh number. The density of streamlines increases with increasing values of Casson viscoplastic fluid parameter upto 1. Overall, the Casson fluid parameter plays a vital role in controlling the convective heat transfer within the enclosure. The computations are relevant to hybrid solar collectors, materials fabrication (polymer melts), etc.