Top PDF Mixed convection boundary layer flow over a moving vertical flat plate in an external fluid flow with viscous dissipation effect.

Mixed convection boundary layer flow over a moving vertical flat plate in an external fluid flow with viscous dissipation effect.

Mixed convection boundary layer flow over a moving vertical flat plate in an external fluid flow with viscous dissipation effect.

Mixed convection flows, or combined forced and free convec- tion flows, arise in many transport processes both naturally and in engineering applications. They play an important role, for example, in atmospheric boundary-layer flows, heat exchangers, solar collectors, nuclear reactors and in electronic equipment. Such processes occur when the effects of buoyancy forces in forced convection or the effects of forced flow in free convection become significant. The interaction of forced and free convection is especially pronounced in situations where the forced flow velocity is low and/or the temperature differences are large. This flow is also a relevant type of flow appearing in many industrial processes, such as manufacture and extraction of polymer and rubber sheets, paper production, wire drawing and glass-fiber production, melt spinning, continuous casting, etc. (Tadmor and Klein [1]). This flow has also many industrial applications such as heat treatment of material traveling between a feed roll and wind-up roll or conveyer belts, extrusion of steel, cooling of a large metallic plate in a bath, liquid films in condensation process and in aerodynam- ics, etc. As per standard texts books by Bejan [2], Kays and Crawford [3], Bergman et al. [4] and other literatures the free and mixed convection flow occur in atmospheric and oceanic circulation, electronic machinery, heated or cooled enclosures, electronic power supplies, etc. This topic has also many applications such as its influence on operating temperatures of power generating and electronic devices. In addition it should be mentioned that this type of flow plays a great role in thermal
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Natural Convection Heat and Mass Transfer Flow with Hall Current, Rotation, Radiation and Heat Absorption Past an Accelerated Moving Vertical Plate with Ramped Temperature

Natural Convection Heat and Mass Transfer Flow with Hall Current, Rotation, Radiation and Heat Absorption Past an Accelerated Moving Vertical Plate with Ramped Temperature

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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The effects of thermal radiation and viscous dissipation on MHD heat and mass diffusion flow past an oscillating vertical plate embedded in a porous medium with variable surface conditions

The effects of thermal radiation and viscous dissipation on MHD heat and mass diffusion flow past an oscillating vertical plate embedded in a porous medium with variable surface conditions

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. [25] reported the influence of viscous heating dissipation effects in natural convective flows, showing that the heat transfer rates are reduced by an increase in the dissipation parameter. Isreal- Cookey et al. [26] investigated the influence of viscous dissipation and radi- ation on unsteady MHD free convection flow past an infinite heated vertical plate in a porous medium with time dependent suction. Zueco [27] used net- work simulation method (NSM) to study the effects of viscous dissipation and radiation on unsteady MHD free convection flow past a vertical porous plate. Suneetha et al. [28] have analyzed the thermal radiation effects on hydromagnetic free convection flow past an impulsively started vertical plate with variable surface temperature and concentration by taking into account of the heat due to viscous dissipation. Recently Suneetha et al. [29] stud- ied the effects of thermal radiation on the natural conductive heat and mass transfer of a viscous incompressible gray absorbing-emitting fluid flowing past an impulsively started moving vertical plate with viscous dissipation. Very recently Hiteesh [30] studied the boundary layer steady flow and heat trans- fer of a viscous incompressible fluid due to a stretching plate with viscous dissipation effect in the presence of a transverse magnetic field.
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Unsteady Hydromagnetic Natural Convection Flow past an Impulsively Moving Vertical Plate with Newtonian Heating in a Rotating System

Unsteady Hydromagnetic Natural Convection Flow past an Impulsively Moving Vertical Plate with Newtonian Heating in a Rotating System

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).
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Effect of Variable Gravity on Darcy Flow with Impressed Horizontal Gradient and Viscous Dissipation

Effect of Variable Gravity on Darcy Flow with Impressed Horizontal Gradient and Viscous Dissipation

tion to the energy equation has been neglected. However, in recent years it has been noted that in mixed convection and vigorous natural con- vection flows in porous media, viscous dissipa- tion may become more significant. Also grav-ity has been assumed to be constant in most of the experimental and theoretical studies. But this assumption may not give accurate result while considering large scale flows, e.g. flows in ocean, atmosphere or earth’s mantle, be-cause the gravity field is varying with height from earth’s surface. In this cases consider-ing gravity as variable will help one to pro-duce more accurate results. The convection of a fluid through a flat layer bounded above and below by perfectly conducting media with vertical temperature gradient is considered by Horton and Rogers (1945). The instability of a horizontal fluid layer where the gravitational field is varying with height is investigated by Pradhan and Samal (1987). Later Straughan (1989) done the linear instabilty and nonlin-ear energy stability analysis for convection in a horizontal porous layer with variable gravity effect. Alex et al. (2001) investigated the ef-fect of variable gravity on the onset of convec-tion in an isotropic porous medium with inter-nal heat source and inclined temperature gradi-ent. The effect of variable gravity field on the onset of thermosolutal convection in a fluid sat-urated isotropic porous layer is studied by Alex and Patil (2001). Barletta et al. (2009) con-sidered a horizontal porous layer with an adia-batic lower boundary and an isothermal upper boundary and discussed the effect of viscous dissipation on parallel Darcy flow by means of linear stability analysis. The effect of viscous dissipation, on the stability of flow in
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Unsteady Similarity Solution of Free convective boundary layer flow over porous plate with variable properties considering viscous dissipation and Slip Effect

Unsteady Similarity Solution of Free convective boundary layer flow over porous plate with variable properties considering viscous dissipation and Slip Effect

The study of boundary layer flow over porous surface moving with constant velocity in an ambient fluid was initiated by Sakiadis [1]. Erickson et al. [2] extended Sakiadis [1] problem to include blowing or suction at the moving porous surface. Subsequently Tsou et al. [3] presented a combined analytical and experimental study of the flow and temperature fields in the boundary layer on a continuous moving surface. R. Ellahi et al. [4] investigated numerical analysis of unsteady flows with viscous dissipation and nonlinear slip effects. Excellent reviews on this topic are provided in the literature by Nield and Bejan [5], Vafai [6], Ingham and Pop [7] and Vadasz [8]. Recently, Cheng and Lin [9] examined the melting effect on mixed convective heat transfer from a permeable over a continuous Surface embedded in a liquid saturated porous medium with aiding and opposing external flows. The unsteady boundary layer flow over a stretching sheet has been studied by Devi et al. [10], Elbashbeshy and Bazid [11], Tsai et al. [12] and Ishak [13].
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Chemical reaction and radiation effects on MHD free convection from an impulsively started infinite vertical plate with viscous dissipation

Chemical reaction and radiation effects on MHD free convection from an impulsively started infinite vertical plate with viscous dissipation

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.
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Unsteady Hydromagnetic Flow of a Heat Absorbing Dusty Fluid Past a Permeable Vertical Plate with Ramped Temperature

Unsteady Hydromagnetic Flow of a Heat Absorbing Dusty Fluid Past a Permeable Vertical Plate with Ramped Temperature

when the fluid is driven by a constant pressure gradient and subjected to a uniform external magnetic field applied perpendicular to the plates with Navier slip boundary condition. In all the above investigations a solution for the flow and heat transfer is obtained assuming the temperature at the interface of the plate as constant. However, there exist several problems of physical interest which may require non-uniform conditions. Gireesha et al. (2011) obtained the solution for the boundary layer flow and heat transfer of a dusty fluid over a stretching sheet with non-uniform heat source/sink. They considered two types of heating processes namely (i) prescribed surface temperature and, (ii) prescribed surface heat flux. Ramesh et al. (2012) analyzed the steady two-dimensional MHD flow of a dusty fluid near the stagnation point over a permeable stretching sheet with the effect of non- uniform source/sink. Recently, the effects of ramped surface temperature on the flow and heat transfer of a viscous, incompressible, and electrically conducting dusty fluid in the presence of a transverse magnetic field are studied by (Nandkeolyar et al. 2013 ; Nandkeolyar and Das 2013). They assumed that the surface temperature increases up to a specific time and then it becomes constant. They also compared the flow of dusty fluids through a wall having ramped temperature with that of a flow past an isothermal wall.
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J. Braz. Soc. Mech. Sci. & Eng.  vol.34 número4

J. Braz. Soc. Mech. Sci. & Eng. vol.34 número4

The study of flow, heat and mass transfer about natural convection of non-Newtonian fluids in porous media has gained much attention from the researchers because of its engineering and industrial applications. These applications include design of chemical processing equipment, formation and dispersion of fog, distributions of temperature and moisture over agricultural fields and groves of fruit trees and damage of crops due to freezing and pollution of the environment, etc. Several investigators have extended the convection of heat and mass transfer problems to fluids exhibiting non-Newtonian rheology. Different models have been proposed to explain the behavior of non-Newtonian fluids. Among these, the power law model gained importance. Although this model is merely an empirical relationship between the stress and velocity gradients, it has been successfully applied to non-Newtonian fluids experimentally. Free convection from a horizontal line heat source in a power-law fluid-saturated porous medium was studied by Nakayama (1993). The study of free convection in boundary layer flows of power law fluids past a vertical flat plate with suction/injection was done by Sahu and Mathur (1996). They observed that the suction/injection has significant effect on the velocity and temperature fields. Free convection heat and mass transfer of non-Newtonian power law fluids with yield stress from a vertical flat plate in a saturated porous media was studied by Rami and Arun (2000). They concluded that the velocity, temperature, and concentration profiles as well as the local heat and mass transfer rates are significantly affected by the fluid rheology in addition to the buoyancy ratio and the Lewis number of the fluid. The flow of natural convection heat and mass transfer
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Analytical solution of conjugate turbulent forced convection boundary layer flow over plates

Analytical solution of conjugate turbulent forced convection boundary layer flow over plates

When the temperature distribution of the solid body and that of the fluid flow are coupled, the resulting problem is known conjugate heat transfer. This problem, for the first time, was studied by Perelman [1] and Luikov et al. [2]. Perelman [1] used the method of the asymptotic solution to solve the integral equation occurring in the conjugate heat- transfer problem. A generalized Fourier sine transform was presented by Luikov et al. [2] for the semi-infinite plate. Trevino and Linan [3] modeled the external heating of a flat plate cooled under a convective laminar flow with and accounted for the axial heat condu c- tion in the plate by solving the integro-diffrential equation using perturbation. Determina- tion of plate temperature in case of combined conduction, convection and radiation heat exchange is carried out by Sohal and Howel [4]. Later, Karvinen [5] presented an approxi- mate method is presented by for calculating heat transfer from a flat plate in forced flow and compared the results with experimental data and previous results obtained in [4] for the case of combined convective heat exchange with the environment, conduction in the plate and internal heat sources. Forced convection conjugate heat transfer in a laminar plane wall jet was considered by Kanna and Das [6]. A problem of conduction-convection in fins [7, 8] and in cavities [9, 10] and the combined effect of conduction and radition in a T-Y shaped fin [11] are carried out in recent years.
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MHD Natural Convection Flow of an incompressible electrically conducting viscous fluid through porous medium from a vertical flat plate

MHD Natural Convection Flow of an incompressible electrically conducting viscous fluid through porous medium from a vertical flat plate

Because of its application for MHD natural convection flow in the nuclear engineering where convection aids the cooling of reactors, the natural convection boundary layer flow of an electrically conducting fluid up a hot vertical wall in the presence of strong magnetic field has been studied by several authors, such as Sparrow and Cess [7], Reley [8] and Kuiken [9]. Simultaneous occurrence of buoyancy and magnetic field forces in the flow of an electrically conducting fluid up a hot vertical flat plate in the presence of a strong cross magnetic field was studied by Sing and Cowling [10] who had shown that regardless of strength of applied magnetic field there will always be a region in the neighborhood of the leading edge of the plate where electromagnetic forces are unimportant. Creamer and Pai [11] presented a similarity solution for the above problem with uniform heat flux by formulating it in terms of both a regular and inverse series expansions of characterizing coordinate that provided a link between the similarity states closed to and far from the leading edge. Hossain and Ahmed [13] studied the combined effect of the free and forced convection with uniform heat flux in the presence of strong magnetic field. Hossain et al [14] also investigated
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Effects of Thermal Radiation and Chemical Reaction on MHD Free Convection Flow past a Flat Plate with Heat Source and Convective Surface Boundary Condition

Effects of Thermal Radiation and Chemical Reaction on MHD Free Convection Flow past a Flat Plate with Heat Source and Convective Surface Boundary Condition

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.
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Homotopy analysis method for mixed convective boundary layer flow of a nanofluid over a vertical circular cylinder

Homotopy analysis method for mixed convective boundary layer flow of a nanofluid over a vertical circular cylinder

generalized 3-D MHD flow over a porous stretching sheet [17], the wire coating analysis using MHD Oldroyd 8-constant fluid [18], the viscous flow over a non-linearly stretching sheet [19], the off-centered stagnation flow towards a rotating disc [20], the nano boundary layer flows [21], the boundary-layer flow about a heated and rotating down-pointing vertical cone [22], the 2-D viscous flow in a rectangular domain bounded by two moving porous walls [23], the unsteady laminar MHD flow near forward stagnation point of an impulsively rotating and translating sphere in presence of buoyancy forces [24], the non-simi- larity boundary-layer flows over a porous wedge [25], the steady flow and heat transfer of a Sisko fluid in annular pipe [26], the steady flow of an Oldroyd 8-constant fluid due to a suddenly moved plate [27], the MHD flow of non-Newtonian nanofluid and heat transfer in coaxial po- rous cylinder [28], the non-Newtonian nanofluids with Reynolds' model and Vogel's model [29], and the flow of non-Newtonian nanofluid in a pipe [30]. These new solutions have never been reported by all other previous analytic methods. This shows the great potential of the HAM for strongly non-linear problems in science and engineering.
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Transient MHD Free Convective Flow of an Optically Thick Gray Gas Past a Moving Vertical Plate in the Presence of Thermal Radiation and Mass Diffusion

Transient MHD Free Convective Flow of an Optically Thick Gray Gas Past a Moving Vertical Plate in the Presence of Thermal Radiation and Mass Diffusion

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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Unsteady Free Convection Fluid Flow over an Inclined Plate in the Presence of a Magnetic Field with Thermally Stratified High Porosity Medium

Unsteady Free Convection Fluid Flow over an Inclined Plate in the Presence of a Magnetic Field with Thermally Stratified High Porosity Medium

MHD free convection over an inclined plate in a thermally stratified high porous medium in the presence of a magnetic field has been studied. The dimensionless momentum and temperature equations have been solved numerically by explicit finite difference technique with the help of a computer programming language Compaq Visual Fortran 6.6a. The obtained results of these studies have been discussed for the different values of well known parameters with different time steps. Also, the stability conditions and convergence criteria of the explicit finite difference scheme has been analyzed for finding the restriction of the values of various parameters to get more accuracy. The effects of various governing parameters on the fluid velocity, temperature, local and average shear stress and Nusselt number has been investigated and presented graphically.
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Forced convective heat transfer in boundary layer flow of Sisko fluid over a nonlinear stretching sheet.

Forced convective heat transfer in boundary layer flow of Sisko fluid over a nonlinear stretching sheet.

Polymeric suspensions such as waterborne coatings are identi- fied to be non-Newtonian in nature and are proven to follow the Sisko fluid model [14]. The Sisko fluid model was originally proposed for high shear rate measurements on lubricating greases [15]. Khan et al. [16] examined the steady flow and heat transfer of a Sisko fluid in annular pipe. Then, Khan and Shahzad [17,18] developed the boundary layer equations for Sisko fluid over planer and radially stretching sheets and found the analytical solutions for only integral values of the power-law index. The utmost studies relating to the heat transfer of Sisko fluid involve only one dimensional flows and literature survey indicates that no work has so far been communicated with regards to heat transfer in a boundary layer flow for Sisko fluid over a nonlinear stretching sheet with variable surface temperature and variable heat flux.
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Mixed Convection Flow of Couple Stress Fluid in a Vertical Channel with Radiation and Soret Effects

Mixed Convection Flow of Couple Stress Fluid in a Vertical Channel with Radiation and Soret Effects

Since the boundaries in the x direction are of infinite dimensions, without loss of generality, we assume that the physical quantities depend on y only. The fluid properties are assumed to be constant except for density variations in the buoyancy force term. In addition, the thermo diffusion with thermal radiation effects considered. The flow is a mixed convection flow taking place under thermal buoyancy and uniform pressure gradient in the flow direction. The flow configuration and the coordinates system are shown in Figure 1. The fluid velocity u is assumed to be parallel to the x-axis, so that only the x-component u of the velocity vector does not vanish but the transpiration cross-flow velocity v 0 remains
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Numerical simulation and parametric study of laminar mixed convection nanofluid flow in flat tubes using two phase mixture model

Numerical simulation and parametric study of laminar mixed convection nanofluid flow in flat tubes using two phase mixture model

To make sure that the results are independ- ent of the generated grid, four different grids with 60 × 40 × 80, 75 × 50 × 120, 90 × 60 × × 160, and 105 × 70 × 200 elements along the x-, y-, and z-axes have been generated. Differ- ent parameters such as dimensionless tempera- ture (θ) along the x and y, dimensionless axial velocity along the centerline, and the local Nusselt number have been calculated for these four grids and their values have been compared with one another in fig. 2. As this figure shows, all the four generated grids successfully pass the grid independency test for the temperature along the x-axis and axial velocity, but the 60 × 40 × 80 grid fails the grid independency test for the other two parameters. Therefore, the 75 × 50 × 120 grid will be used in all the simula- tions. Figure 3 shows the structure non-uniform generated grid for the flat tube of present paper. As shown in this figure, the grids are finer near the tubes entrance and near the wall where the velocity and temperature gradients are high. Validations of the numerical simulations
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Numerical solution of MHD flow in presence of induced Magnetic field and hall current Effect Over an Infinite Rotating vertical Porous plate through porous medium

Numerical solution of MHD flow in presence of induced Magnetic field and hall current Effect Over an Infinite Rotating vertical Porous plate through porous medium

Abo-Eldahab and Elbarbary [8] have studied the Hall current effects on MHD free-convection flow past a semi-infinite vertical plate with mass transfer. The effect of Hall current on the steady magneto hydrodynamics flow of an electrically conducting, incompressible Burger’s fluid between two parallel electrically insulating infinite planes have been studied by M. A. Rana and A. M. Siddiqui [9].

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Radiative MHD compressible Couette flow in a parallel channel with a naturally permeable wall

Radiative MHD compressible Couette flow in a parallel channel with a naturally permeable wall

Heat transfer in a radiating fluid with slug flow in a parallel plate channel was in- vestigated by Viskanta [18] who formulated the problem in terms of integro-differential equa- tions and solved by an approximate method. Helliwell [19] discussed the stability of thermally radiative magnetofluiddynamic channel flow. Elsayed et al. [20] provided numerical solution for simultaneous forced convection and radiation in parallel plate channel and presented anal- ysis for the case of non-emitting “blackened” fluid. Helliwell et al. [21] discussed the radia- tive heat transfer in horizontal magnetohydrodynamic channel flow considering the buoyancy effects and an axial temperature gradient. Elbashbeshy et al. [22] studied heat transfer over an unsteady stretching surface embedded in a porous medium in the presence of thermal radia- tion and heat source or sink. The viscous heating aspects in fluids were investigated for its practical interest in polymer industry and the problem was invoked to explain some rheologi- cal behavior of silicate melts. The importance of viscous heating has been demonstrated by Gebhart [23], Gebhart et al. [24], Magyari et al. [25], and Rees et al. [26].
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