A STUDY OF TIME DEPENDENT NATURAL CONVECTION FLOW IN A VERTICAL POROUS CHANNEL
A STUDY OF TIME DEPENDENT NATURAL CONVECTION FLOW IN A VERTICAL POROUS CHANNEL
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Date
2014-12
Authors
TAFIDA, Mohammed Kabir
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Abstract
The transient motion of a viscous incompressible
uid in vertical porous channel is rst anal-
ysed considering the e ect of transpiration and heat generation in the channel. In the second
part of the problem, natural convection
ow of an incompressible viscous
uid in a vertical
channel is analysed when the porous plates are subjected to isothermal and adiabatic condi-
tions. The governing equations are solved using the Laplace transform method. Due to the
di culties that are associated with the analytical inversion of the obtained results from the
Laplace to the time domain, the Riemann-Sum approach is employed to do the inversion,
thus obtaining the temperature, velocity, skin-friction and rate of heat transfer. To validate
the Riemann-sum approach used, the steady state solution for velocity and temperature are
obtained analytically. An excellent agreement is found between the steady state solutions and
the transient solutions at large values of time. From the course of investigation, it is revealed
that heat generation leads to an increase in heat transfer on the cold plate while it decreases
it on the heated plate.
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Description
IN PARTIAL FULFILMENT FOR THE AWARD
OF MASTER OF SCIENCE IN
MATHEMATICS
DEPARTMENT OF MATHEMATICS
AHMADU BELLO UNIVERSITY, ZARIA,
NIGERIA
DECEMBER, 2014
Keywords
TIME DEPENDENT,, NATURAL,, CONVECTION,, FLOW,, VERTICAL POROUS, CHANNEL.