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

Beg, OA; Devi, TS; Lakshmi, CV; Venkatadri, K; Prasad, VR

Abstract

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 (MAC) 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 i.e. 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 up to 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.

Citation

Beg, O., Devi, T., Lakshmi, C., Venkatadri, K., & Prasad, V. (2020). Simulation of unsteady natural convection flow of a Casson viscoplastic fluid in a square enclosure utilizing a MAC algorithm. Heat Transfer - Asian Research, 49(4), 1769-1787. https://doi.org/10.1002/htj.21690

• Journal Article Type: Article
• Acceptance Date: Feb 4, 2020
• Online Publication Date: Feb 19, 2020
• Publication Date: Apr 21, 2020
• Deposit Date: Feb 10, 2020
• Publicly Available Date: Feb 19, 2021
• Journal: Heat Transfer - Asian Research
• Print ISSN: 1099-2871
• Electronic ISSN: 1523-1496
• Publisher: Wiley
• Volume: 49
• Issue: 4
• Pages: 1769-1787
• DOI: https://doi.org/10.1002/htj.21690
• Publisher URL: https://doi.org/10.1002/htj.21690
• Related Public URLs: https://onlinelibrary.wiley.com/journal/15231496
• Additional Information: Access Information : This is the peer reviewed version of the following article: Devi, TS, Lakshmi, CV, Venkatadri, K, Prasad, VR, Bég, OA, Reddy, MS. Simulation of unsteady natural convection flow of a Casson viscoplastic fluid in a square enclosure utilizing a MAC algorithm. Heat Transfer. 2020; 49: 1769– 1787, which has been published in final form at https://doi.org/10.1002/htj.21690. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions