@Article{cmc.2021.015710,
AUTHOR = {H. F. Wong, Muhammad Sohail, Z. Siri, N. F. M. Noor},
TITLE = {Numerical Solutions for Heat Transfer of An Unsteady Cavity with Viscous Heating},
JOURNAL = {Computers, Materials \& Continua},
VOLUME = {68},
YEAR = {2021},
NUMBER = {1},
PAGES = {319--336},
URL = {http://www.techscience.com/cmc/v68n1/41826},
ISSN = {1546-2226},
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.},
DOI = {10.32604/cmc.2021.015710}
}