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
Journal Title
Journal ISSN
Volume Title
Publisher
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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Keywords
Mathematics