Mohd Rohni, Azizah
(2013)
Multiple Similarity Solutions Of
Steady And Unsteady
Convection Boundary Layer Flows In
Viscous Fluids And Nanofluids.
PhD thesis, Universiti Sains Malaysia.
Abstract
For many complex problems in convection boundary layer flow and heat transfer,
multiple solutions may exist due to the nonlinearity of the differential equations,
variation of geometric or fluid mechanical parameters. It is difficult to visualize the
occurrence of multiple solutions experimentally, therefore mathematical computation
is important to provide the details flow structure and to notice the occurrence of
multiple solutions. This thesis aims to study the possible multiple similarity solutions
that might exist in boundary layer flows and heat transfer. This is done by
considering five different problems which are two problems in viscous fluid, one
problem in nanofluid and the remaining two are in porous medium and in porous
medium filled with nanofluid, respectively. For the problems in viscous fluid and
nanofluid, different situations of shrinking sheet have been considered. On the other
hand, vertical plate in porous medium and vertical cylinder in porous medium filled
by nanofluid have also been considered. The basic governing equations in partial
differential equations form for each problem are first transformed into similarity
equations in nonlinear ordinary differential equations form by similarity approach.
The resulting systems are then solved numerically using the shooting technique with
the aid of shootlib fuction in Maple software. This technique involves Runge-Kutta
method together with Newton-Raphson correction.
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