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Some exact solutions of the oscillatory motion of a generalized second grade fluid in an annular region of two cylinders

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Acta Mechanica Sinica 2010年第4期26卷 541-550页

作者： A.Mahmood c.fetecau N.A.Khan M.Jamil Department of Mathematics COMSATS Institute of Information Technology Department of Mathematics Technical University of Iasi Department of Mathematics University of Karachi Abdus Salam School of Mathematical Sciences GC University

The velocity field and the associated shear stress corresponding to the longitudinal oscillatory flow of a generalized second grade fluid, between two infinite coaxial circular cylinders, are determined by means of the Laplace and Hankel transforms. Initially, the fluid and cylinders are at rest and at t = 0＋ both cylinders suddenly begin to oscillate along their common axis with simple harmonic motions having angular frequencies Ω1 and Ω2. The solutions that have been obtained are presented under integral and series forms in terms of the generalized G and R functions and satisfy the governing differential equation and all imposed initial and boundary conditions. The respective solutions for the motion between the cylinders, when one of them is at rest, can be obtained from our general solutions. Furthermore, the corresponding solutions for the similar flow of ordinary second grade fluid and Newtonian fluid are also obtained as limiting cases of our general solutions. At the end, the effect of different parameters on the flow of ordinary second grade and generalized second grade fluid are investigated graphically by plotting velocity profiles.

关键词： Generalized second grade fluid Velocity field Shear stress Longitudinal oscillatory flow Laplace and Hankel transforms

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Non-axisymmetric Homann stagnation-point flow of Walter’s B nanofluid over a cylindrical disk

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Applied Mathematics and Mechanics(English Edition) 2020年第5期41卷 725-740页

作者： M.KHAN M.SARFRAZ J.AHMED L.AHMAD c.fetecau Department of Mathematics Quaid-i-Azam UniversityTaxila 47050Pakistan Department of Basic Sciences University of Engineering and TechnologySheringal Upper Dir 18000Pakistan Department of Mathematics Shaheed Benazir Bhutto UniversitySheringal Upper Dir 18000Pakistan Academy of Romanian Scientists Bucuresti 050094Romania

The study of non-axisymmetric Homann stagnation-point flow of Walter’s B nanofluid along with magnetohydrodynamic(MHD) and non-linear Rosseland thermal radiation over a cylindrical disk in the existence of the time-independent free stream is considered. Moreover, the notable impacts of thermophoresis and Brownian motion are analyzed by Buongiorno’s model. The momentum, energy, and concentration equations are converted into the dimensionless coupled ordinary differential equations via similarity transformations, which are later numerically solved by altering the values of the pertinent parameters. The numerical and asymptotic solutions for the large shear-to-strain rate ratio γ =a/bfor the parameters of the displacement thicknesses and the wall-shear stress are computed by perturbative expansion and analyzed. Furthermore, the technique bvp4c in MATLAB is deployed as an efficient method to analyze the calculations for the non-dimensional velocities, temperature, displacement thickness, and concentration profiles. It is observed that the two-dimensional displacement thickness parameters α andβ are reduced due to the viscoelasticity and magnetic field effects. Moreover, when the shear-to-strain rate ratio approaches infinity, α is closer to its asymptotic value, while βand the three-dimensional displacement thickness parameter δ1 show the opposite *** outcomes of the viscoelasticity and the magnetic field on the skin friction are also determined. It is concluded that ■ reaches its asymptotic behavior when the shearto-strain rate ratio approaches infinity. Meanwhile, ■ shows different results.

关键词： Walter’s B fluid cylindrical disk nanofluid magnetic field non-linear thermal radiation stagnation-point flow

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Peristaltic Flow of couple Stress Fluid in a Non-Uniform Rectangular Duct Having compliant Walls

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communications in Theoretical Physics 2016年第1期65卷 66-72页

作者： R.Ellahi M.Mubashir Bhatti c.fetecau K.Vafai Department of Mechanical Engineering University of California Riverside Riverside USA Department of Mathematics and Statistics FBAS IIUI Islamabad Pakistan Shanghai Institute of Applied Mathematics and Mechanics Shanghai University Shanghai 200444 China Department of Mathematics Technical University of Iasi Romania Academy of Romanian Scientists 050094 Bucuresti Romania

The present study investigates the peristaltic flow of couple stress fluid in a non-uniform rectangular duct with compliant *** modeling is based upon the laws of mass and linear *** solutions are carried out by the eigen function expansion method under long-wavelength and low-Reynolds number *** features of the flow characteristics are analyzed by plotting the graphs of various values of physical parameters of *** bolus scheme is also presented through streamlines.

关键词： peristaltic flow couple stress fluid compliant walls eigen function expansion method analyticalsolutions

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