On heat and mass transfer in chemically reacting and radiating viscoelastic MHD flow through porous medium in vertical channel

Khem Chand¹, Dinesh Kumar¹ and K.D. singh²

¹Department of Mathematics and Statistics, Himachal Pradesh University, Shimla-171005 (India)

²Department of Mathematics (ICDEOL), Himachal Pradesh University, Shimla-171005

*Corresponding Author E-mail: khemthakur99@gmail.com; dineshrana2582@gmail.com ; kdsinghshimla@gmail.com

ABSTRACT:

An investigation of heat and mass transfer effect on incompressible chemically reacting, radiating and electrical conducting viscoelastic fluid through porous medium in porous vertical channel has been carried out. The magnetohydrodynamics (MHD) flow is assumed to be laminar and fully developed. A uniform magnetic field is applied in the direction perpendicular to the plane of the plates. The equations governing the flow are solved by perturbation technique. The velocity, temperature, concentration fields, coefficient of skin friction, rate of heat and mass transfer are evaluated numerically and discussed with the help of graphs and tables.

KEYWORDS: Chemically reacting, MHD, porous medium, radiating, and viscoelastic fluid.

Mathematical Subject Classification (2010): 76D05 and 76D10

1. INTRODUCTION:

The analysis of viscoelastic fluid flow is one of the important fields of fluid dynamics. The complex stress-strain relationship of viscoelastic fluid flow mechanisms are used in geophysics, chemical engineering (absorption, filtration), petroleum engineering, hydrology, soil-physics, bio-physics and paper and pulp technology. Walters liquid (Model B) is a type of viscoelastic fluid which resists shear flow and strains linearly with time under the application of an applied stress but when the stress is removed it quickly returns to its original position. Various blood flow problems are also explained by using the viscoelastic boundary layer theory [1].

Now a day the physics of simultaneous heat and mass transfer has attracted the attention of various researchers because of its wide range of applications in science and technology. It is used in food processing, wet-bulb thermometer and polymer solution and also in various fluids flows related engineering problems [2-3]. In our daily life, the combined heat and mass transfer phenomenon is observed in the formation of fog. The convective flow associated with the combined heat and mass transfer has many applications in various branches of science and engineering. The good list of references is found in [4-6].

Flow through the porous media with heat and mass transfer are seen in wide range of applications such as solar power collector, chemical catalytic reactor, insulation of chemical reactor, fluid film lubrication and analysis of polymer in chemical engineering. Representative studies in this area can be found in [7-9].

Flow and mass transfer with chemical reaction is of great practical importance, because of its universal occurrence in many branches of science and engineering [10–13]. Recently, Hayat et al. [14] investigated the mass transfer in magnetohydrodynamic (MHD) flow of the UCM (upper convective Maxwell) fluid over a porous shrinking sheet in the presence of a chemical reaction.

The role of thermal radiation is of major importance in the design of many advanced energy convection systems operating at high temperature and knowledge of radiative heat transfer becomes very important in nuclear power plants, gas turbines and the various propulsion devices for aircraft, missiles and space vehicles. Good list of references are found in [15-18].

Motivated by above studies we intend to analyse the effect of heat and mass transfer on MHD free convective flow of incompressible, electrically conducting and chemically reacting viscoelastic fluid through a highly porous medium bounded by two infinite vertical plate in the presence of the magnetic field applied in the direction perpendicular to plane of the plates.

2. Formulation of the problem

Consider the flow of a viscoelastic, incompressible and electrically conducting fluid through a highly porous medium bounded between two infinite vertical plates at distance ‘’ apart. We introduce a Cartesian co-ordinate system with - axis oriented vertically upward of this channel and - axis is taken perpendicular to the planes of the plates. A uniform magnetic field with magnetic flux density vector is applied perpendicular to the plane of plates. Since the plate of the channel occupying the planes are of infinite extent, all the physical quantities depends on y and t only except pressure. The schematic diagram of the physical problem is shown in the Figure 1.

6. CONCLUSIONS:

In the present paper flow of chemically reacting and radiating MHD oscillatory viscoelastic fluid through porous channel is studied. The closed form solution of the governing equation under the prescribed boundary condition is obtained. The conclusion of the study is as follows

1. The flow accelerated significantly with the increase of Grashof number, modified Grashof number, viscoelastic parameter, Schmidt number and frequency of oscillation.

2. The amplitude of skin friction increases with the amplitude of pressure gradient, Grashof number, modified Grashof number, viscoelastic parameter, Schmidt number while it decreases with the increase of frequency of oscillation.

3. The amplitude of mass transfer coefficient decreases with Reynolds number, Schmidt number and chemical reaction parameter.

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Received on 04.01.2014 Accepted on 29.01.2014

Int. J. Tech. 4(1): Jan.-June. 2014; Page 227-233