Natural convection in a square cavity with uniformly heated and/or insulated walls using marker-and-cell method

Hidayathulla Khan, BMd; Venkatadri, K; Beg, OA; Ramachandra Prasad, V; Mallikarjuna, B

Abstract

In this study, a numerical investigation has been performed using the computational Harlow-Welch MAC (Marker and Cell) finite difference method to analyse the unsteady state two-dimensional natural convection in lid-driven square cavity with left wall maintained at constant heat flux and remaining walls kept thermally insulated. The significant parameters in the present study are Reynolds number (Re), thermal Grashof number (Gr) and Prandtl number (Pr) and Peclét number (Pe =PrRe). The structure of thermal convection patterns is analysed via streamline, vorticity, pressure and temperature contour plots. The influence of the thermophysical parameters on these distributions is described in detail. Validation of solutions with earlier studies is included. Mesh independence is also conducted. It is observed that an increase in Prandtl number intensifies the primary circulation whereas it reduces the heat transfer rate. Increasing thermal Grashof number also decreases heat transfer rates. Furthermore the isotherms are significantly compressed towards the left (constant flux) wall with a variation in Grashof number while Peclét number is fixed. The study is relevant to solar collector heat transfer simulations and also crystal growth technologies.

Citation

Hidayathulla Khan, B., Venkatadri, K., Beg, O., Ramachandra Prasad, V., & Mallikarjuna, B. (2018). Natural convection in a square cavity with uniformly heated and/or insulated walls using marker-and-cell method. International Journal of Applied and Computational Mathematics, 4(61), https://doi.org/10.1007/s40819-018-0492-z

• Journal Article Type: Article
• Acceptance Date: Jan 29, 2018
• Online Publication Date: Feb 20, 2018
• Publication Date: Feb 20, 2018
• Deposit Date: Feb 13, 2018
• Publicly Available Date: Feb 20, 2019
• Journal: International Journal of Applied and Computational Mathematics
• Print ISSN: 2349-5103
• Electronic ISSN: 2199-5796
• Publisher: Springer
• Volume: 4
• Issue: 61
• DOI: https://doi.org/10.1007/s40819-018-0492-z
• Publisher URL: http://dx.doi.org/10.1007/s40819-018-0492-z
• Related Public URLs: http://www.springer.com/mathematics/applications/journal/40819