Kumari and Nath  have studied development of two-dimensional bound- ary layer with an applied magnetic field due to an impulsive motion. Muthuku- maraswamy and Ganesan  have studied unsteadyflowpastan impulsively started verticalplate with heat and mass transfer. Kim  presented an analysis ofanunsteadyMHDconvectionflowpast a vertical moving plate embedded in a porous medium inthepresenceof transverse magnetic field. Helmy  studied MHDunsteadyfreeconvectionflowpast a verticalporousplate. Raptis  analyzed the thermal radiation and freeconvectionflow through a porous medium bounded by a vertical infinite porousplate by using a regular perturbation technique. Pantokratoras  studied Non-Darcian forced convection heat transfer over a flat platein a porous medium with variable viscosity and variable Prandtl number. Sacheti et al. have stud- ied exact solutions for unsteady magneto-hydrodynamics freeconvectionflow with constant heat flux. Ibrahim [?] studied the effects ofchemicalreaction and radiation absorption on transient hydro magnetic natural convectionflow with wall transpiration and heat source. Anjalidevi and Kandasamy  have examined theeffectof a chemicalreactionontheflowinthepresenceof heat transfer and magnetic field. Mansour et al. analyzed theeffectofchemicalreaction and viscous onMHD natural convection flows saturated inporous media with suctionorinjection. However, in engineering and technology, there are occasions where a heat source is needed to maintain the desired heat transfer. At the same time, thesuction velocity has also to be normal to theporousplate.
unsteadyMHDfree convective heat transfer flow along a verticalporous flat plate with internal heat generation. In many chemical engineering processes, there does occur thechemicalreaction between a foreign mass and the fluid in which theplate 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. 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. have studied theeffectof homogeneous chemicalreactionof first order and freeconvectiononthe oscillating infinite verticalplate with variable temperature and mass diffusion. Das et al. have studied the effects of mass transfer onflowpastan impulsively started infinite verticalplate with constant heat flux and chemicalreaction. K.Sudhakar and R. Srinivasa Raju et al. have studied chemicalreactioneffectonanunsteadyMHDfreeconvectionflowpastan infinite vertical accelerated plate with constant heat flux, thermal diffusion and diffusion thermo. S. Shivaiah and J. Anand Rao et al. studied chemicalreactioneffectonanunsteadyMHDfreeconvectionflowpast a verticalporousplateinthepresenceofsuctionorinjection. Chaudhary and Jha  studied the effects ofchemical reactions onMHD micropolar fluid flowpast a verticalplatein slip-flow regime. Anjalidevi et al. have examined theeffectofchemicalreactionontheflowinthepresenceof heat transfer and magnetic field. Moreover, Al-Odat and Al-Azab  studied the influence of magnetic field onunsteadyfree convective heat and mass transfer flow along an impulsively started semi-infinite verticalplate taking into account a homogeneous chemicalreactionof first order. Thechemicalreaction, heat and mass transfer onMHDflow over a vertical stretching surface with heat source and thermal stratification have been presented by Kandasamy et al.. Ahmed Sahin.et al. have studied influence ofchemicalreactionon transient MHDfree convective flow over a verticalplatein slip-flow regime.
The objectives ofthe present study are to investigate thermal radiation of a viscous incompressible unsteady chemically reacting and hydromagnetic fluid flowpastan impulsively started verticalplate 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 inthe 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 ofthe Prandtl number and radiation parameter N, the velocity and temperature ofthe fluid increase sharply neat the cylinder as the time t increase, which is totally absent inthe absence of radiation effects. It is observed that thepresenceofchemicalreaction parameter K(>0) leads to decrease inthe velocity field and concentration and rise inthe thermal boundary thickness.
Convectioninthepresenceof 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., Effectof Volumetric heat source/ sink on mixed convection stagnation point flowonan isothermal verticalplateinporous media has been discussed in . In reference internal heat generation and radiation effects on a certain freeconvectionflow has been discussed and reference  discussed the numerical study ofthe combined free-forced convection and mass transfer flowpast a verticalporousplatein a porous medium with heat generation and thermal diffusion.
ous applications, hydromagnetic freeconvectionflowinthe stokes problem for a porousvertical limiting surface with constant suction has been analyzed by Nanousis et al. . Singh  studied MHDfreeconvectionflowinthe stokes problem for a porousverticalplate. Numerous scientists works on a similarity solution ofanunsteady one-dimensional hydromagnetic heat transfer flow with variable suctionorinjection. In this study, a time depen- dent similarity parameter was introduced onthe basis ofthe proposal put forward by Hasimoto . 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 , Sattar , Sattar et al. , Alam et al.  and Rahman and Sattar  are worth mention- ing.
H. L. Agarwal and P. C. Ram  have studied the effects of Hall Current onthe hydro-magnetic freeconvection with mass transfer in a rotating fluid. H. S. Takhar and P. C. Ram  have studied the effects of Hall current on hydro-magnetic free convective flow through a porous medium. B. K. Sharma and A. K. Jha  have analyzed analytically the steady combined heat and mass transfer flow with induced magnetic field. B. P. Garg  has studied combined effects of thermal radiations and hall current on moving verticalporousplatein a rotating system with variable temperature. Dufour and Soret Effects on Steady MHDFreeConvection and Mass Transfer Fluid Flow through a Porous Medium in A Rotating System have been investigated by Nazmul Islam and M. M. Alam . Hall Current Effects on Magneto hydrodynamics Fluid over an Infinite Rotating VerticalPorousPlate Embedded inUnsteady Laminar Flow have been studied by Anika et al . S. F. Ahmmed and M. K. Das  have investigated Analytical Study onUnsteadyMHDFreeConvection and Mass Transfer FlowPast a VerticalPorousPlate.
An investigation ofunsteady magnetohydrodynamic free convective flow and mass transfer during the motion of a viscous incompressible fluid through a por- ous medium, bounded by an infinite verticalporous surface, in a rotating system is presented. Theporous plane surface and theporous medium are assumed to rotate in a solid body rotation. Thevertical 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 ontheflow characteristics are discussed. It is observed that the primary velocity component decreases with the increase in ei- ther ofthe rotation parameter, the permeability parameter, orthe Hartmann number. It is also noted that the primary skin friction increases whenever there is an increase inthe Grashof number orthe modified Grashof number. It is clear that the heat transfer coefficient in terms ofthe Nusselt number decreases inthe case of both air and water when there is an increase inthe Hartmann number. It is observed that the magnitude ofthe secondary velocity profiles increases when- ever there is an increase in either ofthe Grashof number orthe modified Grashof number for mass transfer orthe permeability oftheporous media. Concentration profiles decreases with an increase inthe 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, freeconvection flows with conjugate effects of heat and mass transfer past a verticalplate have been studied extensively inthe 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]. Onthe other hand, considerable interest has been developed inthe study of interaction between magnetic field and theflowof electrically conducting fluids in a porous medium due to its applications in modern technology . Toki et al.  have studied theunsteadyfreeconvection flows of incompressible viscous fluid near a porous infinite plate with arbitrary time dependent heating plate. The effects ofchemicalreactionin two dimensional steady freeconvectionflowofan electrically conducting viscous fluid through a porous medium bounded by vertical surface with slip flow region has been studied by Senapati1 et al. . Khan et al.  analyzed the effects of radiation and thermal diffusion onMHDfreeconvectionflowofan 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 ofthe distance from the leading edge. Nakayama and Koyama (1987) analyzed combined free and forced convectionflowin Darcian and non- Darcian porous medium. Lai and Kulacki (1991) studied non-Darcy mixed convectionflow along a vertical wall in a fluid saturated porous medium. Hsieh et al. (1993) obtained non-similar solution for free and forced convectionflow from a vertical surface in a porous medium. Rees (1999) analyzed freeconvection 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 flowpast a verticalplatein a porous medium. Reddy et al. (2013) studied unsteady hydromagnetic natural convectionflowpast a moving verticalplatein a porous medium inthepresenceof radiation and chemicalreaction. Comprehensive reviews of convective flowinporous media are candidly presented inthe 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 inpresenceofsuction and blowing. Kamel  investigated theunsteadyMHDconvection through a porous medium with combined heat and mass transfer inpresenceof heat source/sink. Devi and Kandaswamy  estimated theeffectofchemicalreaction, heat and mass transfer on non-linear MHDflowpastan accelerating surface with heat source and thermal stratification inthepresenceofsuctionorinjection.
Sposito and Ciafalo (2006) studied fully developed flowofan 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 theflow 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 inan electrically conducting fluid flowing inan 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 convectionflow 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 MHDflowin a vertical channel by taking into account theeffectof viscous and ohmic dissipations, analytically by perturbation series method and numerically by finite difference technique. Umavathi and Chamkha (2011) analyzed theeffectof heat and mass transfer on mixed convective flowof a viscous incompressible fluid past a vertical infinite plateinthepresenceof heat source or sink. Garandet and Alboussiere (1992) proposed analytical solutions to the equations ofMHD that was used to model theeffectof a transverse magnetic field on buoyancy driven convectionin a two-dimensional cavity, inthe case of high Hartmaan number limit. Blosseville et al. (2007) investigated analytically a fully developed buoyant flowin a straight, horizontal rectangular duct with an axial temperature gradient inan arbitrary oriented, transverse magnetic field with insulated walls. Aruna et al. (2011) studied the developed MHD mixed convectionflowin 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 onMHDfreeconvection and mass transfer flowpast a verticalporousplatein a porous medium. They have discussed both the steady and unsteady cases. Diffusion-thermo and thermal-diffusion effects onfree convective heat and mass transfer flowin a porous medium with time dependent temperature and concentration have been investigated by Alam et al. (2007). Manna et al. (2007) have studied anunsteady viscous flowpast a flat platein a rotating system. Thermal radiation effecton a transient MHDflow with mass transfer pastan impulsively started verticalplate has been described by Alam and Sarmah (2009). Rajesh and Varma (2009) have presented the radiation and mass transfer effects onanMHDfree convective flowpastan exponentially accelerated verticalplate with variable temperature. Muthucumaraswamy et al. (2009) have studied anunsteadyflowpastan accelerated infinitely long verticalplate with variable temperature and uniform mass diffusion. Muthucumaraswamy et al. (2009) have also discussed the heat and mass transfer ontheflowpastan accelerated verticalplate with variable mass diffusion. Jha and Ajibade (2009) have investigated the diffusion-thermo effects onfree convective heat and mass transfer flowin a vertical channel with symmetric boundary conditions. The combined effects of heat and mass transfer by mixed convective MHDflowpast a porousplate with chemicalreactioninthepresenceof heat source have been described by Ahamed and Zueco (2010). Rajesh and Varma (2010) have investigated the radiation effects onanMHDflow through a porous medium with variable temperature or variable mass diffusion. Makinde (2010) has discussed anMHD heat and mass transfer over a moving verticalplate with a convective surface boundary condition. The effects of thermal radiation onanMHDfree convective flowpast
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 inan 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 inMHD pumps, MHD bearings etc. Convectioninporous media has applications in geothermal energy recovery, oil extraction, thermal energy storage and flow through filtering devices. Convective heat transfer inporous 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 , Bejan and Kraus  and Ingham et al.  excellently describe the extent ofthe 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 onthe solar surface. The study of effects of magnetic field onfreeconvectionflow 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 ofthe 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. Inthe literature, exten- sive research work is available to examine theeffectof natural convectiononflowpast a plate.
486 transfer. Afify (2009) discussed theMHDfree convective heat and mass transfer flow over a stretching sheet inthepresenceofsuction/injection with thermal diffusion and diffusion thermo effects. The influence of dust particles ontheflowof a viscous fluid has several important applications. The dust particles tend to retard theflow 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. Thepresenceof solid particles such as ash or soot in combustion energy generators and their effecton performance of such devices led to studies of particulate suspension in electrically conducting fluid inthepresenceof magnetic field. Saffman (1962) initiated the study of dusty fluids and discussed the stability ofthe laminar flowof a dusty gas in which the dust particles are uniformly distributed Chamkha (2000b) investigated theunsteady laminar hydromagnetic fluid particle flow and heat transfer in channels and circular pipes considering two phase continuum models. The effects of Hall current onthe Couette flow with heat transfer of a dusty conducting fluid inthepresenceof uniform suction/injection was studied by Attia (2005). Ghosh and Ghosh (2008) considered the problem of hydromagnetic rotating flowof a dusty fluid near a pulsating plate when theflow is generated inthe fluid particle system due to velocity tooth pulses subjected ontheplateinthepresenceof a transverse magnetic field. Makinde and Chinyoka (2010) investigated theunsteady 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  and Siegel and Howell . 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 freeconvection. For an impulsively started infinite vertical isothermal plate, Ganesan et al.  studied the effects of radiation and freeconvection, by using Rosseland approxima- tion, Brewster . Problem of radiative heat transfer with hydromagnetic flow and viscous dissipation over a stretching surface inthepresenceof variable heat flux is solved analytically by Kumar . Hossain and Takhar , Raptis and Massals , and Hossain et al.  studied the radiation effectonfree and forced convection flows past a verticalplate, including various physical aspects. Aboeldahab Emad  studied the radiation effecton heat transfer inan electrically conducting fluid at the stretching surface. At high operating temperature, ra- diation effect can be quite significant, Ghaly and Elbarbary . Heat and mass transfer ef- fects on moving plateinthepresenceof thermal radiation have been studied by Muthucuma- raswamy and Kumar  using Laplace technique. For the problem of coupled heat and mass transfer inMHDfreeconvection, theeffectof both viscous dissipation and ohmic heating are not studied inthe previous investigations. However, it is more realistic to include these two effects to explore the impact ofthe magnetic field onthe thermal transport inthe boundary layer. With this awareness, theeffectof ohmic heating ontheMHDfreeconvection heat transfer has been examined for a Newtonian fluid by Hossain . Chen  studied the problem of combined heat and mass transfer ofan electrically conducting fluid inMHD 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 ofthe 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 effectonthe surrounding liquids play an important role inthe heat transfer. In view of these applications, Nield and Kuznetsov ([22, 23]) analyzed thefree convective boundary layer flows in a porous medium saturated by nanofluid by taking Brownian motion and thermophoresis effects into consideration. Inthe first article, the authors have assumed that nanoparticles are suspended inthe nanofluid using either surfactant or surface charge technology and hence they have concluded that this prevents particles from agglomeration and deposition ontheporous matrix. Chamkha et al.  carried out a boundary layer analysis for the natural convectionpastan isothermal sphere in a Darcy porous medium saturated with a nanofluid. Nield and Kuznetsov  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 ofthe nanofluid is itself a binary fluid such as salty water. Recently, a boundary layer analysis for the natural convectionpast a horizontal platein a porous medium saturated with a nanofluid is analyzed by Gorla and Chamkha , N. Kishan et.al , studied theunsteadyMHDflowof 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 ofchemical technologies, such as polymer production and food processing. In nature, thepresenceof pure air or water is impossible. Some foreign mass may be present either naturally or mixed with the air or water. Theeffectofthepresenceof foreign mass onthefreeconvectionflowpast a semi-infinite verticalplate was studied by Gebhart and Pera (1971). Thepresenceof a foreign mass in air or water causes some kind ofchemicalreaction. During a chemicalreaction between two species, heat is also generated (Bird et al., 1992). In most cases ofchemicalreaction, thereaction rate depends onthe concentration ofthe species itself. A reaction is said to be first order if the rate ofreaction is directly proportional to concentration itself (Cussler, 1988). Chemicalreaction 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 ofthe 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 freeconvection laminar flowofan incompressible Viscoelastic fluid. Later, he was studied theMHD combined free and forced convectionflow through two parallel porous walls. Elabashbeshy  studied heat and mass transfer along a verticalplateinthepresenceof magnetic field. Samad, Karim and Mohammad  calculated numerically theeffectof thermal radiation on steady MHDfree convectoin flow taking into account the Rosseland diffusion approximaion. Loganathan and Arasu  analyzed the effects of thermophoresis particle deposition on non-Darcy MHD mixed convective heat and mass transfer past a porous wedge inthepresenceofsuctionorinjection. Ghara, Maji, Das, Jana and Ghosh  analyzed theunsteadyMHD Couette flowof a viscous fluid between two infinite non-conducting horizontal porous plates with the consideration of both Hall currents and ion-slip. The radiation effecton steady freeconvectionflow near isothermal stretching sheet inthepresenceof magnetic field is investigated by Ghaly et al. . Also, Ghaly  analyzed theeffectofthe radiation on heat and mass transfer onflow and thermal field inthepresenceof magnetic field for horizontal and inclined plates.
High temperature thermal radiation ofan optically thick gray gas becomes significant to the relevance of space technology in such way that the foundation of space laboratory inthe 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 theeffectof 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 ofthe 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 ofthe participating parameters onthe 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 ofanunsteady hydromagnetic freeconvectionflowof viscoelastic fluid (Walter’s B’) pastan infinite verticalporous flat plate through porous medium. The temperature is assumed to be oscillating with time and theeffectofthe Hall current is taken into account. Assuming constant suction at theplate, closed form solutions have been obtained for velocity and temperature profiles. Theeffectofthe various parameters, entering into the problem, onthe primary, secondary velocity profiles, the axial and transverse components of skin-friction are shown graphically followed by quantitative discussion.