Top PDF Chemical reaction effect on an unsteady MHD free convection flow past a vertical porous plate in the presence of suction or injection

Kumari and Nath [9] have studied development of two-dimensional bound- ary layer with an applied magnetic field due to an impulsive motion. Muthuku- maraswamy and Ganesan [10] have studied unsteady flow past an impulsively started vertical plate with heat and mass transfer. Kim [11] presented an analysis of an unsteady MHD convection flow past a vertical moving plate embedded in a porous medium in the presence of transverse magnetic field. Helmy [12] studied MHD unsteady free convection flow past a vertical porous plate. Raptis [13] analyzed the thermal radiation and free convection flow through a porous medium bounded by a vertical infinite porous plate by using a regular perturbation technique. Pantokratoras [14] studied Non-Darcian forced convection heat transfer over a flat plate in a porous medium with variable viscosity and variable Prandtl number. Sacheti et al.[16] have stud- ied exact solutions for unsteady magneto-hydrodynamics free convection flow with constant heat flux. Ibrahim [?] studied the effects of chemical reaction and radiation absorption on transient hydro magnetic natural convection flow with wall transpiration and heat source. Anjalidevi and Kandasamy [17] have examined the effect of a chemical reaction on the flow in the presence of heat transfer and magnetic field. Mansour et al.[18] analyzed the effect of chemical reaction and viscous on MHD natural convection flows saturated in porous media with suction or injection. However, in engineering and technology, there are occasions where a heat source is needed to maintain the desired heat transfer. At the same time, the suction velocity has also to be normal to the porous plate.

unsteady MHD free convective heat transfer flow along a vertical porous flat plate with internal heat generation. In many chemical engineering processes, there does occur the chemical reaction between a foreign mass and the fluid in which the plate is moving. These processes take place in numerous industrial applications viz., Polymer production, manufacturing of ceramics or glassware and food procession. Cramer K. R. and Pai, S. I.et al.[11] taken transverse applied magnetic field and magnetic Reynolds number are assumed to be very small, so that the induced magnetic field is negligible. Muthucumaraswamy et al.[12] have studied the effect of homogeneous chemical reaction of first order and free convection on the oscillating infinite vertical plate with variable temperature and mass diffusion. Das et al.[13] have studied the effects of mass transfer on flow past an impulsively started infinite vertical plate with constant heat flux and chemical reaction. K.Sudhakar and R. Srinivasa Raju et al.[14] have studied chemical reaction effect on an unsteady MHD free convection flow past an infinite vertical accelerated plate with constant heat flux, thermal diffusion and diffusion thermo. S. Shivaiah and J. Anand Rao et al.[15] studied chemical reaction effect on an unsteady MHD free convection flow past a vertical porous plate in the presence of suction or injection. Chaudhary and Jha [16] studied the effects of chemical reactions on MHD micropolar fluid flow past a vertical plate in slip-flow regime. Anjalidevi et al.[17] have examined the effect of chemical reaction on the flow in the presence of heat transfer and magnetic field. Moreover, Al-Odat and Al-Azab [18] studied the influence of magnetic field on unsteady free convective heat and mass transfer flow along an impulsively started semi-infinite vertical plate taking into account a homogeneous chemical reaction of first order. The chemical reaction, heat and mass transfer on MHD flow over a vertical stretching surface with heat source and thermal stratification have been presented by Kandasamy et al.[19]. Ahmed Sahin.et al.[20] have studied influence of chemical reaction on transient MHD free convective flow over a vertical plate in slip-flow regime.

The objectives of the present study are to investigate thermal radiation of a viscous incompressible unsteady chemically reacting and hydromagnetic fluid flow past an impulsively started vertical plate with heat and mass transfer is analyzed. The fluid is a gray, absorbing-emitting but non- scattering medium and the Rosseland approximation is used to describe the radiative heat flux in the energy equation. The governing equations are solved using an implicit finite-difference scheme of Crank-Nicolson type. Numerical results for the transient velocity, the temperature, the concentration, the local as well as average skin-friction, the rate of heat and mass transfer are shown graphically. It is found that as small values of the Prandtl number and radiation parameter N, the velocity and temperature of the fluid increase sharply neat the cylinder as the time t increase, which is totally absent in the absence of radiation effects. It is observed that the presence of chemical reaction parameter K(>0) leads to decrease in the velocity field and concentration and rise in the thermal boundary thickness.

Convection in the presence of internal heat source/ sink has several applications in fields of geophysical science, fire and safety engineering, nuclear science, chemical engineering, heat exchangers, petroleum reservoir etc., Effect of Volumetric heat source/ sink on mixed convection stagnation point flow on an isothermal vertical plate in porous media has been discussed in [10]. In reference[7] internal heat generation and radiation effects on a certain free convection flow has been discussed and reference [1] discussed the numerical study of the combined free-forced convection and mass transfer flow past a vertical porous plate in a porous medium with heat generation and thermal diffusion.

ous applications, hydromagnetic free convection flow in the stokes problem for a porous vertical limiting surface with constant suction has been analyzed by Nanousis et al. [8]. Singh [9] studied MHD free convection flow in the stokes problem for a porous vertical plate. Numerous scientists works on a similarity solution of an unsteady one-dimensional hydromagnetic heat transfer flow with variable suction or injection. In this study, a time depen- dent similarity parameter was introduced on the basis of the proposal put forward by Hasimoto [10]. Introducing this similarity parameter, the governing boundary layer equations were reduced to non-linear ordinary differential equations, which are similar in time. Later many articles have been published in this line, the works of which are Sattar and Hossain [11], Sattar [12], Sattar et al. [13], Alam et al. [14] and Rahman and Sattar [15] are worth mention- ing.

H. L. Agarwal and P. C. Ram [1] have studied the effects of Hall Current on the hydro-magnetic free convection with mass transfer in a rotating fluid. H. S. Takhar and P. C. Ram [2] have studied the effects of Hall current on hydro-magnetic free convective flow through a porous medium. B. K. Sharma and A. K. Jha [3] have analyzed analytically the steady combined heat and mass transfer flow with induced magnetic field. B. P. Garg [4] has studied combined effects of thermal radiations and hall current on moving vertical porous plate in a rotating system with variable temperature. Dufour and Soret Effects on Steady MHD Free Convection and Mass Transfer Fluid Flow through a Porous Medium in A Rotating System have been investigated by Nazmul Islam and M. M. Alam [5]. Hall Current Effects on Magneto hydrodynamics Fluid over an Infinite Rotating Vertical Porous Plate Embedded in Unsteady Laminar Flow have been studied by Anika et al [6]. S. F. Ahmmed and M. K. Das [7] have investigated Analytical Study on Unsteady MHD Free Convection and Mass Transfer Flow Past a Vertical Porous Plate.

An investigation of unsteady magnetohydrodynamic free convective flow and mass transfer during the motion of a viscous incompressible fluid through a por- ous medium, bounded by an infinite vertical porous surface, in a rotating system is presented. The porous plane surface and the porous medium are assumed to rotate in a solid body rotation. The vertical surface is subjected to uniform con- stant suction perpendicular to it and the temperature at this surface fluctuates in time about a non-zero constant mean. Analytical expressions for the velocity, temperature and concentration fields are obtained using the perturbation tech- nique. The effects of rotation parameter, permeability parameter, Hartmann number, and frequency parameter on the flow characteristics are discussed. It is observed that the primary velocity component decreases with the increase in ei- ther of the rotation parameter, the permeability parameter, or the Hartmann number. It is also noted that the primary skin friction increases whenever there is an increase in the Grashof number or the modified Grashof number. It is clear that the heat transfer coefficient in terms of the Nusselt number decreases in the case of both air and water when there is an increase in the Hartmann number. It is observed that the magnitude of the secondary velocity profiles increases when- ever there is an increase in either of the Grashof number or the modified Grashof number for mass transfer or the permeability of the porous media. Concentration profiles decreases with an increase in the Schmidt number.

In many practical situations such as condensation, evaporation and chemical reactions the heat transfer process is always accompanied by the mass transfer process. Perhaps, it is due to the fact that the study of combined heat and mass transfer is helpful in better understanding of a number of technical transfer processes. Besides, free convection flows with conjugate effects of heat and mass transfer past a vertical plate have been studied extensively in the literature due to its engineering and industrial applications in food processing and polymer production, fiber and granular insulation and geothermal systems [1–3]. Some recent attempts in this area of research are given in [4–9]. On the other hand, considerable interest has been developed in the study of interaction between magnetic field and the flow of electrically conducting fluids in a porous medium due to its applications in modern technology [10]. Toki et al. [11] have studied the unsteady free convection flows of incompressible viscous fluid near a porous infinite plate with arbitrary time dependent heating plate. The effects of chemical reaction in two dimensional steady free convection flow of an electrically conducting viscous fluid through a porous medium bounded by vertical surface with slip flow region has been studied by Senapati1 et al. [12]. Khan et al. [13] analyzed the effects of radiation and thermal diffusion on MHD free convection flow of an incompressible viscous fluid near an oscillating plate embedded in a porous medium.

boundary layer flow along a heated vertical flat plate embedded in a fluid-saturated porous medium, which was investigated by Cheng and Minkowycz (1977). They obtained similarity solutions for the case when wall temperature varies as a power function of the distance from the leading edge. Nakayama and Koyama (1987) analyzed combined free and forced convection flow in Darcian and non- Darcian porous medium. Lai and Kulacki (1991) studied non-Darcy mixed convection flow along a vertical wall in a fluid saturated porous medium. Hsieh et al. (1993) obtained non-similar solution for free and forced convection flow from a vertical surface in a porous medium. Rees (1999) analyzed free convection boundary layer flow from an isothermal vertical flat plate embedded in a fluid saturated layered porous medium. Jana et al. (2012) studied natural convection boundary layer flow from an inclined flat plate with finite dimensions embedded in a porous medium in a rotating environment. Khan and Pop (2013) investigated the Cheng and Minkowycz problem for triple diffusive natural convection boundary layer flow past a vertical plate in a porous medium. Reddy et al. (2013) studied unsteady hydromagnetic natural convection flow past a moving vertical plate in a porous medium in the presence of radiation and chemical reaction. Comprehensive reviews of convective flow in porous media are candidly presented in the form of books and monographs by Ingham and Pop (2002), Ingham et al. (2004), Vafai (2005) and Nield and Bejan (2006).

accelerating surface with heat source in presence of suction and blowing. Kamel [9] investigated the unsteady MHD convection through a porous medium with combined heat and mass transfer in presence of heat source/sink. Devi and Kandaswamy [10] estimated the effect of chemical reaction, heat and mass transfer on non-linear MHD flow past an accelerating surface with heat source and thermal stratification in the presence of suction or injection.

Sposito and Ciafalo (2006) studied fully developed flow of an electrically conducting fluid between parallel walls under the simultaneous influence of a driving pressure head, buoyancy and MHD forces, where the fluid was assumed to be internally heated and the flow was modeled as one-dimensional and incompressible. Al-Khawaja et al. (1994) solved numerically the problem of fully developed, laminar, steady, forced convection heat transfer in an electrically conducting fluid flowing in an electrically insulated, horizontal circular pipe in a vertical uniform transverse magnetic. Al-Khawaja et al. (1999) also studied the same problem for free- and-forced convection flow numerically using finite difference schemes for Grashof numbers 0 to 106 and Hartmaan numbers 0 to 500. Umavathi and Malashetty (2005) solved the problem of combined free and forced convective MHD flow in a vertical channel by taking into account the effect of viscous and ohmic dissipations, analytically by perturbation series method and numerically by finite difference technique. Umavathi and Chamkha (2011) analyzed the effect of heat and mass transfer on mixed convective flow of a viscous incompressible fluid past a vertical infinite plate in the presence of heat source or sink. Garandet and Alboussiere (1992) proposed analytical solutions to the equations of MHD that was used to model the effect of a transverse magnetic field on buoyancy driven convection in a two-dimensional cavity, in the case of high Hartmaan number limit. Blosseville et al. (2007) investigated analytically a fully developed buoyant flow in a straight, horizontal rectangular duct with an axial temperature gradient in an arbitrary oriented, transverse magnetic field with insulated walls. Aruna et al. (2011) studied the developed MHD mixed convection flow in a vertical channel, where the problem was described by means of partial differential equations and the solutions were obtained by an implicit finite difference technique coupled with a marching

plate with variable suction. Alam et al. (2006a), (2006b) have studied the Dufour and Soret effects on MHD free convection and mass transfer flow past a vertical porous plate in a porous medium. They have discussed both the steady and unsteady cases. Diffusion-thermo and thermal-diffusion effects on free convective heat and mass transfer flow in a porous medium with time dependent temperature and concentration have been investigated by Alam et al. (2007). Manna et al. (2007) have studied an unsteady viscous flow past a flat plate in a rotating system. Thermal radiation effect on a transient MHD flow with mass transfer past an impulsively started vertical plate has been described by Alam and Sarmah (2009). Rajesh and Varma (2009) have presented the radiation and mass transfer effects on an MHD free convective flow past an exponentially accelerated vertical plate with variable temperature. Muthucumaraswamy et al. (2009) have studied an unsteady flow past an accelerated infinitely long vertical plate with variable temperature and uniform mass diffusion. Muthucumaraswamy et al. (2009) have also discussed the heat and mass transfer on the flow past an accelerated vertical plate with variable mass diffusion. Jha and Ajibade (2009) have investigated the diffusion-thermo effects on free convective heat and mass transfer flow in a vertical channel with symmetric boundary conditions. The combined effects of heat and mass transfer by mixed convective MHD flow past a porous plate with chemical reaction in the presence of heat source have been described by Ahamed and Zueco (2010). Rajesh and Varma (2010) have investigated the radiation effects on an MHD flow through a porous medium with variable temperature or variable mass diffusion. Makinde (2010) has discussed an MHD heat and mass transfer over a moving vertical plate with a convective surface boundary condition. The effects of thermal radiation on an MHD free convective flow past

Transient natural convection is of fundamental interest in many industrial and environmental situations such as air conditioning systems, atmospheric flows, motors, thermal regulation process, cooling of electronic devices, and security of energy systems. Buoyancy is also of importance in an environment where differences between land and air temperatures can give rise to compli- cated flow patterns. Magnetohydrodynamic has attracted the attention of a large number of scholars due to its diverse applications. In astrophysics and geophysics, it is applied to study the stellar and solar structures, interstellar matter, radio propagation through the ionosphere etc. In engineering it finds its application in MHD pumps, MHD bearings etc. Convection in porous media has applications in geothermal energy recovery, oil extraction, thermal energy storage and flow through filtering devices. Convective heat transfer in porous media has received considerable attention in recent years owing to its importance in various technological applications such as fibre and granular insulation, electronic system cooling, cool combustors, and porous material regenerative heat exchangers. Books by Nield and Bejan [1], Bejan and Kraus [2] and Ingham et al. [3] excellently describe the extent of the research infor- mation in this area. The phenomena of mass transfer is also very common in theory of stellar structure and observable effects are detectable, at least on the solar surface. The study of effects of magnetic field on free convection flow is important in liquid-metals, electrolytes and ionized gases. The ther- mal physics of hydromagnetic problems with mass transfer is of interest in power engineering and metallurgy. Thermal radiation in fluid dynamics has become a significant branch of the engineering sciences and is an essential as- pect of various scenarios in mechanical, aerospace, chemical, environmental, solar power, and hazards engineering. Viscous mechanical dissipation effects are important in geophysical flows and also in certain industrial operations and are usually characterized by the Eckert number. In the literature, exten- sive research work is available to examine the effect of natural convection on flow past a plate.

486 transfer. Afify (2009) discussed the MHD free convective heat and mass transfer flow over a stretching sheet in the presence of suction/injection with thermal diffusion and diffusion thermo effects. The influence of dust particles on the flow of a viscous fluid has several important applications. The dust particles tend to retard the flow and to decrease the fluid temperature. Such flows are encountered in a wide variety of engineering problem such as nuclear reactor cooling, rain erosion, paint spraying, transport, waste water treatment, combustion, etc. The presence of solid particles such as ash or soot in combustion energy generators and their effect on performance of such devices led to studies of particulate suspension in electrically conducting fluid in the presence of magnetic field. Saffman (1962) initiated the study of dusty fluids and discussed the stability of the laminar flow of a dusty gas in which the dust particles are uniformly distributed Chamkha (2000b) investigated the unsteady laminar hydromagnetic fluid particle flow and heat transfer in channels and circular pipes considering two phase continuum models. The effects of Hall current on the Couette flow with heat transfer of a dusty conducting fluid in the presence of uniform suction/injection was studied by Attia (2005). Ghosh and Ghosh (2008) considered the problem of hydromagnetic rotating flow of a dusty fluid near a pulsating plate when the flow is generated in the fluid particle system due to velocity tooth pulses subjected on the plate in the presence of a transverse magnetic field. Makinde and Chinyoka (2010) investigated the unsteady fluid flow and heat transfer of a dusty fluid between two parallel plates with variable viscosity and thermal conductivity

When the temperature of surrounding fluid is high, the radiation effects play an im- portant role that cannot be ignored, Modest [28] and Siegel and Howell [29]. The effects of radiation on temperature have become more important industrialized. Many processes in en- gineering areas occur at high temperature and acknowledge radiation heat transfer become very important for the design of pertinent equipment. Nuclear power plants, gas turbines and the various propulsion devices for aircraft, missiles, satellites and space vehicles are examples of such engineering areas. In such cases one has to take into account the effects of radiation and free convection. For an impulsively started infinite vertical isothermal plate, Ganesan et al. [30] studied the effects of radiation and free convection, by using Rosseland approxima- tion, Brewster [31]. Problem of radiative heat transfer with hydromagnetic flow and viscous dissipation over a stretching surface in the presence of variable heat flux is solved analytically by Kumar [32]. Hossain and Takhar [33], Raptis and Massals [34], and Hossain et al. [35] studied the radiation effect on free and forced convection flows past a vertical plate, including various physical aspects. Aboeldahab Emad [36] studied the radiation effect on heat transfer in an electrically conducting fluid at the stretching surface. At high operating temperature, ra- diation effect can be quite significant, Ghaly and Elbarbary [37]. Heat and mass transfer ef- fects on moving plate in the presence of thermal radiation have been studied by Muthucuma- raswamy and Kumar [38] using Laplace technique. For the problem of coupled heat and mass transfer in MHD free convection, the effect of both viscous dissipation and ohmic heating are not studied in the previous investigations. However, it is more realistic to include these two effects to explore the impact of the magnetic field on the thermal transport in the boundary layer. With this awareness, the effect of ohmic heating on the MHD free convection heat transfer has been examined for a Newtonian fluid by Hossain [39]. Chen [40] studied the problem of combined heat and mass transfer of an electrically conducting fluid in MHD natu- ral convection, adjacent to a vertical surface with ohmic heating.

It is interesting to note that the Brownian motion of nanoparticles at molecular and nanoscale levels are a key nanoscale mechanism governing their thermal behaviors. In nanofluid systems, due to the size of the nanoparticles, the Brownian motion takes place, which can affect the heat transfer properties. As the particle size scale approaches to the nanometer scale, the particle Brownian motion and its effect on the surrounding liquids play an important role in the heat transfer. In view of these applications, Nield and Kuznetsov ([22, 23]) analyzed the free convective boundary layer flows in a porous medium saturated by nanofluid by taking Brownian motion and thermophoresis effects into consideration. In the first article, the authors have assumed that nanoparticles are suspended in the nanofluid using either surfactant or surface charge technology and hence they have concluded that this prevents particles from agglomeration and deposition on the porous matrix. Chamkha et al. [24] carried out a boundary layer analysis for the natural convection past an isothermal sphere in a Darcy porous medium saturated with a nanofluid. Nield and Kuznetsov [25] investigated the cross-diffusion in nanofluids, with the aim of making a detailed comparison with regular cross diffusion effects and the cross- diffusion effects peculiar to nanofluids, and at the same time investigating the interaction between these effects when the base fluid of the nanofluid is itself a binary fluid such as salty water. Recently, a boundary layer analysis for the natural convection past a horizontal plate in a porous medium saturated with a nanofluid is analyzed by Gorla and Chamkha [26], N. Kishan et.al [27], studied the unsteady MHD flow of heat and mass transfer of Cu-water and TiO 2 -water nanofluids over stretching sheet with a non-uniform heat/source/sink

In many transport processes existing in nature and in industrial applications, heat and mass transfer is a consequence of buoyancy effects caused by diffusion of heat and chemical species. The study of such processes is useful for improving a number of chemical technologies, such as polymer production and food processing. In nature, the presence of pure air or water is impossible. Some foreign mass may be present either naturally or mixed with the air or water. The effect of the presence of foreign mass on the free convection flow past a semi-infinite vertical plate was studied by Gebhart and Pera (1971). The presence of a foreign mass in air or water causes some kind of chemical reaction. During a chemical reaction between two species, heat is also generated (Bird et al., 1992). In most cases of chemical reaction, the reaction rate depends on the concentration of the species itself. A reaction is said to be first order if the rate of reaction is directly proportional to concentration itself (Cussler, 1988). Chemical reaction effects on heat and mass transfer laminar boundary layer flow have been studied by many authors (Apelblat, 1982; Das et al., 1994; Andersson et al., 1994; Fan et al., 1997; Takha et al., 2000; .Muthucumaraswamy and P.Ganesan,

design of heat exchangers, induction pumps, and nuclear reactors, in oil exploration and in space vehicle propulsion. Thermal radiation in fluid dynamics has become a significant branch of the engineering sciences and is an essential aspect of various scenarios in mechanical, aerospace, chemical, environmental, solar power and hazards engineering. Bhaskara Reddy and Bathaiah [18, 19] analyze the Magnetohydrodynamic free convection laminar flow of an incompressible Viscoelastic fluid. Later, he was studied the MHD combined free and forced convection flow through two parallel porous walls. Elabashbeshy [20] studied heat and mass transfer along a vertical plate in the presence of magnetic field. Samad, Karim and Mohammad [21] calculated numerically the effect of thermal radiation on steady MHD free convectoin flow taking into account the Rosseland diffusion approximaion. Loganathan and Arasu [22] analyzed the effects of thermophoresis particle deposition on non-Darcy MHD mixed convective heat and mass transfer past a porous wedge in the presence of suction or injection. Ghara, Maji, Das, Jana and Ghosh [23] analyzed the unsteady MHD Couette flow of a viscous fluid between two infinite non-conducting horizontal porous plates with the consideration of both Hall currents and ion-slip. The radiation effect on steady free convection flow near isothermal stretching sheet in the presence of magnetic field is investigated by Ghaly et al. [24]. Also, Ghaly [25] analyzed the effect of the radiation on heat and mass transfer on flow and thermal field in the presence of magnetic field for horizontal and inclined plates.

High temperature thermal radiation of an optically thick gray gas becomes significant to the relevance of space technology in such way that the foundation of space laboratory in the zero gravity is established by the concept of gray body radiation. If the temperature of surrounding fluid is rather high, radiation effects play an important role and this situation does not exist in space technology. In such cases one has to take into account the effect of thermal radiation and mass diffusion. It takes place in numerous industrial applications, e.g. polymer production, manufacturing of ceramics or glassware, and food processing Cussler (1998). For some industrial applications such as glass production, furnace design, propulsion systems, plasma physics and spacecraft re-entry aerothermodynamics which operate at higher temperatures and radiation effect can also be significant. A clear understanding of the nature of interaction between thermal and concentration buoyancies is necessary. Consolidated effects of heat and mass transfer problems are of importance in many chemical formulations and reactive chemicals. Therefore, considerable attention had been paid in recent years to study the influence of the participating parameters on the velocity field. More such engineering application can be seeing in electrical power generation systems when the electrical energy is extracted directly from a moving conducting fluid. The study of magnetohydrodynamic flow for electrically conducting fluid past heated surface has attracted the interest of many researches in view of its important applications in many engineering problems such as plasma studies, petroleum industries MHD power generations, cooling of nuclear reactors, the boundary layer control in aerodynamics and crystal

The purpose of this paper is to present a theoretical analysis of an unsteady hydromagnetic free convection flow of viscoelastic fluid (Walter’s B’) past an infinite vertical porous flat plate through porous medium. The temperature is assumed to be oscillating with time and the effect of the Hall current is taken into account. Assuming constant suction at the plate, closed form solutions have been obtained for velocity and temperature profiles. The effect of the various parameters, entering into the problem, on the primary, secondary velocity profiles, the axial and transverse components of skin-friction are shown graphically followed by quantitative discussion.