Heat and Mass Transfer in Three Dimensional Free Convective Oscillatory Flow in Porous Medium with Constant Heat and Mass Flux in Presence Radiation for an optically Thin Fluid.

Suresh Rana¹, Virender Singh²

¹Department of Mathematics, Government College Shahpur (H.P) 176206

²Department of Mathematics, Government College Jawalamukhi (H.P) 176031

Corresponding Author E mail:sureshrana428@gmail.com; virenderbharoli@gmail.com

ABSTRACT:-

A theoretical analysis of free convective flow of viscous incompressible fluid through a porous medium bounded by a flat porous plate subject to periodic suction and constant heat and mass flux has been presented. The flow becomes three dimensional due to variation of suction velocity in transverse direction. Analytical expression for velocity, temperature, concentration and skin friction are obtained using perturbation technique. Numerical solutions are obtained for different values Grash of number (G_r) ,mass Grashof number(Gc), Prandtl number (Pr),Schmidt number (Sc) and Radiation (R) .It is found that non-dimensional velocity increases with increase of Gr, Gc and Sc and decreases with increase of R ,non-dimensional temperature decreases with increasing of R, Concentration decreases with increase of Sc. and skin friction co-efficient increases with increase of Gr and R but effect of Gr is more than R.

KEY WORDS: Free convection, oscillatory flow, sinusoidal suction, mass transfer, radiation.

INTRODUCTION:-

The Oscillatory flows are always important from technical point of view. Such a study was first initiated by Lighthill (1) who studied a two-dimensional flow of incompressible, viscous fluid. By assuming that the velocity of main stream fluctuates in magnitude, he completely solved the problem .The Stuart (2) extended this idea to study a two-dimensional flow past an infinite porous, flat plate with constant suction when the free stream oscillates in time about a constant mean. The phenomenon of free convective flow with simultaneous heat and mass transfer has been a subject of interest of many researchers because of its varied applications in natural science, engineering sciences and in industry. Such phenomenons are observed in bounyancy induced motion in atmosphere, in water bodies, quasi-solid bodies such as earth etc.

The flows through porous media are very much prevalent in nature and therefore, the study of such flows has become of principal interest in many scientific and engineering applications. This type of flows has shown their great importance in petroleum engineering to study the movements of natural gas, oil and water through the oil reservoirs; in chemical engineering for the filtration and water purification processes. Further, to study the underground water resources and seepage of water in river beds one need the knowledge of the fluid flow through porous medium. Therefore, there are number of practical uses of the fluid flow through porous media. The porous medium is in fact a non-homogeneous medium but for the sake of analysis, it may be possible to replace it with a homogeneous fluid which has dynamical properties equal to those of non-homogeneous continuum. Thus one can study the flow of hypothetical fluid under the action of the properly averaged external flow and the complicated problem of the flow through a porous medium reduces to the flow problem of homogeneous fluid with some additional resistance. Ahmadi and Manvi (3) have derived the general equation of motion and applied the results to some basic flow problems. Ram and Mishra (4) applied these equations to study the MHD flow of conducting fluid through porous media. The hydrodynamic channel, which is a classical problem ; the exact solution is obtained by Schlichting (5). A series of investigations have been made by different scholars where the porous medium is either bounded by a channel or by a plane surface, [Raptis (6), Raptis and Perdikis (7), Singh et al (8). The three dimensional Couette flow through porous media has been studied by Singh and Sharma (9). Ali and Mehmood (10) studied the homotopy analysis of unsteady boundary layer flow adjacent to a permeable stretching surface in a porous medium. Three dimensional oscillatory flow through a porous medium with periodic permeability was studied by Singh K.D. et. al. (11).

Radiative heat transfer flow is very important in manufacturing industries for the design of reliable equipments, nuclear plants, gas turbines and various propulsion devices for aircraft, missiles, satellites and space vehicles. Similarly, the effects of thermal radiation on the forced and free convection flows are important in the context of space technology and processes involving high temperature. Based on these applications England and Emery (12) studied the thermal radiation effect on optically thin grey gas bounded by a stationary vertically plate. Hayat et.al (13) studied the effect of thermal radiation on the flow of second grade fluid .Raptis et.al.(14) studied the effect of radiation on thin grey gas flowing past vertical infinite plate in the presence of magnetic field. Cookey el al. (15) studied the influence of viscous dissipation and radiation on unsteady MHD free convection flow past an infinite heated vertical plate in the porous medium with time dependent suction.

Thus, the aim of this paper is to study the effect of radiation on unsteady oscillatory free convective flow through a porous medium with constant heat and mass flux. Numerical calculations are carried out to investigate the effect of thermal Grashof number(Gr), mass Grashof number(Gc),Prandtl number (Pr),Radiation parameter (R) etc. on velocity (u), cross flow velocity(w),temperature (θ),concentration (c),skin friction (τ_x) and results are illustrated graphically.

REFERENCES:-

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2. Stuart,J.T. ; A solution of the Navier –Stokes and energy equations illustrating the response of skin friction and temperature of an infinite plate thermometer to fluctuations in the stream velocity. Proc.Roy. Soc.A 231, 116 (1955).

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15. Cookey, C.I., Ogulu, A. and Omubo Pepple, V.M., Influence of viscous dissipation and radiation on unsteady MHD free convection flow past an infinite heated vertical plate in a porous medium with time dependent suction. Int. J. Heat Mass Transfer, 46, 2305-2311 (2003).

Received on 24.08.2016 Accepted on 09.09.2016

Int. J. Tech. 2016; 6(2): 174-184.

DOI: 10.5958/2231-3915.2016.00027.4