Heat transfer in the MHD flow of a power law fluid over a non-isothermal stretching sheet

Prasad, K. V.; Vajravelu, K.

doi:10.1016/j.ijheatmasstransfer.2009.05.022

Cited by 69 publications

(44 citation statements)

References 34 publications

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“…The coupled non-linear ordinary differential equations (14) and (15) together with the boundary conditions (16) and (17) are solved numerically by an efficient and accurate finite difference scheme known as Keller Box method (for details see Prasad et al [9], Ishak et al [36] and Cebeci and Bradshaw [40] and Keller [41]). This method is unconditionally stable and has a second order accuracy.…”

Section: Numerical Proceduresmentioning

confidence: 99%

“…In Ref. [10], the solutions presented in some figures do not seem to satisfy the asymptotic conditions at infinity: This happened due to the magnification of the figures. In the present paper, the attention has been paid to avoid it.…”

Section: Introductionmentioning

confidence: 98%

“…Until recently, this study has been largely concerned with the flow and heat transfer characteristics in various physical situations [4][5][6][7][8][9]. Watanabe and Pop [4] investigated the heat transfer in thermal boundary layers of magnetohydodynamic Newtonian/non-Newtonian flows over a flat plate.…”

Section: Introductionmentioning

confidence: 99%

“…Abo-Eldahab and Salem [8] studied the influence of transverse magnetic field on the flow and heat transfer of an electrically conducting fluid over a stretching sheet with a uniform free stream. Prasad et al [9] studied the effect of variable thermal conductivity on MHD flow and heat transfer of a power-law fluid over a non-isothermal stretching sheet with internal heat generation/absorption. Prasad and Vajravelu [10] examined the MHD flow and heat transfer phenomena in a power law fluid over a porous stretching surface, taking into account the internal heat generation/absorption, viscous dissipation, work done by stress, variable thermal conductivity, and thermal radiation.…”

Section: Introductionmentioning

confidence: 99%

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Mixed convection heat transfer over a non-linear stretching surface with variable fluid properties

Prasad

Vajravelu

Datti

2010

International Journal of Non-Linear Mechanics

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a b s t r a c tThis article presents a numerical solution for the steady two-dimensional mixed convection MHD flow of an electrically conducting viscous fluid over a vertical stretching sheet, in its own plane. The stretching velocity and the transverse magnetic field are assumed to vary as a power function of the distance from the origin. The temperature dependent fluid properties, namely, the fluid viscosity and the thermal conductivity are assumed to vary, respectively, as an inverse function of the temperature and a linear function of the temperature. A generalized similarity transformation is introduced to study the influence of temperature dependent fluid properties. The transformed boundary layer equations are solved numerically, using a finite difference scheme known as Keller Box method, for several sets of values of the physical parameters, namely, the stretching parameter, the temperature dependent viscosity parameter, the magnetic parameter, the mixed convection parameter, the temperature dependent thermal conductivity parameter and the Prandtl number. The numerical results thus obtained for the flow and heat transfer characteristics reveal many interesting behaviors. These behaviors warrant further study of the effects of the physical parameters on the flow and heat transfer characteristics. Here it may be noted that, in the case of the classical Navier-Stokes fluid flowing past a horizontal stretching sheet, McLeod and Rajagopal (1987) [42] showed that there exist an unique solution to the problem. This may not be true in the present case. Hence we would like to explore the non-uniqueness of the solution and present the findings in the subsequent paper.

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Section: Numerical Proceduresmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Mixed convection heat transfer over a non-linear stretching surface with variable fluid properties

Prasad

Vajravelu

Datti

2010

International Journal of Non-Linear Mechanics

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“…However, it is well known that these properties may change with temperature, especially the thermal conductivity. Available literature [15][16][17] on variable thermal conductivity shows that this type of work has not been carried out for non-Newtonian fluid obeying the Ostwald-de Waele power-law model.…”

Section: Introductionmentioning

confidence: 99%

Unsteady flow and heat transfer in a thin film of Ostwald–de Waele liquid over a stretching surface

Vajravelu

Prasad

2012

Communications in Nonlinear Science and Numerical Simulation

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a b s t r a c tIn this paper, the effects of viscous dissipation and the temperature-dependent thermal conductivity on an unsteady flow and heat transfer in a thin liquid film of a non-Newtonian Ostwald-de Waele fluid over a horizontal porous stretching surface is studied. Using a similarity transformation, the time-dependent boundary-layer equations are reduced to a set of non-linear ordinary differential equations. The resulting five parameter problem is solved by the Keller-Box method. The effects of the unsteady parameter on the film thickness are explored numerically for different values of the power-law index parameter and the injection parameter. Numerical results for the velocity, the temperature, the skin friction and the wall-temperature gradient are presented through graphs and tables for different values of the pertinent parameter. One of the important findings of the study is that the film thickness increases with an increase in the power-law index parameter (as well as the injection parameter). Quite the opposite is true with the unsteady parameter. Furthermore, the wall-temperature gradient decreases with an increase in the Eckert number or the variable thermal conductivity parameter. Furthermore, the surface temperature of a shear thinning fluid is larger compared to the Newtonian and shear thickening fluids. The results obtained reveal many interesting behaviors that warrant further study of the equations related to non-Newtonian fluid phenomena, especially the shear-thinning phenomena.

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Combined effects of internal heat generation and higher order chemical reaction on the non‐darcian forced convective flow of a viscous incompressible fluid with variable viscosity and thermal conductivity over a stretching surface embedded in a porous medium

Rahman¹

2011

Can J Chem Eng

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In this paper, we study the combined effects of internal heat generation and higher order chemical reaction on a steady two‐dimensional non‐Darcian forced convective flow of a viscous incompressible fluid with variable dynamic viscosity and thermal conductivity in a fluid saturated porous medium passing over a linear stretching sheet. Using similarity transformations, the governing nonlinear‐coupled partial differential equations are made dimensionless and solved numerically for similarity solutions using very robust computer algebra software Maple 8. The non‐dimensional velocity, temperature and concentration distributions are presented graphically for various pertinent parameters such as relative temperature difference parameter, Darcy number, porosity parameter, reaction rate parameter and the order of the chemical reaction. The variations of Prandtl number and Schmidt number within the boundary layer are also displayed graphically when the fluid dynamic viscosity and thermal conductivity are temperature dependent. From the present numerical computations it is found that Prandtl number as well as Schmidt number must be taken as variables within the flow domain when the fluid's dynamic viscosity and thermal conductivity are variable. In the presence of internal heat generation, dynamic viscosity and thermal conductivity of the fluid are found to be higher than when it is absent. Increasing Darcy number reduces dynamic viscosity as well as thermal conductivity whereas increasing pore size reduces the Schmidt number and increases the Prandtl number within the boundary layer. For higher order reaction the rate of increase in mass transfer function is less compared to the rate of increase for the lower order reaction. © 2011 Canadian Society for Chemical Engineering

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Heat transfer in the MHD flow of a power law fluid over a non-isothermal stretching sheet

Cited by 69 publications

References 34 publications

Mixed convection heat transfer over a non-linear stretching surface with variable fluid properties

Mixed convection heat transfer over a non-linear stretching surface with variable fluid properties

Unsteady flow and heat transfer in a thin film of Ostwald–de Waele liquid over a stretching surface

Combined effects of internal heat generation and higher order chemical reaction on the non‐darcian forced convective flow of a viscous incompressible fluid with variable viscosity and thermal conductivity over a stretching surface embedded in a porous medium

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