It is well known that the characteristics of heat transfer are dependent on the thermal boundary conditions. Here a conjugate convective type flow or Newtonianheating is considered. Newtonianheating is a kind of wall-to-ambient heating process where the rate of heat transfer from the bounding surface with a finite heat capacity is proportional to the local surface temperature. This type of situation occurs in many important engineering devices such as in heat exchangers, gas turbines and also in seasonal thermal energy storage systems. Therefore, the interaction of conduction-convection coupled effects is of much significance from practical point of view and it must be considered when evaluating the conjugate heat transfer processes in many engineering applications. Merkin (1994) initiated the study of free convection boundary layer flow over a vertical surface withNewtonianheating while Lesnic et al. (1999, 2000) analyzed free convection boundary layer flowpastvertical and horizontal surfaces in a porous medium generated by Newtonianheating. Chaudhary and Jain (2006) investigated unsteady free convectionflowpastanimpulsively started verticalplatewithNewtonianheating. Salleh et al. (2009) discussed forced convection boundary layer flow at a forward stagnation point withNewtonianheating. Narahari and Ishak (2011) investigated the effects of thermal radiation on unsteady free convectionflow of an optically thick fluid past a movingverticalplatewithNewtonianheating. They considered three cases of interest, namely, (i) impulsive movement of the plate; (ii) uniformly accelerated movement of the plate and (iii) exponentially accelerated
It is noticed that when the density of an electrically conducting fluid is low and/or applied magnetic field is strong, Hall current plays a vital role in determining flow-features of the fluid flow problems because it induces secondary flowin the flow-field (Sutton and Sherman (1965). Taking into account of this fact, Aboeldahab and Elbarbary (2001) and Seth et al. (2012) investigated the effects of Hall current on hydromagnetic free convection boundary layer flowpast a flat plate considering different aspects of the problem. It is noteworthy that Hall current induces secondary flowin the flow-field which is also the characteristics of Coriolis force. Therefore, it is essential to compare and contrast the effects of these two agencies and also to study their combined effects on such fluid flow problems. Narayana et al. (2013) studied the effects of Hall current and radiation- absorption on MHD naturalconvection heat and mass transfer flow of a micropolar fluid in a rotating frame of reference. Recently, Seth et al. (2013a) investigated the effects of Hall current and rotation on unsteadyhydromagneticnaturalconvectionflow of a viscous, incompressible, electrically conducting and heat absorbing fluid pastanimpulsivelymovingverticalplatewith ramped temperature in a porous medium taking into account the effects of thermal diffusion. Aim of the present investigation is to study unsteadyhydromagneticnaturalconvection heat and mass transfer flowwith Hall current of a viscous, incompressible, electrically conducting, temperature dependent heat absorbing and optically thin heat radiating fluid pastan accelerated movingverticalplate through fluid saturated porous medium in a rotating environment when temperature of the plate has a temporarily ramped profile. This problem has not yet received any attention from the researchers although naturalconvection heat and mass transfer flow of a heat absorbing and radiating fluid resulting from such ramped temperature profile of a platemovingwith time dependent velocity may have strong bearings on numerous problems of practical interest where initial temperature profiles are of much significance in designing of so many hydromagnetic devices and in several industrial processes occurring at high temperatures where the effects of thermal radiation and heat absorption play a vital role in the fluid flow characteristics.
Raptis et al.  discussed the effect of thermal radiation on MHD Flow. Saha and Hossain  studied the naturalconvectionflowwith combined buoyancy effects due to thermal and mass diffusion in a thermally stratified media. Das et al.  estimated numerically the effect of mass transfer on unsteadyflowpastan accelerated vertical porous platewith suction. Mazumdar and Deka  analyzed the MHD flowpastanimpulsively started infinite verticalplatein presence of thermal radiation. Das and his co- workers  discussed the magnetohydrodynamic unsteadyflow of a viscous stratified fluid through a porous medium past a porous flat movingplatein the slip flow regime with heat source. In a separate paper Das et al.  analyzed the mass transfer effects on MHD flow and heat transfer past a vertical porous plate through a porous medium under oscillatory suction and heat source. Recently, Das and his associates  reported the hydromagnetic convective flowpast a vertical porous plate through a porous medium with suction and heat source. More recently, Das and Tripathy  estimated the effect of periodic suction on three dimensional flow and heat transfer past a vertical porous plate embedded in a porous medium.
In all the investigations mentioned above, viscous mechanical dissipation is neglected. A number of authors have considered viscous heating effects on Newtonian flows. Mahajan et al.  reported the influence of viscous heating dissipation effects innatural convective flows, showing that the heat transfer rates are reduced by an increase in the dissipation parameter. Isreal- Cookey et al.  investigated the influence of viscous dissipation and radi- ation on unsteady MHD free convectionflowpastan infinite heated verticalplatein a porous medium with time dependent suction. Zueco  used net- work simulation method (NSM) to study the effects of viscous dissipation and radiation on unsteady MHD free convectionflowpast a vertical porous plate. Suneetha et al.  have analyzed the thermal radiation effects on hydromagnetic free convectionflowpastanimpulsively started verticalplatewith variable surface temperature and concentration by taking into account of the heat due to viscous dissipation. Recently Suneetha et al.  stud- ied the effects of thermal radiation on the natural conductive heat and mass transfer of a viscous incompressible gray absorbing-emitting fluid flowing pastanimpulsively started movingverticalplatewith viscous dissipation. Very recently Hiteesh  studied the boundary layer steady flow and heat trans- fer of a viscous incompressible fluid due to a stretching platewith viscous dissipation effect in the presence of a transverse magnetic field.
Kumari and Nath  have studied development of two-dimensional bound- ary layer withan applied magnetic field due to an impulsive motion. Muthuku- maraswamy and Ganesan  have studied unsteadyflowpastanimpulsively started verticalplatewith heat and mass transfer. Kim  presented an analysis of anunsteady MHD convectionflowpast a verticalmovingplate embedded in a porous medium in the presence of transverse magnetic field. Helmy  studied MHD unsteady free convectionflowpast a vertical porous plate. Raptis  analyzed the thermal radiation and free convectionflow through a porous medium bounded by a vertical infinite porous plate 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 free convectionflowwith constant heat flux. Ibrahim [?] studied the effects of chemical reaction and radiation absorption on transient hydro magnetic naturalconvectionflowwith wall transpiration and heat source. Anjalidevi and Kandasamy  have examined the effect of a chemical reaction on the flowin the presence of heat transfer and magnetic field. Mansour et al. analyzed the effect of chemical reaction and viscous on MHD naturalconvection 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.
Free convectionflowpast a verticalplate has been extensively studied and continues to receive much attention due to its industrial and technological applications. It is encountered, for instance, in the cooling of nuclear reactors or in the study of environmental heat transfer processes. Soundalgekar and Gupta  and Singh and Kumar  studied the free convectionflow over an accelerated, respectively exponentially accelerated, infinite verticalplate, while Merkin  presented a discussion on the similarity solutions. Transient free convectionflowpastan infinite verticalplate has been studied, for instance, by Ingham  and Das et al. . Many other unsteady free convection flows over an infinite plate, taking into account radiative, porous or magnetic effects, have also been investigated under different sets of boundary conditions. Some of the most recent and interesting results seem to be those obtained by Toki and Tokis , Toki , Rajesh , Narahari and Ishak , Narahari and Nayan , Samiulhaq et al. [11,12] and Narahari and Debnath . In their work, Narahari and Debnath, for instance, consider the unsteady magnetohydrodynamic free convectionflowwith constant heat flux and heat generation or absorption, and obtain exact solutions when the plate is exponentially or uniformly accelerated. Free convective boundary layer flows withNewtonianheating or thermal slip conditions have been numerically investigated by Uddin et al. , respectively Khan et al. . However, in all these works, boundary conditions for velocity are imposed, although in some problems, the force applied on the boundary is specified. In this case, unlike the usual ‘‘no slip’’ condition, a boundary condition on the shear stress has to be used.
The influence of internal heat generation in a problem reveals that it affects the temperature distribution strongly. Internal heat generation is related in the fields of disposal of nuclear waste, storage of radioactive materials, nuclear reactors safely analysis, fire and combustion studies and in many industrial processes. Consideration of internal heat generation becomes a key factor in many engineering applications. Heat generation can be assumed to be constant or space temperature dependent. Crepeau and Clarksean (1997) applied a space dependent heat generation in their study on flow and heat transfer from verticalplate. They observed that the exponentially decaying heat generation model can be used in mixtures where a radioactive material is surrounded by inert alloys. Makinde (2011) computed similarity solutions for naturalconvection from a movingverticalplatewith internal heat generation. It was found that an increase in the exponentially decaying internal heat generation causes a further increase in both velocity and thermal boundary layer thicknesses. Ganga et al (2015) studied the effects of internal heat generation or absorption on magnetohydrodynamic and radiative boundary layer flow of nanofluid over a verticalplatewith viscous and ohmic dissipation.
conductivity. Hossain  studied the viscous and Joule heating effects on MHD free convectionflowwith variable plate temperature. Soundelgekar et al.  presented transient free convection of dissipative fluid pastan infinite vertical porous plate. Takhar et al.  presented radiation effects on MHD free convectionflow of a radiating gas past a semi infinite verticalplate. Soundalgekar and Mohammed  presented free convection effects on MHD flowpastanimpulsively started infinite vertical isothermal plate. Gokhale  studied magneto hydrodynamic transient-free convectionpast a semi infinite verticalplatewith constant heat flux. Sattar and Maleque  studied unsteady MHD naturalconvectionflow along an accelerated porous platewith hall current and mass transfer in a rotating porous medium. Sattar et al.  studied free convectionflow and heat transfer through a porous vertical flat plate immersed in a Porous Medium. Abdus Samad and Mansur Rahman  presented thermal radiation interaction withunsteady MHD flowpast a vertical porous plate immersed in a porous medium.
H. L. Agarwal and P. C. Ram  have studied the effects of Hall Current on the hydro-magnetic free convectionwith 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 flowwith induced magnetic field. B. P. Garg  has studied combined effects of thermal radiations and hall current on movingvertical porous platein a rotatingsystemwith variable temperature. Dufour and Soret Effects on Steady MHD Free Convection and Mass Transfer Fluid Flow through a Porous Medium in A RotatingSystem have been investigated by Nazmul Islam and M. M. Alam . Hall Current Effects on Magneto hydrodynamics Fluid over an Infinite RotatingVertical Porous Plate Embedded inUnsteady Laminar Flow have been studied by Anika et al . S. F. Ahmmed and M. K. Das  have investigated Analytical Study on Unsteady MHD Free Convection and Mass Transfer FlowPast a Vertical Porous Plate.
Muthucumaraswamy and Ganesh  studied unsteadyflow of an incompressible flu- id pastanimpulsively started verticalplatewith heat and mass transfer. Acharya et al.  dis- cussed magnetic field effects on free convection and mass transfer flow through porous me- dium with constant suction and constant heat flux. Chaudhary and Jain  analyzed combined heat and mass transfer effects on MHD free convectionflowpastan oscillating plate embedded in porous medium. Dinarvand and Rashidi  studied a reliable treatment of homotopy analy- sis method for 2-D viscous flowin a rectangular domain bounded by two moving porous walls. Muthuraj and Srinivas  discussed heat transfer effects on MHD oscillatory flowinan asymmetric wavy channel. Muthucumaraswamy et al.  analyzed chemical reaction effects on infinite verticalplatewith uniform heat flux and variable mass diffusion. Singh and Verma  discussed heat transfer effects in a 3-D flow through a porous medium with a periodic permeability. Gersten and Gross  analyzed flow and heat transfer effects along a plane wall with periodic suction. Singh  discussed the effect of injection/suction parameter on 3-D Couette flowwith transpiration cooling. Gupta and Johari  studied the effect of MHD in- compressible flowpast a highly porous medium which was bounded by a vertical infinite por- ous plate. Singh et al.  analyzed the heat transfer effects on 3-D fluctuating flow through a porous medium with a variable permeability. Rashidi and Sadri  analyzed the solution of the laminar viscous flowin a semi-porous channel in the presence of a uniform magnetic field by using the differential transform method. Rashidi and Erfani  discussed a new analytical study of MHD stagnation-point flowin porous media with heat transfer.
The previous studies, dealing with the transport phenomena of momentum and heat transfer, have dealt with one component phases which posses a natural tendency to reach equilibrium conditions. However, there are activities, especially in industrial and chemical engineering processes, where a system contains two or more components whose concentrations vary from point to point. In such a system there is a natural tendency for mass to be transferred, minimizing the concentration differences within the system and the transport of one constituent, from a region of higher concentration to that of a lower concentration. This is called mass transfer. Stokes  gave the first exact solution to the Navier–Stokes equation for the flow of a viscous incompressible fluid pastanimpulsively started infinite horizontal plate. Panda et al  analyzed anunsteady free convictive flow and mass transfer of a rotating elastic-viscous liquid through porous media past a vertical porous plate. Sattar  discussed the free convection and mass transfer flow though a porous medium pastan infinite vertical porous platewith time dependent temperature and concentration. The application of boundary layer techniques to mass transfer has been of considerable assistance in developing the theory of separation processes and chemical kinetics. The phenomenon of heat and mass transfer has been the object of extensive research due to its applications in Science and Technology.
growth. Until recently this study has been largely concerned withflow and heat transfer characteristics in various physical situations. Radiative magnetohydrodynamic flows arise in many areas of technology and applied physics including oxide melt materials processing (Shu et al. (2004)), astrophysical fluid dynamics (Stone and Norman (1992); Vishwakarma et al. (1987)), plasma flow switch performance (Bowers et al. (1990)), MHD energy pumps operating at very high temperatures (Biberman et al.(1979)) and hypersonic aerodynamics (Ram and Pandey (1980)). Takhar et al. (1996) investigated the effects of radiation on the MHD free convectionflow of radiating gas past a semi-infinite verticalplate. Raptis and Masslas (1998) studied unsteady magnetohydrodynamics convectionin a gray, absorbing- emitting but non-scattering fluid regime using the Rosseland radiation model. A similar study was communicated by Raptis and Perdikis(2000). Azzam (2002) considered thermal radiation flux influence on hydromagnetic mixed convective steady optically-thick laminar boundary layer flow also using Rosseland approximation. Helliwell and Mosa (1979) reported on thermal radiation effects in buoyancy-driven hydromagneticflowin a horizontal channel flowwithan axial temperature gradient in the presence of Joule and Viscous heating. Yasar and Moses (1992) developed a
In this paper, we study the unsteady free convectionflowpast a vertical porous platewithNewtonianheating. At time t 0 , both the fluid and the plate are at rest with constant temperature T . At time t > 0 , the plate is given an impulsive motion in the vertically upward direction against gravitational field with a uniform velocity U 0 while fluid is sucked from the platewith velocity v = v 0 , where v 0 > 0 is the suction velocity
The study of an electrically conducting fluid in engineering applications is of considerable interest, especially in metallurgical and metal working processes or in the separation of molten metals from non-metallic inclusions by the application of a magnetic field. The phase change problem occurs in casting welding, purification of metals and in the formation of ice layers on the oceans as well as on aircraft surfaces. Because of its importance, accurate and robust methods of modelling phase change problems are of great interest. The velocity field in the liquid phase has a significant effect in determining the quality of the final product, and therefore, it is a great interest to study the fluid and solid phases. Recently, a significant number of studies have been conducted using computational fluid dynamics to enhance the physical and understand mathematical modelling capabilities in liquid – solid phase change as mentioned in introduction to convectionin porous medium. High temperature plasmas, cooling of nuclear reactors, liquid metal fluids, magneto hydrodynamics (MHD) accelerators, and power generation systems are important applications for radiation heat transfer from a vertical wall to conductive grey fluids. Hossain and Takhar (1996)
Recently, Alam and Huda  analyzed a new approach for local similarity solutions of anunsteadyhydromagnetic free convective heat transfer flow along a permeable flat surface.But the effect of internal heat generation was absent on the flow field. So, the main objective of the present study is to extend the work of Alam and Huda  to free con- vective heat transfer flow along a vertical porous flat platewith internal heat generation/absorption.This problem has not been introduced in the open literature, despite its fundamental significance. Using similarity transforma- tion, the governing partial differential equations are reduce to a non-linear ordinary differential equation which are solved numerically by applying sixth-order Runge-Kutta method with Nachtsheim-Swigert shooting iteration technique.
The boundary layer flowpast a stretching surface in the presence of a magnetic field has much practical relevance in polymer processing and in other several industrial processes. Along with this, a new dimension is added to the study of flow and heat transfer effects over a stretching surface by considering the effect of thermal radiation. Thermal radiation effects may play an important role in controlling heat transfer in industry where the quality of the final product depends to a great extend on the heat controlling factors and the knowledge of radiative heat transfer in the system can perhaps lead to a desired product with sought qualities. High temperature plasmas, cooling of nuclear reactors and liquid metal fluids are some important applications of radiative heat transfer. The radiative flow of an electrically conducting fluid with high temperature in the presence of a magnetic field are encountered in electrical power generation, astrophysical flows, solar power technology, space vehicle re-entry, nuclear engineering applications and in other industrial areas.
Borkakati and Srivastava investigated free and forced convection and MHD flow. In a fluid, the variation of temperature causes variation of density. This in turn raises force of buoyancy which governs the fluid motion. This type of unsteady fluid motion under the action of uniform magnetic field applied externally reduces the heat transfer and the skin friction considerably. This process of reduction of heat transfer and skin friction of the fluid motion has various engineering applications such as nuclear reactor, power transformation etc. Borkakati and Chakraborty investigated the nature and behaviour of a viscous, incompressible, electrically conducting fluid over a flat plate which is movingwith a uniform speed in a quiescent fluid in presence of a uniform magnetic field. In their conclusion they have found that for an incompressible fluid, both the fluid velocity and temperature gradually decreases with the increase of viscosity parameter. Elbashbeshy studied heat and mass transfer in the same problem in presence of variable transverse magnetic field. The unsteady problem in a channel was studied numerically by Attia with temperature dependence viscosity. He also considered steady state solution for velocity and temperature. In his study he analyzed the effect of viscosity parameter defined as ratio of viscosity of the fluid at two different temperatures. In the recent years, Attia studied anunsteady magnetohydrodynamic flow and heat transfer
with numerical solution obtained by shooting method with fourth- order-Runge-Kutta algorithm. Bhargava et al.  studied mixed convectionflow of a Micropolar fluid over a porous stretching sheet by implementing finite element method. The stagnation point flow of a micropolar fluid over a stretching surface has been discussed by Nazar et al. . The steady MHD mixed convectionflow towards a vertical stretching surface immersed inan incompressible micropolar fluid was investigated by Ishak et al. .
Consider anunsteady MHD free convectionflowpast infinite vertical porous plate which is thermally stratified. Let us consider anunsteady free convective flow of an electrically conducting viscous fluid through a porous medium along a semi-infinite vertical porous plate y 0 in a rotatingsystem under the influence of transversely applied magnetic field. The flow is assumed to be in the x -direction which is taken along the platein the upward direction and y -axis is normal to it. Initially the fluid is at rest, after the whole system is allowed to rotate with a constant angular velocity about the y-axis. Since the systems rotate about the y-axis, so it is assumed as (0, ,0) . The temperature of the plate raised from T w to T ,
Recently, inding analytical approximating solutions of nonlinear equations has widespread applications in numerical mathematics and applied mathematics and there has appeared an ever increas- ing interest of scientists and engineers in analytical techniques for studying nonlinear problems. Homotopy Analysis Method has been proposed by Liao and a systematic and clear exposition on this method is given in [1-2]. HAM is a powerful mathemati- cal technique and has already been applied to several nonlinear problems [3-21]. This method contains an auxiliary parameter h which provides us with a simple way to adjust and control the convergence region of the solutions. The equations modeling non- Newtonian incompressible luid low give rise to highly nonlinear differential equations. Such non-Newtonian luids ind wide ap- plications in commerce, industry and have now become the focus of extensive study.