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

• Published in: Computers, materials & continua Vol. 68; no. 1; pp. 319 - 336
• Main Authors: F. Wong, H., Sohail, Muhammad, Siri, Z., F. M. Noor, N.
• Format: Journal Article
• Language: English
• Published: Henderson Tech Science Press 01.01.2021
• Subjects: Boundary conditions; CAD; Compressible fluids; Computational fluid dynamics; Computer aided design; Equilibrium flow; Finite difference method; Finite element method; Fluid flow; Heat flux; Heat transfer; Heating; Laminar flow; Newtonian fluids; Partial differential equations; Prandtl number; Reynolds number; Slip; Stream functions (fluids); Temperature distribution; Thermal energy; Time dependence; Transient analysis; Two dimensional flow; Vorticity
• ISSN: 1546-2226; 1546-2218; 1546-2226
• DOI: 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.