We investigate the problem of the unsteady mixed convection peristaltic mechanism. The flow includes a temperature-dependent viscosity with thermal diffusion and diffusion-thermo effects. The peristaltic flow is between two vertical walls, one of which is deformed in the shape of traveling transversal waves exactly like peristaltic pumping and the other of which is a parallel flat plate wall. The equations of momentum, energy, and concentration are subject to a set of appropriate boundary conditions by assuming that the solution consists of two parts: a mean part and a perturbed part. The solution of the perturbed part has been obtained by using the long-wave approximation. The mean part has been solved and coincides with the approximation of Ostrach. The mean part (zeroth order), the first order, and the total solution of the problem have been evaluated numerically for several sets of values of the parameters entering the problem. The skin friction, and the rate of heat and mass transfer at the walls are obtained and illustrated graphically.
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. In [4] an unsteady MHD non-Newtonian flow between two parallel fixed porous walls was studied using the Eyring Powell model [5], and in first approximation an exact solution of the velocity distribution was obtained if the pressure gradient in the direction of the motion is an arbitrary function of time. In second approximation a numerical solution was obtained when the pressure gradient is constant. A non-0932-0784 / 03 / 0400-0204 $ 06.00 c 2003 Verlag der Zeitschrift für Naturforschung, Tübingen · http://znaturforsch.com Newtonian fluid flow between two parallel walls, one of them moving with a uniform velocity under the action of a transverse magnetic field, was studied in [6].The present paper treats the flow of a pulsatile nonNewtonian incompressible and electrically conducting fluid in a magnetic field. Possible applications of these calculations are the flow of oil under ground, where there is a natural magnetic field and the earth is considered as a porous solid, and the motion of blood through arteries where the boundaries are porous.Couple stresses are the consequence of assuming that the mechanical action of one part of a body on another across a surface is equivalent to a force and moment distribution. In the classical nonpolar theory, moment distributions are not considered and the mechanical action is assumed to be equivalent to a force distribution only. The state of stress is measured by a stress tensor τ i j and a couple stress tensor M i j . The purpose of the present paper is to investigate the effect of couple stresses on the flow by obtaining the effect of the couple stress parameter besides other parameters entering the problem on the velocity distribution. The field equations are [7]:The continuity equationρ + ρv i,i = 0, Cauchy's first law of motion ρa i = T ji, j + ρ f i , and Cauchy's second law of motion M ji, j + ρ i + e i jk T jk = 0, where ρ is the density of the fluid, v i are the velocity components, a i the components of the acceleration, T i j is the second order stress tensor, M i j the second order couple stress tensor, f i the body force per unit volume, i the body Unauthenticated Download Date | 5/11/18 6:27 AM
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