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Unsteady three-dimensional MHD flow due to impulsive motion with heat and mass transfer past a stretching sheet in a saturated porous medium

Rajagopal K., Veena P. H., Pravin V. K.

International Journal of Applied Mechanics and Engineering

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2013

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Vol. 18, no. 1

137--151

EN

The development of velocity, temperature and concentration fields of an incompressible viscous electrically conducting fluid, caused by impulsive stretching of the surface in two lateral directions and by suddenly increasing the surface temperature from that of the surrounding fluid in a saturated porous medium is studied. The partial differential equations governing the unsteady laminar boundary layer flow are solved analytically. For some particular cases, closed form solutions are obtained, and for large values of the independent variable asymptotic solutions are found. The surface shear stress in x and y directions and the surface heat transfer and surface mass transfer increase with the magnetic parameter and with permeability parameter and the stretching ratio, and there is a smooth transition from the short-time solution to the long-time solution.

2

Free convective heat and mass transfer flow over a non-isothermal stretching sheet with added heat source and thermal diffusion in a saturated porous medium

Pravin V. K., Rajagopal K., Veena P. H., Umesh K. S.

International Journal of Applied Mechanics and Engineering

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2011

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Vol. 16, no 1

177-194

EN

The present paper deals with the study of MHD free convection and mass transfer flow of an incompressible viscous fluid past a continuously moving non-isothermal infinite vertical sheet in non-Darcy porous media in the presence of large suction under the influence of uniform magnetic field considering heat source and thermal diffusion with viscous dissipation, inertia term and stress work. Introducing the usual similarity transformations, the equations of momentum, energy and concentration are made linear. To obtain the solution of the problem, ordinary differential equations are solved analytically. The effects of various physical parameters such as the magnetic parameter, permeability parameter, inertia parameter, suction/blowing parameter on heat transfer characteristics are analysed. One of the important findings of our study is that of increasing the value of the inertia parameter k3 decreases the velocity profile and to increase the temperature profile.

3

Diffusion of chemically reactive species of an electrically conducting visco-elastic fluid immersed in a porous medium over a stretching sheet with prescribed surface concentration and prescribed wall mass flux

Rajagopal K., Veena P. H., Pravin V. K.

International Journal of Applied Mechanics and Engineering

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2008

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Vol. 13, no 2

457-472

EN

In this paper, we present a mathematical analysis of mass transfer phenomena in a magneto hydrodynamic visco-elastic fluid immersed in a porous medium with prescribed surface concentration and prescribed wall mass flux. The influence of reaction rate on the transfer of chemically reactive species is studied. The flow is caused solely by the linearly stretching sheet and the reactive species is emitted from this sheet and undergoes an isothermal and homogeneous one stage reaction as it diffuses into the surrounding fluid. Several non-dimensional similarity transformations are introduced to reduce the concentration conservation equation to an ordinary differential equation in both the cases. (PST and PHF). An exact analytical solution due to Siddappa and Abel (ZAMP 36, 1985) is adopted for velocity, whereas the concentration equation is solved analytically for first order reactions in both the PST and PHF cases. The computations showed that the effect of destructive chemical reaction is to reduce the thickness of the concentration boundary layer and increase the mass transfer rate from the sheet to the surrounding fluid in the presence of a transverse magnetic field. This effect is more effective for zero and first order reactions than for thesecond and higher order. The effect of various physical parameters are analysed in the PST and PHF cases. The effects of all these parameters on wall concentration gradient are also discussed.

4

Application of a constitutive equation for softening, yield and permanent deformation to finite plane simple shear

Huntley H., Wineman A., Rajagopal K.

Archives of Mechanics

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2000

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Vol. 52, nr 3

443-479

EN

The finite homogenous simple shear deformation of an incompressible material is considered. The response is modeled with a constitutive equation that reflects a continuous process of microstructural transformation as the deformation increases beyond a threshold value. The original and transformed portions of the material are both taken to respond as incompressible elastic solids. It is shown that the transformation can lead to softening of the response with increasing deformation and to a local maximum in the shear stress-shear strain curve. The existence of permanent deformation after release of the shearing traction is demonstrated. It is confirmed that a process of increasing deformation followed by decreasing deformation to the point of zero shear traction is a dissipative cycle. A special case is then considered in which both the original and transformed materials are assumed to respond as neo-Hookean solids. The critical volume fraction of transforming material at which the shear stress-shear strain curve loses monotonicity is found analytically. Representations are obtained for the dependence of the residual shear deformation on the fraction of transforming material; on the ratio of moduli of the original and transformed materials; and on the maximum shear reached before unloading.