Stability Analysis Of Magnetohydrodynamic Flow And Heat Transfer Over A Moving Flat Plate In Ferrofluids With Slip Effects

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Date
2018-08
Authors
Ramli, Norshafira
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Universiti Sains Malaysia
Abstract
A study of the stability analysis on the boundary layer flow has become a great interest in the field of fluid dynamics. This analysis is essential because it helps to identify which solution is stable if there exists non-unique solutions in the computation. In this thesis, the stability analysis is applied on the problems of the steady, two-dimensional, laminar, magnetohydrodynamic (MHD) flow and heat transfer over a moving flat plate in ferrofluids with suction and slip boundary conditions. It aims attention on the problem of forced and mixed convection immersed in an incompressible fluid. The three problems considered are; (1) MHD forced convection flow over a moving flat plate in ferrofluids with suction and second-order slip effects; (2) MHD mixed convection flow over a moving flat plate in ferrofluids with suction and slip effects; and (3) MHD mixed convection flow over a moving flat plate in ferrofluids with thermal radiation, suction and second-order slip effects. In order to solve these problems, the dimensional partial differential equations that governed the boundary layer flows are first transformed into non-dimensional equations by using appropriate dimensionless variables. These equations are then reconstructed into the form of nonlinear ordinary differential equations by applying the similarity transformation. The resulting system is solved numerically using the shooting method which is done with the aid of shootlib function in Maple software. This method is associated with the Runge-Kutta fourth order method together with Newton-Raphson as a correction scheme. Further, if there are non-unique solutions, the stability analysis is performed to identify which solution is stable, by implementing bvp4c solver in Matlab. The effects of the mixed convection parameter, magnetic parameter, radiation parameter, moving parameter, mass transfer parameter, first-order surface slip parameter, second-order surface slip parameter and volume fraction of solid ferroparticles on the dimensionless velocity and temperature, as well as the skin friction coefficient and local Nusselt number are discussed in the form of tabular and graphical presentation. For this present study, the results are considered based on three preferred ferroparticles, namely magnetite, cobalt ferrite and manganese-zinc ferrite in water- and kerosene-based fluids. It is found that the mixed convection parameter, magnetic parameter, moving parameter, as well as the volume fraction of solid ferroparticles help to enhance both skin friction coefficient and heat transfer rate. In addition, the presence of suction and radiation parameter serves the heat transfer rate to increase, while the slip factor provides an enormous reduction of the skin friction coefficient. The results display the existence of dual and triple solutions for certain range of the mixed convection, moving (a plate moving towards the origin) dan mass transfer (suction) parameters. Further, the stability analysis showed that there is an initial decay of disturbance for the first solution, while the second and third solutions showed an initial growth of disturbance, indicated that the first solution is stable and thus physically realizable, while the second and third solutions are not.
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Mathematics
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