It is well known that the characteristics of heat transfer are dependent on the thermal boundary conditions. Here a conjugate convective type **flow** or **Newtonian** **heating** is considered. **Newtonian** **heating** 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 **with** **Newtonian** **heating** while Lesnic et al. (1999, 2000) analyzed free **convection** boundary layer **flow** **past** **vertical** and horizontal surfaces **in** a porous medium generated by **Newtonian** **heating**. Chaudhary and Jain (2006) investigated **unsteady** free **convection** **flow** **past** **an** **impulsively** started **vertical** **plate** **with** **Newtonian** **heating**. Salleh et al. (2009) discussed forced **convection** boundary layer **flow** at a forward stagnation point **with** **Newtonian** **heating**. Narahari and Ishak (2011) investigated the effects of thermal radiation on **unsteady** free **convection** **flow** of **an** optically thick fluid **past** a **moving** **vertical** **plate** **with** **Newtonian** **heating**. They considered three cases of interest, namely, (i) impulsive movement of the **plate**; (ii) uniformly accelerated movement of the **plate** and (iii) exponentially accelerated

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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 **flow** **in** 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 **flow** **past** a flat **plate** considering different aspects of the problem. It is noteworthy that Hall current induces secondary **flow** **in** 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 **natural** **convection** 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 **unsteady** **hydromagnetic** **natural** **convection** **flow** of a viscous, incompressible, electrically conducting and heat absorbing fluid **past** **an** **impulsively** **moving** **vertical** **plate** **with** ramped temperature **in** a porous medium taking into account the effects of thermal diffusion. Aim of the present investigation is to study **unsteady** **hydromagnetic** **natural** **convection** heat and mass transfer **flow** **with** Hall current of a viscous, incompressible, electrically conducting, temperature dependent heat absorbing and optically thin heat radiating fluid **past** **an** accelerated **moving** **vertical** **plate** 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 **natural** **convection** heat and mass transfer **flow** of a heat absorbing and radiating fluid resulting from such ramped temperature profile of a **plate** **moving** **with** 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.

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Raptis et al. [11] discussed the effect of thermal radiation on MHD **Flow**. Saha and Hossain [12] studied the **natural** **convection** **flow** **with** combined buoyancy effects due to thermal and mass diffusion **in** a thermally stratified media. Das et al. [13] estimated numerically the effect of mass transfer on **unsteady** **flow** **past** **an** accelerated **vertical** porous **plate** **with** suction. Mazumdar and Deka [14] analyzed the MHD **flow** **past** **an** **impulsively** started infinite **vertical** **plate** **in** presence of thermal radiation. Das and his co- workers [15] discussed the magnetohydrodynamic **unsteady** **flow** of a viscous stratified fluid through a porous medium **past** a porous flat **moving** **plate** **in** the slip **flow** regime **with** heat source. **In** a separate paper Das et al. [16] 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 [17] reported the **hydromagnetic** convective **flow** **past** a **vertical** porous **plate** through a porous medium **with** suction and heat source. More recently, Das and Tripathy [18] estimated the effect of periodic suction on three dimensional **flow** and heat transfer **past** a **vertical** porous **plate** embedded **in** a porous medium.

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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**.

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Free **convection** **flow** **past** a **vertical** **plate** 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 [1] and Singh and Kumar [2] studied the free **convection** **flow** over **an** accelerated, respectively exponentially accelerated, infinite **vertical** **plate**, while Merkin [3] presented a discussion on the similarity solutions. Transient free **convection** **flow** **past** **an** infinite **vertical** **plate** has been studied, for instance, by Ingham [4] and Das et al. [5]. 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 [6], Toki [7], Rajesh [8], Narahari and Ishak [9], Narahari and Nayan [10], Samiulhaq et al. [11,12] and Narahari and Debnath [13]. **In** their work, Narahari and Debnath, for instance, consider the **unsteady** magnetohydrodynamic free **convection** **flow** **with** 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 **with** **Newtonian** **heating** or thermal slip conditions have been numerically investigated by Uddin et al. [14], respectively Khan et al. [15]. 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.

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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 **vertical** **plate**. 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 **natural** **convection** from a **moving** **vertical** **plate** **with** 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 **vertical** **plate** **with** viscous and ohmic dissipation.

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conductivity. Hossain [13] studied the viscous and Joule **heating** effects on MHD free **convection** **flow** **with** variable **plate** temperature. Soundelgekar et al. [14] presented transient free **convection** of dissipative fluid **past** **an** infinite **vertical** porous **plate**. Takhar et al. [15] presented radiation effects on MHD free **convection** **flow** of a radiating gas **past** a semi infinite **vertical** **plate**. Soundalgekar and Mohammed [16] presented free **convection** effects on MHD **flow** **past** **an** **impulsively** started infinite **vertical** isothermal **plate**. Gokhale [17] studied magneto hydrodynamic transient-free **convection** **past** a semi infinite **vertical** **plate** **with** constant heat flux. Sattar and Maleque [18] studied **unsteady** MHD **natural** **convection** **flow** along **an** accelerated porous **plate** **with** hall current and mass transfer **in** a **rotating** porous medium. Sattar et al. [19] studied free **convection** **flow** and heat transfer through a porous **vertical** flat **plate** immersed **in** a Porous Medium. Abdus Samad and Mansur Rahman [20] presented thermal radiation interaction **with** **unsteady** MHD **flow** **past** a **vertical** porous **plate** immersed **in** a porous medium.

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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**.

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Muthucumaraswamy and Ganesh [4] studied **unsteady** **flow** of **an** incompressible flu- id **past** **an** **impulsively** started **vertical** **plate** **with** heat and mass transfer. Acharya et al. [5] 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 [6] analyzed combined heat and mass transfer effects on MHD free **convection** **flow** **past** **an** oscillating **plate** embedded **in** porous medium. Dinarvand and Rashidi [7] studied a reliable treatment of homotopy analy- sis method for 2-D viscous **flow** **in** a rectangular domain bounded by two **moving** porous walls. Muthuraj and Srinivas [8] discussed heat transfer effects on MHD oscillatory **flow** **in** **an** asymmetric wavy channel. Muthucumaraswamy et al. [9] analyzed chemical reaction effects on infinite **vertical** **plate** **with** uniform heat flux and variable mass diffusion. Singh and Verma [10] discussed heat transfer effects **in** a 3-D **flow** through a porous medium **with** a periodic permeability. Gersten and Gross [11] analyzed **flow** and heat transfer effects along a plane wall **with** periodic suction. Singh [12] discussed the effect of injection/suction parameter on 3-D Couette **flow** **with** transpiration cooling. Gupta and Johari [13] studied the effect of MHD **in**- compressible **flow** **past** a highly porous medium which was bounded by a **vertical** infinite por- ous **plate**. Singh et al. [14] analyzed the heat transfer effects on 3-D fluctuating **flow** through a porous medium **with** a variable permeability. Rashidi and Sadri [15] analyzed the solution of the laminar viscous **flow** **in** a semi-porous channel **in** the presence of a uniform magnetic field by using the differential transform method. Rashidi and Erfani [16] discussed a new analytical study of MHD stagnation-point **flow** **in** porous media **with** heat transfer.

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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 [15] gave the first exact solution to the Navier–Stokes equation for the **flow** of a viscous incompressible fluid **past** **an** **impulsively** started infinite horizontal **plate**. Panda et al [16] analyzed **an** **unsteady** free convictive **flow** and mass transfer of a **rotating** elastic-viscous liquid through porous media **past** a **vertical** porous **plate**. Sattar [17] discussed the free **convection** and mass transfer **flow** though a porous medium **past** **an** infinite **vertical** porous **plate** **with** 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.

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growth. Until recently this study has been largely concerned **with** **flow** 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 **convection** **flow** of radiating gas **past** a semi-infinite **vertical** **plate**. Raptis and Masslas (1998) studied **unsteady** magnetohydrodynamics **convection** **in** 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 **hydromagnetic** **flow** **in** a horizontal channel **flow** **with** **an** axial temperature gradient **in** the presence of Joule and Viscous **heating**. Yasar and Moses (1992) developed a

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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 **convection** **in** 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)

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Recently, Alam and Huda [18] analyzed a new approach for local similarity solutions of **an** **unsteady** **hydromagnetic** 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 [18] to free con- vective heat transfer **flow** along a **vertical** porous flat **plate** **with** 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.

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The boundary layer **flow** **past** 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.

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Borkakati and Srivastava[1] 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[2] investigated the nature and behaviour of a viscous, incompressible, electrically conducting fluid over a flat **plate** which is **moving** **with** 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[3] 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[4] **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[5] studied **an** **unsteady** magnetohydrodynamic **flow** and heat transfer

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Consider **an** **unsteady** MHD free **convection** **flow** **past** infinite **vertical** porous **plate** which is thermally stratified. Let us consider **an** **unsteady** free convective **flow** of **an** electrically conducting viscous fluid through a porous medium along a semi-infinite **vertical** porous **plate** y 0 **in** a **rotating** **system** under the influence of transversely applied magnetic field. The **flow** is assumed to be **in** the x -direction which is taken along the **plate** **in** 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 ,

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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.

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