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Hameed M.,University of South Carolina | Khan A.A.,IIUI | Ellahi R.,IIUI | Ellahi R.,University of California at Riverside | Raza M.,IIUI
Engineering Science and Technology, an International Journal | Year: 2015

This study is concerned with the peristaltic flow of the fractional second grade fluid confined in a cylindrical tube. The effects of magnetic field in the presence of heat transfer are taken into account. Mathematical modeling is based upon continuity, momentum and energy equations. This analysis is carried out under the constraints of long wavelength (0 << λ → ∞) and low Reynolds number (Re → 0). Closed form solutions for velocity, temperature field and pressure gradient are obtained. Numerical integration is used to analyze the novel features of pressure rise and friction force. Effects of pertinent parameters such as Hartmann number M, heat source/sink parameter β, Grashof number Gr, material constant λ1, pressure rise ΔP and friction force F alone with Reynolds number Re and Prandtl number Pr are discussed through graphs. It is found that an increase in constant of fractional second grade fluid results in the decrease of velocity profile for the case of fractional second grade fluid whereas the velocity remains unchanged for the case of second grade fluid. It is also observed that the absolute value of heat transfer coefficient increases with an increase in β and aspect ratio φ. It is due to the fact that the nature of heat transfer is oscillatory which is accordance with the physical expectation due to oscillatory nature of the tube wall. It is perceived that with an increase in Hartmann number, the velocity decreases. A suitable comparison has been made with the prior results in the literature as a limiting case of the considered problem, for instance, fractional second grade fluid model reduces to second grade models for α1 = 1 and classical Naiver Stokes fluid model can be deduced from this as a special case by taking λ¯1=0. © 2015 Karabuk University


Ellahi R.,IIUI | Rahman S.U.,IIUI | Nadeem S.,Quaid-i-Azam University | Vafai K.,University of California at Riverside
Applied Mathematics and Information Sciences | Year: 2014

The unsteady and incompressible flow of non-Newtonian fluid through composite stenosis is investigated in the present study. The micropolar fluid is treated as a blood flow model. Mild stenosis and slip velocity are also taken into account. The governing equations are given in cylindrical coordinates system. Analytic solutions of velocity and volumetric flow flux are developed interms of modified Bessel functions. The expressions for the impedance (flow resistance) λ, the wall shear stress distribution in the stenotic region Tw and the shearing stress at the stenosis throat Ts are also given. Impact of involved pertinent parameters is sketched and examined by the resistance of impedance and shear stress. The stream lines are also made for different sundry parameters. © 2014 NSP Natural Sciences Publishing Cor.


Ellahi R.,IIUI | Ellahi R.,University of California at Riverside | Shivanian E.,Imam Khomeini International University | Abbasbandy S.,Imam Khomeini International University | And 2 more authors.
International Journal of Numerical Methods for Heat and Fluid Flow | Year: 2016

Purpose-The purpose of this paper is to study the generalized Couette flow of Eyring-Powell fluid. The paper aims to discuss diverse issues befell for the heat transfer, magnetohydrodynamics and slip. Design/methodology/approach-A hybrid technique based on pseudo-spectral collocation is applied for the solution of nonlinear resulting system. Findings-Viscous fluid results which are yet not available can be taken as a limiting case of presented problem. The results for the case of Hartmann flow can be obtained as a special case when plate velocity is zero, i.e. pressure gradient induced flow. The results for the zero fluid slip and no thermal slip also become special cases of this work, and the results can be recovered by setting, and to zero. These solutions are valid not only for small but also for large values of all emerging parameters. Originality/value-This model is investigated for the first time, as the authors know. © 2016 Emerald Group Publishing Limited.


Zeeshan A.,IIUI | Ellahi R.,IIUI | Ellahi R.,University of California | Hassan M.,University of California
European Physical Journal Plus | Year: 2014

In this study, the natural convection boundary layer flow along with inverted cone, magnetic and heat generation on water and ethylene glycol based nanofluids is considered by means of variable wall temperature. Porous medium is also taken into account. The physical problem is first modeled and then the governing equations are transformed into nonlinear ordinary differential equations under the assumptions of the Boussinesq approximation. Analytical solutions of nonlinear coupled equations are obtained by the homotopy analysis method. Correlation of skin friction and heat transfer rate corresponding to active parameters is also presented. Obtained results are illustrated by graphs and tables in order to see the effects of physical parameters. © 2014, Società Italiana di Fisica and Springer-Verlag Berlin Heidelberg.


Vafai K.,University of California Riverside | Khan A.A.,IIUI | Sajjad S.,IIUI | Ellahi R.,University of California Riverside
Zeitschrift fur Naturforschung - Section A Journal of Physical Sciences | Year: 2015

This article is concerned with the peristaltic pumping of an incompressible, electrically conducting third grade fluid in a uniform channel. The Hall effect under the influence of wall properties and heat transfer is taken into account. Mathematical modelling is based upon continuity, momentum, and energy equations. Closed form solutions for velocity, temperature, concentration, and heat transfer coefficient are obtained. Effects of pertinent parameters, such as third grade parameter Γ, Hall parameter M, amplitude ratio ε, Brickman number Br, Soret number Sc, wall tension E1 and elasticity parameters E2 and E3 on the velocity u, temperature θ, concentration ϕ, and heat transfer coefficient Z, are discussed through graphs.


Ellahi R.,IIUI | Hayat T.,Quaid-i-Azam University | Hayat T.,King Saud University | Mahomed F.M.,University of Witwatersrand
Zeitschrift fur Naturforschung - Section A Journal of Physical Sciences | Year: 2010

The present note investigates the influence of slip on the generalized Couette flows of a third-grade fluid. Two flow problems are considered. The resulting equations and the boundary conditions are nonlinear. Analytical solutions of the governing nonlinear problems are found in closed form. © 2010 Verlag der Zeitschrift für Naturforschung, Tübingen.

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