Open Access

ARTICLE

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

H. F. Wong^1,2, Muhammad Sohail³, Z. Siri¹, N. F. M. Noor^1,*

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 the 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.

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