Abstract: The mixed convective flow of MHD incompressible, steady boundary layer in heat transfer over a curved stretching sheet due to temperature dependent thermal conductivity is studied. We use curvilinear coordinate system in order to describe the governing flow equations. Finite difference solutions with central differencing have been used to solve the transform governing equations. Numerical results for the flow velocity and temperature profiles are presented as a function of the non-dimensional curvature radius. Skin friction coefficient and local Nusselt number at the surface of the curved sheet are discussed as well.
Abstract: Exact solution of an unsteady MHD flow of elasticoviscous
fluid through a porous media in a tube of elliptic cross
section under the influence of magnetic field and constant pressure
gradient has been obtained in this paper. Initially, the flow is
generated by a constant pressure gradient. After attaining the steady
state, the pressure gradient is suddenly withdrawn and the resulting
fluid motion in a tube of elliptical cross section by taking into
account of the porosity factor and magnetic parameter of the
bounding surface is investigated. The problem is solved in two-stages
the first stage is a steady motion in tube under the influence of a
constant pressure gradient, the second stage concern with an unsteady
motion. The problem is solved employing separation of variables
technique. The results are expressed in terms of a non-dimensional
porosity parameter, magnetic parameter and elastico-viscosity
parameter, which depends on the Non-Newtonian coefficient. The
flow parameters are found to be identical with that of Newtonian case
as elastic-viscosity parameter, magnetic parameter tends to zero, and
porosity tends to infinity. The numerical results were simulated in
MATLAB software to analyze the effect of Elastico-viscous
parameter, porosity parameter, and magnetic parameter on velocity
profile. Boundary conditions were satisfied. It is seen that the effect
of elastico-viscosity parameter, porosity parameter and magnetic
parameter of the bounding surface has significant effect on the
velocity parameter.
Abstract: MHD chemically reacting viscous fluid flow towards
a vertical surface with slip and convective boundary conditions has
been conducted. The temperature and the chemical species
concentration of the surface and the velocity of the external flow are
assumed to vary linearly with the distance from the vertical surface.
The governing differential equations are modeled and transformed
into systems of ordinary differential equations, which are then solved
numerically by a shooting method. The effects of various parameters
on the heat and mass transfer characteristics are discussed. Graphical
results are presented for the velocity, temperature, and concentration
profiles whilst the skin-friction coefficient and the rate of heat and
mass transfers near the surface are presented in tables and discussed.
The results revealed that increasing the strength of the magnetic field
increases the skin-friction coefficient and the rate of heat and mass
transfers toward the surface. The velocity profiles are increased
towards the surface due to the presence of the Lorenz force, which
attracts the fluid particles near the surface. The rate of chemical
reaction is seen to decrease the concentration boundary layer near the
surface due to the destructive chemical reaction occurring near the
surface.
Abstract: Exact solution of an unsteady MHD flow of elasticoviscous
fluid through a porous media in a tube of spherical cross
section under the influence of magnetic field and constant pressure
gradient has been obtained in this paper. Initially, the flow is
generated by a constant pressure gradient. After attaining the steady
state, the pressure gradient is suddenly withdrawn and the resulting
fluid motion in a tube of spherical cross section by taking into
account of the porosity factor and magnetic parameter of the
bounding surface is investigated. The problem is solved in two-stages
the first stage is a steady motion in tube under the influence of a
constant pressure gradient, the second stage concern with an unsteady
motion. The problem is solved employing separation of variables
technique. The results are expressed in terms of a non-dimensional
porosity parameter (K), magnetic parameter (m) and elasticoviscosity
parameter (β), which depends on the Non-Newtonian
coefficient. The flow parameters are found to be identical with that of
Newtonian case as elastic-viscosity parameter and magnetic
parameter tends to zero and porosity tends to infinity. It is seen that
the effect of elastico-viscosity parameter, porosity parameter and
magnetic parameter of the bounding surface has significant effect on
the velocity parameter.
Abstract: The convective heat and mass transfer in nanofluid
flow through a porous media due to a permeable stretching sheet with
magnetic field, viscous dissipation, chemical reaction and Soret
effects are numerically investigated. Two types of nanofluids, namely
Cu-water and Ag-water were studied. The governing boundary layer
equations are formulated and reduced to a set of ordinary differential
equations using similarity transformations and then solved
numerically using the Keller box method. Numerical results are
obtained for the skin friction coefficient, Nusselt number and
Sherwood number as well as for the velocity, temperature and
concentration profiles for selected values of the governing
parameters. Excellent validation of the present numerical results has
been achieved with the earlier linearly stretching sheet problems in
the literature.
Abstract: In this paper, we have investigated the free convection MHD flow due to heat and mass transfer through porous medium bounded by an infinite vertical non-conducting porous plate with time dependent suction under the influence of uniform transverse magnetic field of strength H0. When Temperature (T) and Concentration (C) at the plate is oscillatory with time about a constant non-zero mean. The velocity distribution, the temperature distribution, co-efficient of skin friction and role of heat transfer is investigated. Here the partial differential equations are involved. Exact solution is not possible so approximate solution is obtained and various graphs are plotted.
Abstract: The problem of magnetohydrodynamics boundary layer flow and heat transfer on a permeable stretching surface in a second grade nanofluid under the effect of heat generation and partial slip is studied theoretically. The Brownian motion and thermophoresis effects are also considered. The boundary layer equations governed by the PDE’s are transformed into a set of ODE’s with the help of local similarity transformations. The differential equations are solved by variational finite element method. The effects of different controlling parameters on the flow field and heat transfer characteristics are examined. The numerical results for the dimensionless velocity, temperature and nanoparticle volume fraction as well as the reduced Nusselt and Sherwood number have been presented graphically. The comparison confirmed excellent agreement. The present study is of great interest in coating and suspensions, cooling of metallic plate, oils and grease, paper production, coal water or coal-oil slurries, heat exchangers technology, materials processing exploiting.
Abstract: In this paper, the problem of heat and mass transfer in unsteady MHD boundary-layer flow of nanofluids over stretching sheet with a non uniform heat source/sink is considered. The unsteadiness in the flow and temperature is caused by the time-dependent stretching velocity and surface temperature. The unsteady boundary layer equations are transformed to a system of non-linear ordinary differential equations and solved numerically using Keller box method. The velocity, temperature, and concentration profiles were obtained and utilized to compute the skin-friction coefficient, local Nusselt number, and local Sherwood number for different values of the governing parameters viz. solid volume fraction parameter, unsteadiness parameter, magnetic field parameter, Schmidt number, space-dependent and temperature-dependent parameters for heat source/sink. A comparison of the numerical results of the present study with previously published data revealed an excellent agreement.
Abstract: An unsteady mixed free convection MHD flow of elastic-viscous incompressible fluid past an infinite vertical porous flat plate is investigated when the presence of heat Source/sink, temperature and concentration are assumed to be oscillating with time and hall effect. The governing equations are solved by complex variable technique. The expressions for the velocity field, temperature field and species concentration are demonstrated in graphs. The effects of the Prandtl number, the Grashof number, modified Grashof number, the Schimidt number, the Hall parameter, Elastic parameter & Magnetic parameter are discussed.
Abstract: In the present study, a numerical analysis is carried
out to investigate unsteady MHD (magneto-hydrodynamic) flow and
heat transfer of a non-Newtonian second grade viscoelastic fluid
over an oscillatory stretching sheet. The flow is induced due to an
infinite elastic sheet which is stretched oscillatory (back and forth) in
its own plane. Effect of viscous dissipation and joule heating are
taken into account. The non-linear differential equations governing
the problem are transformed into system of non-dimensional
differential equations using similarity transformations. A newly
developed meshfree numerical technique Element free Galerkin
method (EFGM) is employed to solve the coupled non linear
differential equations. The results illustrating the effect of various
parameters like viscoelastic parameter, Hartman number, relative
frequency amplitude of the oscillatory sheet to the stretching rate and
Eckert number on velocity and temperature field are reported in
terms of graphs and tables. The present model finds its application in
polymer extrusion, drawing of plastic films and wires, glass, fiber
and paper production etc.
Abstract: Unsteady magnetohydrodynamics (MHD) boundary
layer flow and heat transfer over a continuously stretching surface in
the presence of radiation is examined. By similarity transformation,
the governing partial differential equations are transformed to a set of
ordinary differential equations. Numerical solutions are obtained by
employing the Runge-Kutta-Fehlberg method scheme with shooting
technique in Maple software environment. The effects of
unsteadiness parameter, radiation parameter, magnetic parameter and
Prandtl number on the heat transfer characteristics are obtained and
discussed. It is found that the heat transfer rate at the surface
increases as the Prandtl number and unsteadiness parameter increase
but decreases with magnetic and radiation parameter.
Abstract: The hydromagnetic flow of a Maxwell fluid past a vertical stretching sheet with thermophoresis is considered. The impact of chemical reaction species to the flow is analyzed for the first time by using the homotopy analysis method (HAM). The h-curves for the flow boundary layer equations are presented graphically. Several values of wall skin friction, heat and mass transfer are obtained and discussed.