Few Exact Solutions of Non-Newtonian Fluid in Porous Medium with Hall Effect

Islam, Saiful; Mohyuddin, Muhammad R.; Zhou, Chao

doi:10.1615/jpormedia.v11.i7.50

Cited by 19 publications

(9 citation statements)

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“…e amount of fluid which passes through the porous medium is known as permeability, while porosity is characterized as the sum of fluid held by the fabric. Porous medium has several applications in the field of petroleum, reservoir, and chemical engineering [14][15][16][17][18].…”

Section: Introductionmentioning

confidence: 99%

Exploration of Unsteady Squeezing Flow through Least Squares Homotopy Perturbation Method

Qayyum

Oscar

2021

Journal of Mathematics

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Squeezing flow has many applications in different fields including chemical, mechanical, and electrical engineering as these flows can be observed in many hydrodynamical tools and machines. Due to importance of squeezing flow, in this paper, an unsteady squeezing flow of a viscous magnetohydrodynamic (MHD) fluid which is passing through porous medium has been modeled and analyzed with and without slip effects at the boundaries. The least squares homotopy perturbation method (LSHPM) has been proposed to determine the solutions of nonlinear boundary value problems. To check the validity and convergence of the proposed scheme (LSHPM), the modeled problems are also solved with the Fehlberg–Runge–Kutta method (RKF45) and homotopy perturbation method (HPM) and residual errors are compared with LSHPM. To the best of the authors’ knowledge, the current problems have not been attempted before with LSHPM. Moreover, the impact of different fluid parameters on the velocity profile has been examined graphically in slip and no-slip cases. Analysis shows that the Reynolds number, MHD parameter, and porosity parameter have opposite effects in case of slip and no slip at the boundaries. It is also observed that nonzero slip parameter accelerates the velocity profile near the boundaries. Analysis also reveals that LSHPM provides better results in terms of accuracy as compared to HPM and RKF45 and can be effectively used for the fluid flow problems.

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Section: Introductionmentioning

confidence: 99%

Exploration of Unsteady Squeezing Flow through Least Squares Homotopy Perturbation Method

Qayyum

Oscar

2021

Journal of Mathematics

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“…Some practical applications in these fields include chemical reactors, filtration, geothermal reservoirs, ground water hydrology, and drainage and recovery of crude oil from pores of reservoir rocks [2][3][4][5][6][7].…”

Section: Introductionmentioning

confidence: 99%

Solution of the Fractional Form of Unsteady Squeezing Flow through Porous Medium

Hemeda¹,

Eladdad²,

Lairje³

2017

Mathematical Problems in Engineering

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We propose two friendly analytical techniques called Adomian decomposition and Picard methods to analyze an unsteady axisymmetric flow of nonconducting, Newtonian fluid. This fluid is assumed to be squeezed between two circular plates passing through porous medium channel with slip and no-slip boundary conditions. A single fractional order nonlinear ordinary differential equation is obtained by means of similarity transformation with the help of the fractional calculus definitions. The resulting fractional boundary value problems are solved by the proposed methods. Convergence of the two methods' solutions is confirmed by obtaining various approximate solutions and various absolute residuals for different values of the fractional order.Comparison of the results of the two methods for different values of the fractional order confirms that the proposed methods are in a well agreement and therefore they can be used in a simple manner for solving this kind of problems. Finally, graphical study for the longitudinal and normal velocity profiles is obtained for various values of some dimensionless parameters and fractional orders.

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“…Porosity defines the quantity of fluid that can be held by the material, whereas permeability is the amount of fluid that can pass through it. Various applications include ground water hydrology, chemical reactors, irrigation, drainage, seepage, and recovery of crude oil from pores of reservoir rocks [8][9][10][11][12]. These applications can specifically be classified to engineering fields such as petroleum, reservoir, and chemical engineering.…”

Section: Introductionmentioning

confidence: 99%

Unsteady Squeezing Flow of Casson Fluid with Magnetohydrodynamic Effect and Passing through Porous Medium

Khan

Qayyum

Khan

et al. 2016

Mathematical Problems in Engineering

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An unsteady squeezing flow of Casson fluid having magnetohydrodynamic (MHD) effect and passing through porous medium channel is modeled and investigated. Similarity transformations are used to convert the partial differential equations (PDEs) of non-Newtonian fluid to a highly nonlinear fourth-order ordinary differential equation (ODE). The obtained boundary value problem is solved analytically by Homotopy Perturbation Method (HPM) and numerically by explicit Runge-Kutta method of order 4. For validity purpose, we compare the analytical and numerical results which show excellent agreement. Furthermore, comprehensive graphical analysis has been made to investigate the effects of various fluid parameters on the velocity profile. Analysis shows that positive and negative squeeze numberSqhave opposite effect on the velocity profile. It is also observed that Casson parameterβshows opposite effect on the velocity profile in case of positive and negative squeeze numberSq. MHD parameterMgand permeability constantMphave similar effects on the velocity profile in case of positive and negative squeeze numbers. It is also seen that, in case of positive squeeze number, similar velocity profiles have been obtained forβ,Mg, andMp. Besides this, analysis of skin friction coefficient has also been presented. It is observed that squeeze number, MHD parameter, and permeability parameter have direct relationship while Casson parameter has inverse relationship with skin friction coefficient.

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Few Exact Solutions of Non-Newtonian Fluid in Porous Medium with Hall Effect

Cited by 19 publications

References 0 publications

Exploration of Unsteady Squeezing Flow through Least Squares Homotopy Perturbation Method

Exploration of Unsteady Squeezing Flow through Least Squares Homotopy Perturbation Method

Solution of the Fractional Form of Unsteady Squeezing Flow through Porous Medium

Unsteady Squeezing Flow of Casson Fluid with Magnetohydrodynamic Effect and Passing through Porous Medium

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