Nabil T. M. Eldabe

Peristaltic transport in an asymmetric channel through a porous medium

The problem of peristaltic transport of an incompressible viscous fluid in an asymmetric channel through a porous medium is analyzed. The flow is investigated in a wave frame of reference moving with velocity of the wave under the assumptions of long-wavelength and low-Reynolds number. An explicit form of the stream function is obtained by using Adomian decomposition method. The analysis showed that transport phenomena are strongly dependent on the phase shift between the two walls of the channel. It is indicated that the axial velocity component U in fixed frame increases with increasing the permeability parameter. In the case of high permeability parameter (as K->~), our results are in agreement with Mishra and Ramachandra Rao [M. Mishra, A. Ramachandra Rao, Peristaltic transport of a Newtonian fluid in an asymmetric channel, ZAMP 53 (2003) 532] and Eytan and Elad [O. Eytan, D. Elad, Analysis of intra-uterine fluid motion induced by uterine contractions, Bull. Math. Biol. 61 (1999) 221]. The results given in this paper may throw some light on the fluid dynamic aspects of the intra-uterine fluid flow through a porous medium.

Effect of Couple Stresses on the MHD of a Non-Newtonian Unsteady Flow between Two Parallel Porous Plates

In this paper the MHD of a Non-Newtonian unsteady flow of an incompressible fluid under the effect of couple stresses and a uniform external magnetic field is analysed by using the Eyring Powell model. In the first approximation the solution is obtained by using the Mathematica computational program with assuming a pulsatile pressure gradient in the direction of the motion. In the second order approximation a numerical solution of the non-linear partial differential equation is obtained by using a finite difference method. The effects of different parameters are discussed with the help of graphs in the two cases.

Chebyshev finite difference method for heat and mass transfer in a hydromagnetic flow of a micropolar fluid past a stretching surface with Ohmic heating and viscous dissipation

Numerical solutions are obtained for the problem which involves both the heat and mass transfer in a hydromagnetic flow of a micropolar fluid past a stretching surface with Ohmic heating and viscous dissipation using Chebyshev finite difference method (ChFD). A similarity transformation was employed to change the governing momentum, angular momentum, energy, and concentration partial differential equations into ordinary ones. Numerical calculations have been carried out for various values of magnetic field parameter, material parameter, Prandtl number, Eckert number, Schmidt number, couple stress at the surface, local Nusselt number and Sherwood number. The numerical results indicate that the temperature and the concentration increase, while the velocities, the Nusselt number and the Sherwood number decrease with increasing magnetic field parameter. In all of the above results, the material parameter has the opposite effect of magnetic field parameter. The temperature increases with increasing Eckert number, and decreases with increasing Prandtl number. An increase in the Schmidt number gives an increase in the Sherwood number, or a decrease in the concentration.

Chebyshev finite difference method for MHD flow of a micropolar fluid past a stretching sheet with heat transfer

In this paper, the problem of heat transfer to MHD flow of a micropolar fluid from a stretching sheet with suction and blowing through a porous medium is studied numerically by using Chebyshev finite difference method (ChFD). A similarity solution to governing momentum, angular momentum and energy equations is derived. The effects of surface mass transfer, Prandtl number, magnetic field and porous medium on the velocities and temperature profiles have been studied. The numerical results indicate that, the velocity and the angular velocity increase as the permeability parameter increases but they decrease as the magnetic field increases. Also, the temperature decreases as the permeability parameter increases but it increases as the magnetic field increases.

Effect of couple stresses on pulsatile hydromagnetic poiseuille flow

An analytical study of unsteady magneto-hydrodynamic flow of an incompressible electrically conducting fluid filling the space between two parallel plates is presented, taking into account the couple stresses and pulsation of the pressure gradient effect. The solution of the problem is obtained with the help of perturbation technique. Analytical expression is given for the velocity field, and the effects of the various parameters entering into the problem are discussed with the help of graphs.

Heat and mass transfer in hydromagnetic flow of the non-Newtonian fluid with heat source over an accelerating surface through a porous medium

Abstract An analysis is made to determine the heat and mass transfer occurring in the hydromagnetic flow of the non-Newtonian fluid on a linearly accelerating surface with temperature-dependent heat source subject to suction or blowing. The results are expressed in terms of Kummers function in the case of a surface with prescribed wall temperature. Numerical calculations have been carried out for various values of Prandtl number Pr (0.71 for air), suction or blowing parameter m , temperature parameter r , heat flux parameter S and Schmidt number Sc .

Pulsatile Magnetohydrodynamic Viscoelastic Flow through a Channel Bounded by Two Permeable Parallel Plates.

Velocity profiles for unsteady pulsatile laminar flows of viscoelastic non-Newtonian conducting fluids through a channel have derived using the perturbation method. The induced magnetic field and wall shear have been obtained. The effects of pulsation, elasticity and the magnetic parameter on the velocity, induced magnetic field and wall shear are discussed. Results are illustrated numerically and graphically. It is found that amplitude of the pulsation increases the velocity distribution which would be obtained under steady flow conditions at the same mean pressure gradient. The effect of both the magnetic and elasticity parameters decrease the velocity distribution. Also the properties of the fluid on the induced magnetic field and the skin-friction are discussed.

Thermal-diffusion and diffusion-thermo effects on mixed free-forced convection and mass transfer boundary layer flow for non-Newtonian fluid with temperature dependent viscosity

A numerical study of the laminar mixed free-forced convection of non-Newtonian power law fluid with mass transfer is presented. The flow in boundary layer includes the temperature which dependent on viscosity with thermal-diffusion and diffusion-thermo effects. The equations of momentum, energy and concentration are solved numerically with the aid of the Chebyshev finite difference method. The computation is carried out for wide range of the various material parameters associated with the power law non-Newtonian fluid. The results indicate that all the flow, thermal and concentration fields depend on the material parameters of the problem. During the course of discussion, the skin-friction, the rate of heat and mass transfer are obtained and discussed numerically and illustrated graphically.

Effects of microwave heating on the thermal states of biological tissues

A mathematical analysis of microwave heating equations in one-dimensional multi-layer model has been discussed. Maxwells equations and transient bioheat transfer equation were numerically calculated by using finite difference method to predict the effects of thermal physical properties on the transient temperature of biological tissues. This prediction of the temperature evolution in biological bodies can be used as an effective tool for thermal diagnostics in medical practices.

The stability of plane Couette flow of a power-law fluid with viscous heating

Linear stability analysis is carried out to examine the effect of shear thinning and shear thickening on the stability of plane Couette flow with viscous heating for a power-law fluid that obeys Arrhenius-type law. The relation between shear stress and shear rate is plotted, and the maximum shear stress that must be applied to the system is calculated for different values of the power-law index n. The results showed that the S-shaped curve characterizing the fluid flow that obeys Arrhenius-type law appears at smaller values of the activation energy parameter β, in contrast to the Newtonian case, as a result of shear thinning effect. The resulting eigenvalues are calculated using the Chebyshev collocation method with the QZ algorithm {QZ algorithm is used in solving the singular generalized eigenvalue problem [SIAM J. Numer. Anal. 10, 241 (1973)]}. It is found, for shear thinning/thickening fluid, that the instability occurs at lower/higher values of the Brinkman number Br than in the Newtonian case. Also,...