SOLUTIONS OF CONVECTIVE BOUNDARY LAYER FLOWS VIA SCALING GROUP TRANSFORMATION METHOD
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Date
2014-05
Authors
AL-ASSAFI, ALI ABID MUTLAG
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Abstract
The aim of this thesis is to find similarity solutions for some models in fluid mechanics
using the method of scaling group transformation. In this thesis the steady two-dimensional
incompressible laminar boundary layer on a flat plate as well as wedge flow models both in
porous media and clear media have been studied. The working fluid considered is Newtonian
and non-Newtonian (power-law, micropolar) with slip boundary condition, thermal radiation,
variable viscosity, convective boundary condition and heat generation effects. Scaling group
transformation method reduces the number of the independent variables as well as the dependent
variables and maps the partial differential equations to ordinary differential equations. Using the
symmetry transformations analysis, the similarity transformations have been obtained. Hence,
the governing equations for flow models are transformed into similarity equations. The
transformed equations are solved numerically by the Runge-Kutta-Fehlberg fourth-fifth order
numerical method using Maple 13. The effects of parameters (velocity slip, thermal slip,
Falkner-Skan power-law, thermal conductivity, variable viscosity, suction/injection, power-law
index, thermal radiation, viscosity index, rheological, heat generation, convective heat, Prandtl
number, micropolar, Grashof number, permeability, micro-rotational density, Eckert number,
vortex viscosity and microrotation) on the dimensionless velocity, angular velocity, temperature
and the physical quantities (shear stress, heat transfer rate and couple stress factor) have been
studied and discussed. Good agreements were found between the numerical results of the present
study with published results (where available). The present study find applications in artificial
heart valves, internal cavities, nano/micro devices, synthetic fibers, foodstuffs, extrusion of
molten plastic and as well as in some flows of polymer solutions.
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SOLUTIONS OF CONVECTIVE