Sibanda, Precious.Goqo, Sicelo Praisegod.Nzama, Sibonelo.2022-10-242022-10-2420222022https://researchspace.ukzn.ac.za/handle/10413/21001Masters Degree. University of KwaZulu-Natal, Pietermaritzburg.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.enNusselt number.Sherwood number.Thesis