Viscous heating and cooling process in a mixed convection cavity with free-slip effect

Abstract

Both no-slip and free-slip effects are enforced to the lid-driven cavity walls with Robin boundary condition. Viscous heating and cooling process happen when the shear force applied at the top lid is removed and the cavity is exposed to natural convection. This numerical study is performed for a two-dimensional laminar incompressible fluid flow with unsteadiness. The governing equations of time-dependent vorticity-stream function and thermal energy equation are solved using a finite difference method. Dissipation of viscous-heating of the cavity flow to the ambient is observed. The in-house Matlab® code is firstly verified with Ansys Fluent® finite element method at steady state. With no-slip boundary condition, temperature profile shows a reduction with acumination style at the beginning of the cooling process whereas a blunted profile is shown in free-slip boundary condition with temperature profile reduces dawdlingly. This is due to the movement of fluid is still able to create viscous heating at the outset of cooling process and this effect is even more pronounced at high Reynolds number when subject to free-slip boundary condition.