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

Wong, H.F. and Sohail, Muhammad and Siri, Zailan and Noor, Noor Fadiya Mohd (2021) Numerical Solutions for Heat Transfer of An Unsteady Cavity with Viscous Heating. Computers, Materials & Continua, 68 (1). pp. 319-336. ISSN 1546-2226, DOI

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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. © 2021 Tech Science Press. All rights reserved.

Item Type: Article
Funders: Ministry of Higher Education, Malaysia and University of Malaya ( under the Project No: IIRG006C-19IISS
Uncontrolled Keywords: Lid-driven; viscous heating; vorticity-stream function; finite difference method; finite element method
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science > Institute of Mathematical Sciences
Depositing User: Ms. Juhaida Abd Rahim
Date Deposited: 03 May 2021 08:06
Last Modified: 03 May 2021 08:06

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