Two-dimensional, unsteady, laminar equations of motions of an incompressible fluid with variable viscosity are considered. The problem investigated is the flow for which the vorticity distribution is proportional to the stream function perturbed by a generalized uniform stream making an angle with the positive x-axis. Employing transformation variables, the goveming Navier-Stocks Equations (NSE) are transformed into steady state equations and then simple ordinary differential equations and a class of exact solutions are obtained. Several graphs of physical interest of streamline are also displayed and discussed.
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The flow of a second grade fluid past a porous plate has been studied using a modified model of second grade fluid that has shear dependent viscosity and can predict the normal stress difference. The boundary value problem subject to two different sets of boundary conditions is investigated. In the first instance, we consider that the plate is at temperature higher than the fluid. The second case deals with the analysis of an insulated plate. The differential equations governing the flow are solved using the homotopy analysis method (HAM). Expressions for velocity and temperature profiles are plotted and discussed.
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This paper investigates the propagation of plane waves as well as their reflection and transmission from the plane interface which separates a viscous liquid half space and a magneto elastic solid semi infinite medium containing a distribution of void pores. From the analysis of the propagation of plane waves in a magneto elastic solid medium with voids, it is found that the longitudinal wave in a void solid medium is subject to dispersion of the general wave form. In this case, short wave and long wave approximations have been made. A 'cut of frequency', which depends upon the void parameter, exists below which one of the longitudinal waves cannot propagate at all. Amplitude and energy ratios of various reflected and transmitted waves are presented in each of the four cases when (i) a set of coupled longitudinal waves (ii) a similar set of coupled waves (iii) a transverse wave, propagating through the solid half space (iv) a longitudinal wave propagating through the viscous liquid half space, are made incident at the interface. Numerical computations are made for a specific model and results are presented graphically to highlight the modulations of these ratios due to the variation of incident angle of the incident wave. It is found that the amplitude and energy ratios of various reflected and transmitted waves are functions of angle of incidence and frequency. The effects of viscosity of the liquid, magnetic field as well as void nature of the solid medium on the amplitude and energy ratios have been analyzed from the graphical representations.
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In this paper we present a mathematical analysis of heat and mass transfer phenomena in a visco-elastic fluid flow over a non-isothermal stretching sheet with variable thermal conductivity and variable mass diffusivity. Similarity transformation are used to convert highly non-linear partial differential equations into ordinary differential equations. Several closed form analytical solutions for non-dimensional temperature, concentration, heat flux and mass flux are obtained in the form of confluent hypergeometric functions for two different types of the boundary conditions, namely: (i) wall with prescribed second-order power law temperature and second-order power law concentration (PST) and (ii)wall with prescribed second-order power law heat flux and second-order power law mass flux (PHF). The effect of various physical parameters such as the suction/blowing parameter , heat source/sink parameter [...], Prandtl number Pr, Schmidt number Sc, visco-elastic parameter and permeability parameter on the temperature and concentration profiles are analyzed.
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