On multivariate overlapping grid spectral quasilinearization methods for problems in cavity flow.
Loading...
Date
2022
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
We investigate fluid flow in cavities with different boundary conditions. Three cavity flow problems
of varying complexity are investigated in this study. In the first problem, a flow filled with a porous
medium, and with adiabatic and impermeable walls is considered. The left wall is heated. For the second
problem, we investigate free convection in an enclosed square with porous medium and nanofluid. We
assume that the side walls have a high fixed temperature and a lower fixed temperature for the horizontal
walls. The third problem is more complex, and it involves investigating a square enclosure with porous
medium, a top moving wall, and the side walls heated with a sinusoidally varying temperature. We
analyze the effect of fluid parameters on the fluid flow characteristics such as the streamline distribution,
isoconcentration, isotherms, local Nusselt number, skin friction, and the local Sherwood number. The
flow equations are solved using two recent numerical techniques, namely the multivariate overlapping
grid spectral quasilinearization method (MOGSQLM) and the multivariate spectral quasilinearization
method (MSQLM). The MOGSQLM is an extension of the MSQLM with improved accuracy. Using
the two methods we determine the solution, the residual solution errors and the computational time to
achieve a converged solution. The MOGSQLM is found to be more accurate, and for this reason, only
the MOGSQLM is used to numerically solve the third problem. The MOGSQLM was found to be the
better method in terms of convergence, accuracy, and CPU time. The changes in the Rayleigh number
alter the flow pattern from circular to elliptic with stronger circulation in the core region.
Description
Masters Degree. University of KwaZulu-Natal, Pietermaritzburg.