A STUDY ON FLOW FORMATION OF CONDUCTING FLUID IN MACRO AND MICRO-CHANNELS
A STUDY ON FLOW FORMATION OF CONDUCTING FLUID IN MACRO AND MICRO-CHANNELS
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Date
2015-08
Authors
ISA, SANI
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Abstract
Motion of an electrically conducting fluid in two types of geometries was studied;
the macro-channels formed by two vertical parallel plates and annular
micro-channels formed by two vertical concentric cylinders. The flow was
assumed to be unsteady, fully developed laminar or steady laminar flow of viscous,
incompressible and electrically conducting fluid with magnetic field applied
perpendicular to the flow direction. The governing equations describing
the different flow situations have been formulated and solved semi-analytically
using a combination of Laplace transform technique and the Riemann-sum approximation,
a method of taking the inverse of Laplace transform technique.
However, the corresponding steady state solution and numerical solution by
implicit unite difference method have also been obtained in the case of time
dependent problems as a means of validating the obtained results. An excellent
agreement at large values of time have been recorded. MATLAB
programmes are written to compute and generate line graphs for the velocities,
induced magnetic field, current density, volume flow rate and the skin
frictions. A parametric study depicting the effect of the various dimensionless
parameters on the velocity and skin friction was conducted. These parameters
include the Prandtl number (Pr), the time (t), the suction/injection parameter
(S), the Hartmann number (M), radius ratio (ษณ), rarefaction parameter
( Kn), and the fluid - wall interaction parameter (F). The effects of changing
the parameters mentioned above were observed either to increase, to decrease
or to have no effect on the velocity profiles and the skin friction indicating
the existence of a Lorentz force generated by the interaction of the magnetic
field and the electric field. To understand the fluid flow and the heat transfer
characteristics of buoyancy-induced micropump and microheat exchanger
in microfluidic and thermal systems, fully developed. MHD natural convection
flow in a vertical annular microchannel with asymmetric wall temperature
distributions was studied semi-analytically. Both of the velocity slip and
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the temperature jump conditions were considered because they have counter
effects both on the volume flow rate and the heat transfer rate. Results revealed
that in most of the natural convection situations, the volume flow rate
at microscale is higher than that at macroscale, while the heat transfer rate is
lower. It is, therefore, concluded that the temperature jump condition induced
by the effects of rarefaction and fluid-wall interaction plays an important role
in slip-flow natural convection.
Description
IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE
AWARD OF DOCTOR OF PHILOSOPHY DEGREE IN MATHEMATICS
DEPARTMENT OF MATHEMATICS
FACULTY OF SCIENCE
AHMADU BELLO UNIVERSITY, ZARIA
NIGERIA
Keywords
STUDY,, FLOW FORMATION,, CONDUCTING,, FLUID,, MACRO AND MICRO-CHANNELS