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

• Main Authors: Wong, H.F., Sohail, Muhammad, Siri, Zailan, Noor, Noor Fadiya Mohd
• Format: Article
• Published: Tech Science Press 2021
• Subjects: QA Mathematics
• Online Access: http://eprints.um.edu.my/25936/; https://doi.org/10.32604/cmc.2021.015710

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.