Applications of Group Theoretical Methods to Non‐Newtonian Fluid Flow Models: Survey of Results

Aziz, Taha; Mahomed, F. M.

doi:10.1155/2017/6847647

Cited by 5 publications

(3 citation statements)

References 65 publications

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“…From the invariants I (0) and I (1) of X1 nm we can introduce a new dependent variable w nm (x nm , y nm ) = w given by…”

Section: X1 Preserving Discretization Of the Boussinesq Equationmentioning

confidence: 99%

“…They do not form a group but they can be used to obtain additional reductions leading to explicit solutions. Conditional symmetries and the reductions provided by them have been applied to obtain explicit (new, physically relevant) solutions for problems arising in non-newtonian fluid flow models [1], in magnetohydro dynamics [20], in reaction-diffusion-convection equations [12], in equations of heat and acoustics [18], etc.…”

Section: Introductionmentioning

confidence: 99%

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The discretized Boussinesq equation and its conditional symmetry reduction

Levi¹,

Rodrı́guez²,

Thomova³

2020

J. Phys. A: Math. Theor.

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In this article we show that we can carry out the symmetry preserving discretization of the Boussinesq equation with respect to three of its more significant conditional symmetries. We perform the symmetry reduction of the obtained nonlinear discrete schemes with respect to the conditional symmetries and obtain the reduced discrete equations which unlike in the continuous case, are not always reducible to second order difference equations. A numerical comparison with the exact continuous solution given by Weierstrass elliptic functions is carried out.

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“…From the invariants I (0) and I (1) of X1 nm we can introduce a new dependent variable w nm (x nm , y nm ) = w given by…”

Section: X1 Preserving Discretization Of the Boussinesq Equationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The discretized Boussinesq equation and its conditional symmetry reduction

Levi¹,

Rodrı́guez²,

Thomova³

2020

J. Phys. A: Math. Theor.

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“…Safdar et al [14] worked on the unsteady flow of a liquid film due to stretching sheets using file point symmetries. Aziz and Mahomed [15] studied the theoretical methods for non-Newtonian fluid flow and also its applications. Paliathanasis [16] worked on Lie symmetries using rotating shallow water.…”

Section: Introductionmentioning

confidence: 99%

MHD Casson fluid flow with Navier’s and second order slip due to a perforated stretching or shrinking sheet

et al. 2022

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The present work discusses the laminar boundary layer flow of an electrically conducting Casson fluid due to a horizontal perforated sheet undergoing linear shrinking/stretching with mass transpiration. Navier’s slip and second-order slip conditions are also imposed on the flow. The system is subjected to a transverse magnetic field. The non-Newtonian flow under consideration obeys the rheological equation of state due to the Casson model. The PDEs governing the bounder layer flow is reduced to a nonlinear boundary value problem in ODEs by utilizing appropriate similarity transformations and are expressed analytically. The similarity solution is found to be a function of the Casson parameter, magnetic parameter, mass suction/injection parameter, and the first/second-order slip parameters. Such a solution is either unique, or dual solutions exist in a region defined by the mass transfer induced slip parameter. The results of the present work are found to be an increase of the magnetic effects resulting in expansion of the unique solution region and contraction of the dual solution region for the flow due to the induced Lorentz force. In the unique solution region, an increase in magnitudes of mass suction induced slip and the first/second-order slip parameters result in a reduction of the wall shear stress in the shrinking sheet, while the wall shear stress with mass suction increases with the Casson and the magnetic effects. Similar results exist for the stretching sheet case with mass suction. However, only unique similarity solutions exist only for the case of stretching sheets with mass injection. The current work is a generalization of the classical works of Crane (1970) and Pavlov (1974) for a stretching sheet. Mass suction/injection induced slip enhances and achieves a dominant flow driven by reversing the flow direction of the moving sheet, which allows an adjacent flow against the sheet. The findings have possible industrial applications in fluid-based systems including stretchable/shrinkable things, automated cooling systems, power generation, microelectronics, and present new results to the problem.

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