Farhad Ali

Closed form solutions for unsteady free convection flow of a second grade fluid over an oscillating vertical plate.

Closed form solutions for unsteady free convection flows of a second grade fluid near an isothermal vertical plate oscillating in its plane using the Laplace transform technique are established. Expressions for velocity and temperature are obtained and displayed graphically for different values of Prandtl number Pr, thermal Grashof number Gr, viscoelastic parameter α, phase angle ωτ and time τ. Numerical values of skin friction τ 0 and Nusselt number Nu are shown in tables. Some well-known solutions in literature are reduced as the limiting cases of the present solutions.

MHD Free Convection Flow in a Porous Medium with Thermal Diffusion and Ramped Wall Temperature

An exact analysis is presented to study the unsteady magnetohydrodynamic flow past an impulsively started vertical plate embedded in a porous medium in the presence of thermal diffusion and ramped wall temperature at the plate. The analytical expressions for velocity, temperature and concentration fields are obtained using the Laplace transform technique. The results for skin friction, Nusselt number and Sherwood number are also developed. The analytical results are displayed graphically and discussed.

A modern approach of Caputo–Fabrizio time-fractional derivative to MHD free convection flow of generalized second-grade fluid in a porous medium

The present analysis represents the concept of the Caputo–Fabrizio derivatives of fractional order to MHD flow of a second-grade fluid together with radiative heat transfer. The fluid flow is subjected to an infinite oscillating vertical plate embedded in a saturated porous media. The fluid starts motion due to an oscillating boundary and temperature difference between the plate and the fluid. The problem is modeled in terms of partial differential equations, which consist of momentum equation and heat equation. The Laplace transform method is used to obtain the closed-form solutions for velocity and temperature profiles. In order to understand the physics of the problem under consideration, numerical results are obtained using Mathcad software and brought into light through graphical representations. The influence of various physical parameters is studied and displayed in various figures. The corresponding skin friction coefficient and Nusselt number are provided in tables. A graphical comparison is provided showing a strong agreement with the published results in the open literature.

Effects of wall shear stress on unsteady MHD conjugate flow in a porous medium with ramped wall temperature

This study investigates the effects of an arbitrary wall shear stress on unsteady magnetohydrodynamic (MHD) flow of a Newtonian fluid with conjugate effects of heat and mass transfer. The fluid is considered in a porous medium over a vertical plate with ramped temperature. The influence of thermal radiation in the energy equations is also considered. The coupled partial differential equations governing the flow are solved by using the Laplace transform technique. Exact solutions for velocity and temperature in case of both ramped and constant wall temperature as well as for concentration are obtained. It is found that velocity solutions are more general and can produce a huge number of exact solutions correlative to various fluid motions. Graphical results are provided for various embedded flow parameters and discussed in details.

Unsteady magnetohydrodynamic oscillatory flow of viscoelastic fluids in a porous channel with heat and mass transfer

In this paper, we analyze the effects of slip condition on the unsteady magnetohydrodynamic (MHD) flow of incompressible viscoelastic fluids in a porous channel under the influence of transverse magnetic field and Hall current with heat and mass transfer. The channel flow is induced due to external pressure gradient of oscillatory form. The governing equations for the velocity field, temperature and concentration distributions, are solved using perturbation technique. We present the results for skin friction, Nusselt number and Sherwood number. The numerical results are also computed for skin friction in tabular form. The effects of various indispensable flow parameters are displayed using several graphs. The numerical results show the effects of the physical parameters on the fluid flow as well as on heat and mass transfer and skin friction. The solutions for Newtonian fluids can be obtained as a limiting case from our general solutions when the viscoelastic parameter is zero.

Effects of Wall Shear Stress on MHD Conjugate Flow over an Inclined Plate in a Porous Medium with Ramped Wall Temperature

This study investigates the effects of an arbitrary wall shear stress on unsteady magnetohydrodynamic (MHD) flow of a Newtonian fluid with conjugate effects of heat and mass transfer. The fluid is considered in a porous medium over an inclined plate with ramped temperature. The influence of thermal radiation in the energy equations is also considered. The coupled partial differential equations governing the flow are solved by using the Laplace transform technique. Exact solutions for velocity and temperature in case of both ramped and constant wall temperature as well as for concentration fields are obtained. It is found that velocity solutions are more general and can produce a huge number of exact solutions correlative to various fluid motions. Graphical results are provided for various embedded flow parameters and discussed in detail.

Conjugate Effects of Heat and Mass Transfer on MHD Free Convection Flow over an Inclined Plate Embedded in a Porous Medium

The aim of this study is to present an exact analysis of combined effects of radiation and chemical reaction on the magnetohydrodynamic (MHD) free convection flow of an electrically conducting incompressible viscous fluid over an inclined plate embedded in a porous medium. The impulsively started plate with variable temperature and mass diffusion is considered. The dimensionless momentum equation coupled with the energy and mass diffusion equations are analytically solved using the Laplace transform method. Expressions for velocity, temperature and concentration fields are obtained. They satisfy all imposed initial and boundary conditions and can be reduced, as special cases, to some known solutions from the literature. Expressions for skin friction, Nusselt number and Sherwood number are also obtained. Finally, the effects of pertinent parameters on velocity, temperature and concentration profiles are graphically displayed whereas the variations in skin friction, Nusselt number and Sherwood number are shown through tables.

Heat and Mass Transfer with Free Convection MHD Flow Past a Vertical Plate Embedded in a Porous Medium

An analysis to investigate the combined effects of heat and mass transfer on free convection unsteady magnetohydrodynamic (MHD) flow of viscous fluid embedded in a porous medium is presented. The flow in the fluid is induced due to uniform motion of the plate. The dimensionless coupled linear partial differential equations are solved by using Laplace transform method. The solutions that have been obtained are expressed in simple forms in terms of elementary function and complementary error function . They satisfy the governing equations; all imposed initial and boundary conditions and can immediately be reduced to their limiting solutions. The influence of various embedded flow parameters such as the Hartmann number, permeability parameter, Grashof number, dimensionless time, Prandtl number, chemical reaction parameter, Schmidt number, and Soret number is analyzed graphically. Numerical solutions for skin friction, Nusselt number, and Sherwood number are also obtained in tabular forms.

A note on new exact solutions for some unsteady flows of brinkman-type fluids over a plane wall

Flows of a Brinkman fluid due to a plane boundary moving in its plane are studied using Laplace transform. The solutions that have been obtained for the velocity are presented in simple forms in terms of the complementary error function erfc(.). They satisfy all imposed initial and boundary conditions and can easily be reduced to the similar solutions for Newtonian fluids

Effects of Hall Current and Mass Transfer on the Unsteady Magnetohydrodynamic Flow in a Porous Channel

The combined effects of Hall current and mass transfer on the unsteady magnetohydrodynamic (MHD) flow of a viscous fluid passing through a porous channel have been investigated. The flow in the fluid has been induced due to external pressure gradient. The closed form analytical solutions have been obtained for the velocity, temperature and concentration fields. The analytical expressions for non-dimensional Skin-friction, Nusselt number and Sherwood number have been computed. The influence of various embedded flow parameters have been analyzed through graphs. The solutions obtained show that the influence of Hall parameter and mass transfer phenomenon give some interesting results. It is found that the Hall parameter have an increasing effect on the fluid velocity and approaches to the steady state as the time parameter is increased. The fluid concentration is increased for larger values of Peclet and Schmidt numbers whereas decreased with increase in Soret number and time parameter.