Effects of binary chemical reaction and activation energy on MHD boundary layer heat and mass transfer flow with viscous dissipation and heat generation/absorption

Maleque, Kh. Abdul

Please use this identifier to cite or link to this item: http://dspace.aiub.edu:8080/jspui/handle/123456789/385

Title:	Effects of binary chemical reaction and activation energy on MHD boundary layer heat and mass transfer flow with viscous dissipation and heat generation/absorption
Authors:	Maleque, Kh. Abdul
Issue Date:	6-Jan-2013
Publisher:	Hindawi (International Scholarly Research Notices)
Citation:	51
Series/Report no.:	;284637
Abstract:	We study an unsteady MHD free convection heat and mass transfer boundary layer incompressible fluid flow past a vertical porous plate in the presence of viscous dissipation, heat generation/absorption, chemical reaction, and Arrhenius activation energy. The plate is moving with uniform velocity. The chemical reaction rate in the function of temperature is also considered. The governing partial differential equations are reduced to ordinary differential equations by introducing local similarity transformation (Maleque(2010)) and then are solved numerically by shooting method using the Nachtsheim-Swigert iteration technique. The results of the numerical solution are then presented graphically as well as the tabular form for difference values of the various parameters.
Description:	In free convection boundary layer flows with simultaneous heat mass transfer, one important criterion that is generally not encountered is the species chemical reactions with finite Arrhenius activation energy. The Arrhenius law is usually of the following form [1]: 𝐾 = 𝐵(𝑇 − 𝑇∞) 𝑤 exp [ −𝐸𝑎 𝑘 (𝑇 − 𝑇∞) ] , (1) where 𝐾 is the rate constant of chemical reaction and 𝐵 is the preexponential factor, simply prefactor (constant), is based on the fact that increasing the temperature frequently causes a marked increase in the rate of reactions. 𝐸𝑎 is the activation energy and 𝑘 = 8.61 × 10−5 eV/K is the Boltzmann constant which is the physical constant relating energy at the individual particle level with temperature observed at the collective or bulk level. In areas such as geothermal or oil reservoir engineering, the above phenomenon is usually applicable. Apart from experimental works in these areas, it is also important to make some theoretical efforts to predict the effects of the activation energy in flows mentioned above. But in this regard the very few theoretical works are available in the literature. The reason is that the chemical reaction processes involved in the system are quite complex and generally the mass transfer equation that is required for all the reactions involved also becomes complex. Theoretically, such an equation is rather impossible to tackle. From chemical kinetic viewpoint, this is a very difficult problem, but if the reaction is restricted to binary type a lot of progress can be made. The thermomechanical balance equations for a mixture of general materials were first formulated by Truesdell [2, 3]. Thereafter, Mills [4] and Beevers and Craine [5] have obtained some exact solutions for the boundary layer flow of a binary mixture of incompressible Newtonian fluids. Several problems relating to the mechanics of oil and water emulsions, particularly with regard to applications in lubrication practice, have been considered within the context of a binary mixture theory by Al-Sharif et al. [6] and Wang et al. [7]. A simple model involving binary reaction was studied by Bestman [8]. He considered the motion through the plate to be large which enabled him to obtain analytical solutions (subject to same restrictions) for various values of activation energy by employing the perturbation technique proposed by Singh and Dikshit [9]. Bestman [10] and Alabraba et al. [11] took into account the effect of the Arrhenius activation energy under the different physical conditions. 2 ISRN Thermodynamics Recently Kandasamy et al. [12] studied the combined effects of chemical reaction, heat and mass transfer along a wedge with heat source, and concentration in the presence of suction or injection. Their result shows that the flow field is influenced appreciably by chemical reaction, heat source, and suction or injection at the wall of the wedge. Recently, Makinde et al. [13] studied the problem of unsteady convection with chemical reaction and radiative heat transfer past a flat porous plate moving through a binary mixture in an optically thin environment. More recently Maleque [14] studied the effects of exothermic chemical reaction and activation energy on free convective heat and mass transfer flow past a vertical plate. In the present paper, we investigate a numerical solution of unsteady natural convection heat and mass transfer boundary layer flow past a vertical porous plate taking into account the effects of viscous dissipation, heat generation/absorption, and chemical reaction with Arrhenius activation energy in the presence of uniform magnetic field. The plate is moving with uniform velocity. The chemical reaction rate in the function of temperature is also considered. The governing partial differential equations are reduced to ordinary differential equations by introducing local similarity transformation (Maleque [15]). Numerical solutions to the reduced nonlinear similarity equations are then obtained by adopting Runge-Kutta and shooting methods using the Nachtsheim-Swigert iteration technique. The results of the numerical solution are then presented graphically as well as the tabular form for difference values of the various parameters.
URI:	http://dspace.aiub.edu:8080/jspui/handle/123456789/385
ISSN:	2090-5211
Appears in Collections:	Publication: Journal

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