Dual Solutions Of Convection Boundary Layer Flows In Porous Media, Nanofluid And Viscous Fluid
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Date
2018-05
Authors
Fauzi, Nur Fatihah
Journal Title
Journal ISSN
Volume Title
Publisher
Universiti Sains Malaysia
Abstract
The dual solutions of the boundary layer flows and convective heat transfer equations
can be obtained due to the nonlinearity of the differential equations and the difference
of geometric or fluid mechanical parameters. Experimentally, the existence of
dual or multiple solutions seem difficult to anticipate, thus mathematical computation
is essential to provide the details of flow structure and to observe occurrence of dual
or multiple solutions. This thesis presents a detailed numerical study on dual solutions
for convection boundary layer problems by considering four different problem: (1)
mixed convection flow of sphere through porous medium in presence of heat generation/
absorption at lower stagnation point; (2) magnetohydrodynamics (MHD) stagnation
point flow over a stretching/shrinking sheet in a nanofluid with heat absorption
and convective boundary condition; (3) mixed convection flow on a vertical flat surface
with melting effect in a non-Darcian porous medium; (4) stagnation point flow and
heat transfer over a nonlinear shrinking sheet with suction and slip effects. Using the
similarity transformation, the nonlinear partial differential equations are transformed
into a system of nonlinear ordinary differential equations. The reduced nonlinear ordinary
differential equations are solved using the Keller-box method and the shooting
method involves Runge-Kutta method together with Newton Raphson correction. The
numerical methods used in this study are programmed in Fortran and Maple softwares,
respectively. Numerical computations are carried out for different parameters on fluid
flow and heat transfer for each of the specific problem on hands. It is found that dual
solutions exist in the considered problems of porous media, nanofluid and viscous fluid
which involves sphere, stretching or shrinking sheet and vertical flat surface.
Description
Keywords
The dual solutions of the boundary layer flows , convective heat transfer equations