Exact and numerical solutions of MHD nano boundary-layer flows over stretching surfaces in a porous medium

Aly, Emad H.; Vajravelu, K.

doi:10.1016/j.amc.2013.12.147

Cited by 31 publications

(22 citation statements)

References 18 publications

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“…In this section, the author followed the spirit analysis of obtaining the exact solutions for f (η) and θ(η), as introduced by Aly and Vajravelu [82], Aly and Hassan [83], Aly and Ebaid ( [84], [85]) and Wang [86]. The reader is therefore advised to see these papers for more details.…”

Section: Exact Solutionsmentioning

confidence: 98%

Existence of the multiple exact solutions for nanofluid flow over a stretching/shrinking sheet embedded in a porous medium at the presence of magnetic field with electrical conductivity and thermal radiation effects

Aly

2016

Powder Technology

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Section: Exact Solutionsmentioning

confidence: 98%

Existence of the multiple exact solutions for nanofluid flow over a stretching/shrinking sheet embedded in a porous medium at the presence of magnetic field with electrical conductivity and thermal radiation effects

Aly

2016

Powder Technology

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“…The resulting nonlinear equations (20)- (22) are associated with the boundary conditions equations (23) and 24 the matrix entries ( ) , , where th is the derivative of any selected function, the reader is advised to see [35]. Recently, this approach has been applied in nano boundary layer study ( [34,35]), and further, Aly [40] and Aly and Sayed [41] have used it for investigating the nanofluids flow.…”

Section: Numerical Approachmentioning

confidence: 99%

“…They showed that increase of the slips slows down the velocity, increases the temperature with an impressive effect in the injection case, and decreases the local skin friction and the reduced Nusselt number with significant effects. Recently, Aly and Vajravelu [34] examined the effects of the second-order slip parameter for the nano boundary layer flow over two-dimensional and axisymmetric stretching surfaces in the presence of a transverse magnetic field in a porous medium. They found that this parameter affects considerably the flow characteristics for increasing values of the magnetic parameter and decreasing values of the porosity parameter.…”

Section: Introductionmentioning

confidence: 99%

Radiation and MHD Boundary Layer Stagnation-Point of Nanofluid Flow towards a Stretching Sheet Embedded in a Porous Medium: Analysis of Suction/Injection and Heat Generation/Absorption with Effect of the Slip Model

Aly

2015

Mathematical Problems in Engineering

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In existence of the velocity slip model, suction/injection, and heat source/sink, the boundary layer flow near a stagnation-point over a heated stretching sheet in a porous medium saturated by a nanofluid, with effect of the thermal radiation and magnetic field, has been studied. The governing system of partial differential equations was transformed into a system of nonlinear ordinary equations using the appropriate similarity transforms. Then, the obtained system has been numerically solved by the Chebyshev pseudospectral differentiation matrix (ChPDM) approach. It was found that, at some special cases, the current results are in a very good agreement with those presented in the literature. In addition, the flow velocity, surface shear stress, temperature, and concentration are strongly influenced on applying the slip model, which is, therefore, extremely important to predict the flow characteristics accurately in the nanofluid mechanics. It was proved that this velocity slip condition is mandatory and should be taken into account in nanoscale research; otherwise, false results and a spurious physical sight are to be gained. Further, it was deduced that the influence of the stream velocity and shear stress reaches very rapidly the stable manner for both cases of the velocity ratio. However, when this ratio is equal to one, the skin friction coefficient, reduced Nusselt number, and reduced Sherwood number are constant and equal to zero, 0.721082, and 3.06155, respectively. Furthermore, it was proved that the reduced Nusselt number decreases with increase of Brownian motion and thermophoresis; has a very weak effect on increasing Lewis number; increases with increase of Prandtl number; and is higher in the cases of suction, velocity ratio > 1 and heat source in comparison with injection, velocity ratio < 1, and heat sink, respectively. Moreover, the reduced Sherwood number increases with increase of Brownian motion, thermophoresis, and Lewis number; decreases with increase of Prandtl number; is higher in the cases of suction and velocity ratio > 1 in comparison with injection and velocity ratio < 1, respectively; and is approximately the same in the heat source and heat sink cases. Finally, it was shown that the most effective region for radiation effect is[0,1].

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“…There is still a great deal of theoretical as well as practical interest in this area of research due to wide range of applications and importance. A glance at literature show some recent studies dealing with the MHD flow through porous medium over a stretching sheet [24][25][26][27][28][29][30][31][32] and references therein. Liu and Andersson [33] investigated the heat transfer characteristics over a bi-directional stretching sheet with variable thermal conditions in the presence of a temperature-dependent internal heat source (or sink).…”

Section: Introductionmentioning

confidence: 99%

Heat transfer analysis of MHD flow due to unsteady bi-directional stretching sheet through porous space

Ahmad

Sajid

2016

THERM SCI

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In this article unsteady 3-D MHD boundary layer flow and heat transfer analysis with constant temperature and constant heat flux in a porous medium is considered. The boundary layer flow is governed by a bi-directional stretching sheet. Similarity transformations are used to transform the governing non-linear partial differential equations to ordinary differential equations. Analytical solutions are constructed using homotopy analysis method. Convergence analysis is also presented through tabular data. The quantities of interest are the velocity, temperature, skin friction coefficient,t and Nusselt number. The obtained results are validated by comparisons with previously published work in special cases. The results of this parametric study are shown graphically and the physical aspects of the problem are discussed.

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Exact and numerical solutions of MHD nano boundary-layer flows over stretching surfaces in a porous medium

Cited by 31 publications

References 18 publications

Existence of the multiple exact solutions for nanofluid flow over a stretching/shrinking sheet embedded in a porous medium at the presence of magnetic field with electrical conductivity and thermal radiation effects

Existence of the multiple exact solutions for nanofluid flow over a stretching/shrinking sheet embedded in a porous medium at the presence of magnetic field with electrical conductivity and thermal radiation effects

Radiation and MHD Boundary Layer Stagnation-Point of Nanofluid Flow towards a Stretching Sheet Embedded in a Porous Medium: Analysis of Suction/Injection and Heat Generation/Absorption with Effect of the Slip Model

Heat transfer analysis of MHD flow due to unsteady bi-directional stretching sheet through porous space

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