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

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.