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MHD axisymmetric flow of third grade fluid between porous disks with heat transfer

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Applied Mathematics and Mechanics(English Edition) 2012年第6期33卷 749-764页

作者： T.HAYAT A.SHAFIQ M.NAWAZ A.ALSAEDI Department of Mathematics Quaid-i-Azam University Department of Humanities and Sciences Institute of Space Technology Department of Mathematics Faculty of ScienceKing Abdulaziz University

The magnetohydrodynamic （MHD） flow of the third grade fluid between two permeable disks with heat transfer is investigated. The governing partial differential equa- tions are converted into the ordinary differential equations by suitable transformations. The transformed equations are solved by the homotopy analysis method （HAM）. The expressions for square residual errors are defined, and the optimal values of convergence- control parameters are selected. The dimensionless velocity and temperature fields are examined for various dimensionless parameters. The skin friction coefficient and the Nus- selt number are tabulated to analyze the effects of dimensionless parameters.

关键词： heat transfer axisymmetric flow third grade fluid porous disk skin fric-tion coefficient Nusselt number

Peristaltic motion of third grade fluid in curved channel

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Applied Mathematics and Mechanics(English Edition) 2014年第1期35卷 73-84页

作者： S.HINA M.MUSTAFA T.HAYAT F.E.ALSAADI Department of Mathematical Sciences Fatima Jinnah Women University School of Natural Sciences (SNS) National University of Sciences and Technology (NUST) Department of Mathematics Quaid-i-Azam University Department of Electrical and Computer Engineering Faculty of Engineering

＂ Analysis is performed to study the slip effects on the peristaltic flow of non-Newtonian fluid in a curved channel with wall properties. The resulting nonlinear partial differential equations are transformed to a single ordinary differential equation in a stream function by using the assumptions of long wavelength and low Reynolds number. This differential equation is solved numerically by employing the built-in routine for solving nonlinear boundary value problems （BVPs） through the software Mathematica. In addition, the analytic solutions for small Deborah number are computed with a regular perturbation technique. It is noticed that the symmetry of bolus is destroyed in a curved channel. An intensification in the slip effect results in a larger magnitude of axial velocity. Further, the size and circulation of the trapped boluses increase with an increase in the slip parameter. Different from the case of planar channel, the axial velocity profiles are tilted towards the lower part of the channel. A comparative study between analytic and numerical solutions shows excellent agreement.

关键词： third grade fluid slip condition peristalsis curved channel mathematicalmodeling

Hydromagnetic rotating flow of third grade fluid

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Applied Mathematics and Mechanics(English Edition) 2013年第12期34卷 1481-1494页

作者： T.HAYAT R.NAZ A.ALSAEDI M.M.RASHIDI Department of Mathematics Quaid-i-Azam University Department of Mathematics King Abdulaziz University Geni Mecanique Universite de Sherbrooke

This work investigates the flow of a third grade fluid in a rotating frame of reference. The fluid is incompressible and magnetohydrodynamic （MHD）. The flow is bounded between two porous plates, the lower of which is shrinking linearly. Mathematical modelling of the considered flow leads to a nonlinear problem. The solution of this nonlinear problem is computed by the homotopy analysis method （HAM）. Graphs are presented to demonstrate the effect of several emerging parameters, which clearly describe the flow characteristics.

关键词： third grade fluid shrinking sheet rotating frame magnetohydrodynamic(MHD) flow

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Applied Mathematics and Mechanics(English Edition) 2004年第5期25卷 587-594页

作者： Muhammet Yürüsoy Department of Mechanical Education Faculty of Technical Education Ahmet Necdet Sezer Campus Afyon Kocatepe University

Two dimensional equations of steady motion for third order fluids are expressed in a special coordinate system generated by the potential flow corresponding to an inviscid fluid. For the inviscid flow around an arbitrary object, the streamlines are the phi-coordinates and velocity potential lines are psi-coordinates which form an orthogonal curvilinear set of coordinates. The outcome, boundary layer equations, is then shown to be independent of the body shape immersed into the flow. As a first approximation,assumption that second grade terms are negligible compared to viscous and third grade terms. Second grade terms spoil scaling transformation which is only transformation leading to similarity solutions for third grade fluid. By using Lie group methods,infinitesimal generators of boundary layer equations are calculated. The equations are transformed into an ordinary differential system. Numerical solutions of outcoming nonlinear differential equations are found by using combination of a Runge-Kutta algorithm and shooting technique.

关键词： boundary layer equation Lie group third grade fluid