Effects of heat and mass transfer on peristaltic flow of Williamson fluid in a non‐uniform channel with slip conditions

The combined influence of heat and mass transfer has been explored in a study of peristaltic transport of magnetohydrodynamic Williamson fluid in a non‐uniform channel with flexible walls. The slip conditions are paid due attention and long wavelength and small Reynolds number assumptions are adopted in the problem formulation. The obtained results are valid for small Weissenberg number. A detailed study of involved key parameters in the obtained solutions is made by the sketched graphs. Copyright © 2010 John Wiley & Sons, Ltd.     

Simulation of heat and mass transfer on peristaltic flow of hyperbolic tangent fluid in an asymmetric channel

In the present analysis, the influence of heat and mass transfer on the peristaltic flow of a hyperbolic tangent fluid in an asymmetric channel has been discussed. The highly nonlinear equations are simplified under lubrication approach. The perturbation and numerical solutions of the problem are not only discussed but the validity of the results is also being checked. The graphical results of the problem under discussion are also being brought under consideration to see the behavior of various physical parameters. Copyright © 2012 John Wiley & Sons, Ltd.     

Variable viscosity effects on the peristaltic motion of a third‐order fluid

The effect of variable viscosity on the peristaltic motion of MHD third‐order fluid in a channel is studied using slip condition. The series solution for stream function, longitudinal velocity and pressure gradient are first derived and then discussed in detail. The pressure rise and frictional forces are monitored through numerical integration. Copyright © 2010 John Wiley & Sons, Ltd.     

Effect of heat transfer on the flow of a second‐grade fluid in divergent/convergent channel

This paper studies the effects of a second‐grade fluid on the flow and heat transfer characteristics in a divergent/convergent channel. The momentum and energy equations are first given in a nondimensional form and then solved analytically using the method of homotopy analysis method. Convergence of derived series solutions is shown. Graphical results for the velocity and the temperatures are presented and discussed for various emerging parameters. Copyright © 2009 John Wiley & Sons, Ltd.     

Wall properties and heat transfer analysis of the peristaltic motion in a power‐law fluid

A mathematical analysis has been carried out to investigate the effect of elasticity of the flexible walls on the peristaltic flow of a power‐law fluid. The heat transfer analysis is further examined. Expressions of stream function, velocity, and temperature distributions are presented in closed form under long wavelength and low Reynolds number approximations. The effects of the various parameters entering into the mathematical analysis are sketched and discussed. Copyright © 2012 John Wiley & Sons, Ltd.     

Slip effects on the peristaltic flow of a Jeffrey fluid in an asymmetric channel under the effect of induced magnetic field

In the present study, we investigated the effects of slip and induced magnetic field on the peristaltic flow of a Jeffrey fluid in an asymmetric channel. The governing two‐dimensional equations for momentum, magnetic force function and energy are simplified by using the assumptions of long wavelength and low but finite Reynolds number. The reduced problem has been solved by Adomian decomposition method (ADM) and closed form solutions have been presented. Further, the exact solution of the proposed problem has also been computed and the mathematical comparison shows that both solutions are almost similar. The effects of pertinent parameters on the pressure rise per wavelength are investigated using numerical integration. The expressions for pressure rise, friction force, velocity, temperature, magnetic force function and the stream lines against various physical parameters of interest are shown graphically. Moreover, the behavior of different kinds of wave shape are also discussed. Copyright © 2009 John Wiley & Sons, Ltd.     

Mixed convective heat and mass transfer in a non-Newtonian fluid at a peristaltic surface with temperature-dependent viscosity

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.     

Slip and induced magnetic field effects on peristaltic transport of Johnson-Segalman fluid

The peristaltic flow of a Johnson-Segalman fluid in a planar channel is investigated in an induced magnetic field with the slip condition.The symmetric nature of the flow in a channel is utilized.The velocity slip condition in terms of shear stresses is considered.The mathematical formulation is presented,and the equations are solved under long wavelength and low Reynolds number approximations.The perturbation solutions are established for the pressure,the axial velocity,the micro-rotation component,the stream function,the magnetic-force function,the axial induced magnetic field,and the current distribution across the channel.The solution expressions for small Weissenberg numbers are derived.The flow quantities of interest are sketched and analyzed.     

Flow and heat transfer in a second grade fluid over a stretching sheet

An analysis is carried out to study the flow and heat transfer characteristics in a second grade fluid over a stretching sheet with prescribed surface temperature including the effects of frictional heating, internal heat generation or absorption, and work due to deformation. In order to solve the fourth-order non-linear differential equation, associated with the flow problem, a fourth boundary condition is augmented and a proper sign for the normal stress modulus is used. It is observed that for a physical flow problem the solution is unique. The solutions for the temperature and the heat transfer characteristics are obtained numerically and presented by a table and graphs. Furthermore, it is shown that the heat flow is always from the stretching sheet to the fluid.     

A note on flow and heat transfer of a viscoelastic fluid over a stretching sheet

This paper presents a study of the flow and heat transfer of an incompressible homogeneous second grade fluid past a stretching sheet. The governing partial differential equations are converted into ordinary differential equations by a similarity transformation. The effects of viscous dissipation and work due to deformation are considered in the energy equation and the variations of dimensionless surface temperature and dimensionless surface temperature gradient with various parameters are graphed and tabulated. Two cases are studied, namely, (i) the sheet with constant surface temperature (CST case) and (ii) the sheet with prescribed surface temperature (PST case).     

Peristaltic transport of fourth grade fluid with heat transfer and induced magnetic field

We investigate the influence of an induced magnetic field on the peristaltic flow of an incompressible fourth grade fluid in a symmetric channel with heat transfer. Adopting long wavelength, low Reynolds number and small Deborah number assumptions we derive the solutions for stream function, pressure gradient, temperature, magnetic force function, induced magnetic field and current density. Qualitative agreement is demonstrated between the graphs and expected observations.     

MHD peristaltic flow of a third order fluid in an asymmetric channel

This study is concerned with peristaltic flow of a magnetohydrodynamic (MHD) fluid in an asymmetric channel. Asymmetry in the flow is induced by waves on the channel walls having different amplitudes and phase. A systematic approach based on an expansion of Deborah number is used for the solution series. Analytic expressions have been developed for the stream function, axial velocity and axial pressure gradient. The pressure rise over a wavelength has been addressed through numerical integration. Particular attention has been given to the effects of Hartman number and Deborah number on the pressure rise over a wavelength and the trapping phenomenon. Several limiting solutions of interest are obtained as the special cases of the presented analysis by taking the appropriate parameter(s) to be zero. Copyright © 2009 John Wiley & Sons, Ltd.     

Magnetohydrodynamic peristaltic flow of a hyperbolic tangent fluid in a vertical asymmetric channel with heat transfer

In the present paper we discuss the magnetohydrodynamic (MHD) peristaltic flow of a hyperbolic tangent fluid model in a vertical asymmetric channel under a zero Reynolds number and long wavelength approximation. Exact solution of the temperature equation in the absence of dissipation term has been computed and the analytical ex- pression for stream function and axial pressure gradient are established. The flow is analyzed in a wave frame of reference moving with the velocity of wave. The expression for pressure rise has been computed numerically. The physical features of pertinent parameters are analyzed by plotting graphs and discussed in detail.     

Effects of induced magnetic field on peristaltic flow of Johnson-Segalman fluid in a vertical symmetric channel

In this paper, the influence of heat transfer and induced magnetic field on peristaltic flow of a Johnson-Segalman fluid is studied. The purpose of the present investigation is to study the effects of induced magnetic field on the peristaltic flow of non-Newtonian fluid. The two-dimensional equations of a Johnson-Segalman fluid are simplified by assuming a long wavelength and a low Reynolds number. The obtained equations are solved for the stream function, magnetic force function, and axial pressure gradient by using a regular perturbation method. The expressions for the pressure rise, temperature, induced magnetic field, pressure gradient, and stream function are sketched and interpreted for various embedded parameters.     

On flow of a fourth‐grade fluid with heat transfer

The influence of heat transfer on the steady flow of a fourth‐grade fluid between two stationary parallel porous plates is studied. The flow is engendered under the application of a constant pressure gradient. The concept of homotopy analysis method is utilized for the series solution of the governing problem. Numerical solution has been also carried out. In addition, both analytic and numerical solutions are compared. The variations of embedded parameters into the solution are predicted through the graphical representations. Copyright © 2010 John Wiley & Sons, Ltd.     

Effect of heat transfer on a third grade fluid in a flat channel

The heat transfer analysis on the laminar flow of an incompressible third grade fluid through a porous flat channel is examined. The lower plate is assumed to be at a higher temperature than the upper plate. Analytical solution for temperature distribution is obtained for various values of the controlling parameters and discussed. The obtained analytical solution is also compared with the numerical solution. The comparison shows the fact that the accuracy is remarkable. Copyright © 2009 John Wiley & Sons, Ltd.     

Heat transfer on peristaltic flow of fourth grade fluid in inclined asymmetric channel with partial slip

In this paper, the effects of slip and heat transfer are studied on the peristaltic transport of a magnetohydrodynamic (MHD) fourth grade fluid. The governing equations are modeled and solved under the long wavelength approximation by using a regular perturbation method. Explicit expressions of solutions for the stream function, the velocity, the pressure gradient, the temperature, and the heat transfer coefficient are presented. Pumping and trapping phenomena are analyzed for increasing the slip parameter. Further, the temperature profiles and the heat transfer coefficient are observed for various increasing parameters. It is found that these parameters considerably affect the considered flow characteristics. Comparisons with published results for the no-slip case are found in close agreement.     

Mixed convection effects on heat and mass transfer in a non Newtonian fluid with chemical reaction over a vertical plate

This paper studies mixed convection, double dispersion and chemical reaction effects on heat and mass transfer in a non-Darcy non-Newtonian fluid over a vertical surface in a porous medium under the constant temperature and concentration. The governing boundary layer equations, namely, momentum, energy and concentration, are converted to ordinary differential equations by introducing similarity variables and then are solved numerically by means of fourth-order Runge-Kutta method coupled with double-shooting technique. The velocity, temperature concentration, heat and mass transfer profiles are presented graphically for various values of the parameters, and the influence of viscosity index n, thermal and solute dispersion, chemical reaction parameter χ are observed.     

Modeling of heat and mass transfer in a hydrocarbon fluid under inductive heating

Results of numerical simulations of the thermal action on a high-viscosity hydrocarbon fluid with temperature-dependent viscosity and thermal conductivity are presented. A system of equations of thermal convection in the Boussinesq approximation is used as the constitutive equations to describe the convection of the hydrocarbon fluid. The dynamics of the temperature field and convective structures in the fluid is studied. The spatial motion of the fluid is found to be locally nonuniform; the motion is accompanied by vortex flows; as a result, two regions with significantly different temperatures are formed in the medium. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 1, pp. 95–100, January–February, 2009.     

Influence of heat and mass transfer on a peristaltic motion of a Jeffrey-six constant fluid in an annulus

In the present investigation we have studied the combined heat and mass transfer effects on the peristaltic flow of non-Newtonian fluid. The governing equations are simplified under the assumptions of longwave length low Reynold’s number approximation. The resulting highly nonlinear equations are solved analytically and numerically. At the end the numerical results are discussed pictorially for various emerging parameters of interest.