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Numerical Solutions for Heat Transfer of An Unsteady Cavity with Viscous Heating

H. F. Wong1,2, Muhammad Sohail3, Z. Siri1, N. F. M. Noor1,*
1 Institute of Mathematical Sciences, Faculty of Science, University of Malaya, 50603 Kuala Lumpur, Malaysia
2 Unit of Engineering Design and Product Development, Technology and Engineering Division, Malaysian Rubber Board, 47000 Sungai Buloh, Malaysia
3 Department of Applied Mathematics & Statistics, Institute of Space Technology, 44000 Islamabad, Pakistan
* Corresponding Author: N. F. M. Noor. Email:
(This article belongs to this Special Issue: Role of Computer in Modelling & Solving Real-World Problems)

Computers, Materials & Continua 2021, 68(1), 319-336. https://doi.org/10.32604/cmc.2021.015710

Received 03 December 2020; Accepted 15 January 2021; Issue published 22 March 2021

Abstract

The mechanism of viscous heating of a Newtonian fluid filled inside a cavity under the effect of an external applied force on the top lid is evaluated numerically in this exploration. The investigation is carried out by assuming a two-dimensional laminar in-compressible fluid flow subject to Neumann boundary conditions throughout the numerical iterations in a transient analysis. All the walls of the square cavity are perfectly insulated and the top moving lid produces a constant finite heat flux even though the fluid flow attains the steady-state condition. The objective is to examine the effects of viscous heating in the fully insulated lid-driven cavity under no-slip and free-slip Neumann boundary conditions coupled with variations in Reynolds and Prandtl numbers. The partial differential equations of time-dependent vorticity-stream function and thermal energy are discretized and solved using a self-developed finite difference code in MATLAB® environment. Time dependence of fluid thermodynamics is envisaged through contour and image plots. A commercial simulation software, Ansys Fluent® utilizing a finite element code is employed to verify the finite difference results produced. Although the effect of viscous heating is very minimal, Neumann no-slip and free-slip boundary conditions are able to trap the heat inside the fully insulated cavity as the heat flux is constantly supplied at the top lid. A lower Reynolds number and a greater Prandtl number with free-slip effects reduce temperature distribution in the cavity with a faster velocity than in the no-slip condition as the free-slip behaves as a lubricant.

Keywords

Lid-driven; viscous heating; vorticity-stream function; finite difference method; finite element method

Cite This Article

H. F. Wong, M. Sohail, Z. Siri and N. F. M. Noor, "Numerical solutions for heat transfer of an unsteady cavity with viscous heating," Computers, Materials & Continua, vol. 68, no.1, pp. 319–336, 2021.

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This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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