TY - EJOU
AU - Wong, H. F.
AU - Sohail, Muhammad
AU - Siri, Z.
AU - Noor, N. F. M.
TI - Numerical Solutions for Heat Transfer of An Unsteady Cavity with Viscous Heating
T2 - Computers, Materials \& Continua
PY - 2021
VL - 68
IS - 1
SN - 1546-2226
AB - 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.
KW - Lid-driven; viscous heating; vorticity-stream function; finite difference method; finite element method
DO - 10.32604/cmc.2021.015710