Injection/ suction effect on MHD convective flow through porous medium filled in a vertical porous channel with heat radiation and chemical reaction

K.D. Singh¹*, Khem Chand², Sapna²

¹Railways Vihar, Mansa Devi Campus, Sector-4. Panchkula (Haryana).

²Department of Mathematics & Statistics, Himachal Pradesh University Shimla-171005.

*Corresponding Author Email: kdsinghshimla@gmail.com*, khemthakur99@gmail.com and sapnamaths@gmail.com**

ABSTRACT:

The paper attempt to investigate the effect of injection/ suction on the flow of electrically conducting fluid through a porous channel filled with porous material. A magnetic field of uniform strength is applied perpendicular to the plane of the porous channel. The effect of heat radiation, heat source and chemical reaction has been taken into consideration. The governing equations are solved analytically by using complex variable notation. The expressions for velocity, temperature, concentration, skin friction coefficient, rate of heat transfer and rate of mass transfer have been obtained. The effect of various parameters entering the governing equation have been evaluated numerically and expressed graphically and in tabular form. A detailed discussion is given in the result and discussion section of the research paper.

INTRODUCTION:

The study of the problems of the MHD convective flow with heat and mass transfer have attracted the attention of number of scholars due to its importance in many branches of science and technology. Magnetohyrodynamics is the study of interaction of magnetic fields and electrically conducting fluid in motion. Magnetohydrodynamic convection flows of electrically conducting viscous incompressible fluids in porous channels have gained considerable attention because of numerous applications in physics and engineering. The effect of convection on the flow of heat and mass transfer processes through porous medium plays an important role in agricultural engineering and throws some light on the influence of environment like temperature and pressure on germination of seeds. It is also of great interest in petroleum industry in extracting petrol from crude. The study of flow through porous media is also important in soil physics and geophysics. Channels are frequently used in various applications in designing ventilating and heating buildings, cooling electronic components, drying several types of agriculture products grain and food, and packed bed thermal storage. Convective flows in channels driven by temperature differences of bounding walls have been studied and reported, extensively in literature. Literature related to hydromagnetic free convective channel flow has paramount importance in a number of engineering processes and reported by several scholars like Crammer and Pai(1973), Ferraro and Plumpton (1966), Shercliff (1961) on account of their varied importance. Chang and Lundgren (1964) studied a hydromagnetic flow in a duct. MHD flow between two parallel plates with heat transfer has been investigated by Attia and Kotb (1996). Makinde and Mhone (2005) analyzed the heat transfer to MHD oscillatory flow in a channel filled with porous medium. Mathematical modeling of soret and Hall effects on oscillatory MHD free convective flow of radiating fluid in rotating vertical porous channel filled with porous medium has been investigated by Kumar and Singh (2012). Patil and Kulkarni(2008) has investigated the chemical reaction on free convection flow of a polar fluid through a porous medium in the presence of internal heat generation. An analysis with finite element method of oscillatory chemically reacting MHD free convection heat and mass transfer in a porous medium with Soret and Dufour effects has been presented by Bhargava et al.(2009). Devika et al.(2013) worked on Chemical reaction effects on MHD free convection flow in an irregular channel with porous medium. Chemical reaction effects on radiative MHD oscillatory flow in a porous channel with mass transfer and heat absorption has been analyzed by Vijaylakshmi et al.(2015). Further Vidhya et al.(2015) investigated the chemical reaction effects on radiative MHD oscillatory flow in a porous channel with heat and mass transfer in an asymmetric channel.

Extensive work has been carried out in recent years to study the effect of unsteady MHD free convective flow governed by the impact of injection/suction. The process of suction or blowing has also its importance in many engineering activities such as in the design of thrust bearing, redial diffusers and thermal oil recovery. Magnetic field effects on the free convection and mass transfer flow through porous medium with constant suction and constant heat flux has been investigated by Acharya et al. (2000). Singh (2013) give the results on injection/suction effects on hydromagnetic oscillatory convective flow in a rotating vertical channel with thermal radiation. Attia (2010) studied the effect of suction and injection on unsteady Couette flow with variable properties. Magnetohydrodynamic oscillatory flow in a planer porous channel with suction and injection has been analysed by Ahmed and Khatun (2013). Joseph et al. (2015) presented their work on chemically reacting fluid on unsteady MHD oscillatory slip flow in a planer channel with varying temperature and concentration in the presence of suction/ injection. Recent work on combined effect of suction/injection on MHD free convective flow in a vertical channel with thermal radiation has been analyzed by Jha et al.

Motivated by above studies we have studied the MHD convective flow through porous medium when a constant injection and suction is applied at the left and right infinite porous plates respectively. We have extended the work of Singh (2013) to analyze the effect of chemical reaction on the flow through porous medium filled in porous channel.

RESULTS AND DISCUSSION:

In order to study the influence of injection/suction parameter (), the Prandtl number() , Hartmann number (), the free convection parameter i.e. the thermal Grashof number (), Modified Grashof number (), the heat source parameter (), Schmidt number , radiation parameter and chemical reaction parameter on the flow field in the boundary layer region, the numerical values of the fluid velocity, temperature, concentration and the coefficient of the skin friction , coefficient of the heat transfer and coefficient of Sherwood number is computed from the analytical solutions reported in the previous section are displaced graphically in figures 2 to 4 and in tabular form from table 1 to 4. In our calculation we have taken the value of and .

In figure 2 and 3 , the effect of injection/suction parameter (), Grashoff number , modified Grashoff number , Prandtl number , radiation parameter , permeability parameter and Hartmann number on the fluid velocity is presented. Here we observed that with the increase in injection/ suction parameter (), Prandtl number , radiation parameter , Hartmann number and chemical reaction parameter ,velocity of the fluid decreases, whereas it increases with Grashoff number , modified Grashoff number , permeability parameter and pressure gradient parameter ).

Figure 4 depicts the effect of injection/suction parameter (), Prandtl number and radiation parameter on the temperature profile. It is analyzed from the figure that temperature profile decreases with the increase in injection/ suction parameter (), Prandtl number and radiation parameter .

Tables 1 to 4 expresses numerically the variation of concentration, skin friction , Nusselt number and Sherwood number with various parameters respectively. From table 1, it is analyzed that with the increase in injection/suction parameter () and Schmidt number , concentration of the fluid increases whereas reverse effect is observed for chemical reaction parameter . Concentration of the fluid remains unchanged for various values of radiation parameter . Table 2 depicts that with the increase in Grashoff number , modified Grashoff number , Schmidt number , heat source parameter (), pressure gradient parameter and permeability parameter , the coefficient of skin friction increases whereas decreases with injection/suction parameter (), Prandtl number , chemical reaction parameter , radiation parameter and Hartmann number . Table 3 reveals that Nusselt number increases with increase in heat source parameter (), whereas reverse effect is obtained for injection/suction parameter (), Prandtl number and radiation parameter. Table 3 shows the effect of injection/suction parameter (), Schmidt number , chemical reaction parameter and radiation parameter on Sherwood number , which shows that it decreases with increase in chemical reaction parameter ,while increases with injection/suction parameter () and Schmidt number and remains unchanged for radiation parameter .

REFERENCES:

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16. Singh, K.D. (2013), “Injection/ suction effects on hydromagnetic oscillatory convective flow in a rotating vertical porous channel with thermal radiation” , Proc. Indian Natn. Sci. Acad., Vol. 79, pp. 79-90.

17. Vidhya, M., Vijayalakshmi, R. and Govindarajan, A. (2015), “Chemical reaction effects on radiative MHD oscillatory flow in a porous channel with heat and mass transfer in an asymmetric channel” , APRN J. Engg. Appl. Sci., Vol. 10, pp. 1839-1845.

18. Vijayalakshmi, R., Govindarajan, A., Kumar, J.S. and Siva, E.P. (2015), “Chemical reaction effects on radiative MHD oscillatory flow in a porous channel with mass transfer and heat absorption” , Int. J. Sci. & Engg., Vol. 6, PP. 199-203.

Received on 27.08.2016 Accepted on 11.09.2016

Int. J. Tech. 2016; 6(2): 215-222.

DOI: 10.5958/2231-3915.2016.00033.X