Numerical solutions of magnetohydrodynamic boundary layer flow and heat transfer of various fluids and boundary conditions

Abstract

In this thesis, the boundary layer flow and heat transfer caused by a stretching/shrinking surface in a viscous fluid, nanofluid and hybrid nanofluid is investigated numerically. The study includes the magnetohydrodynamic (MHD) two-dimensional steady and unsteady flows with diverse effects. By utilizing the similarity transformations, the governing nonlinear partial differential equations for all problems are converted into a system of nonlinear ordinary differential equations. The bvp4c package in MATLAB software is used to obtain the numerical results for the five main problems considered in this thesis. The first problem employs the Ag−MgO/water hybrid nanofluid to inspect the MHD mixed convection flow across an inclined permeable stretching/shrinking sheet. In the second problem, the Buongiorno nanofluid model is used to examine the MHD stagnation flow driven by a shrinking sheet with solar radiation impact. A numerical analysis of the MHD unsteady thin film flow induced by an inclined stretching sheet in Al2O3/water nanofluid utilizing the Tiwari and Das model is carried out in the third problem. In this work, the impact of four distinct nanoparticle shapes, namely platelet, cylinder, brick and sphere are investigated. The combined effects of thermal radiation, slip and chemical reaction on MHD mixed convection stagnation point flow of a viscous fluid in a porous medium toward an inclined plate are studied in the fourth problem. The last problem relates to modeling and numerically examining the MHD mixed convection flow in a viscous fluid toward an inclined stretching surface. The stretching velocity and temperature of the surface are presumed to obey the power law. The noteworthy results reveal that the coefficient of skin friction and heat transfer rate decline when the inclination angle boosts in the assisting flow, whilst the reverse result is obtained in the opposing flow case. In nanofluid, an enhancement in the slip parameter is noticed to result in a decrement in the skin friction coefficient and heat transfer rate across the inclined stretching sheet. It is also noticed that the film thickness reduces with the increment in the magnetic and unsteadiness parameters. The local Sherwood and Nusselt numbers decrease by increasing the Brownian motion parameter. The rate of heat transfer is likewise observed to decrease as the thermophoresis parameter is increased, whereas the rate of mass transfer shows the reverse tendency. Further, the presence of the hybrid nanofluid leads to enhancing the skin friction coefficient but has tendency to decline the heat transfer rate on a permeable stretching/shrinking sheet. The range of the shrinking parameter for which the solution exists is expanded by the increase in the magnetic field, thus delaying the separation of the boundary layer from the surface. The existence of dual solutions is detected for a specific variation of the stretching/shrinking parameter. The temporal stability of the dual solutions is also examined, to determine which one of them is stable as time evolves. The results indicate that the first solution is stable and physically feasible, while the second solution is unstable, and thus not physically reliable in the long run.