Slip Analysis at Fluid-Solid Interface in MHD Squeezing Flow of Casson Fluid through Porous Medium

Qayyum, Mubashir; Khan, Hamid; Khan, Omar

doi:10.1016/j.rinp.2017.01.033

Cited by 34 publications

(15 citation statements)

References 31 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…To validate the correctness of the shooting method, the values of (0), − (0) and −∅ (0) are compared with those derived by Rehman et al [37] and Mustafa et al [38] in Table 1, and we establish excellent concurrences with them; henceforth, we can use the present code confidently. The system of highly non-linear ordinary differential equations (ODEs) (8-10) subject to boundary condition (11) is solved by employing the shooting method with the Runge Kutta (RK)-4th order method in MAPLE software. The shooting technique is an iterative method which changes BVPs into equivalent IVPs by using a sequence of initial condition guesses, obtained using an appropriate iterative method until the required accuracy is reached, and then solved by the shooting technique.…”

Section: Resultsmentioning

confidence: 99%

Stability Analysis of the Magnetized Casson Nanofluid Propagating through an Exponentially Shrinking/Stretching Plate: Dual Solutions

et al. 2020

View full text Add to dashboard Cite

In this research, we intend to develop a dynamical system for the magnetohydrodynamic (MHD) flow of an electrically conducting Casson nanofluid on exponentially shrinking and stretching surfaces, in the presence of a velocity and concertation slip effect, with convective boundary conditions. There are three main objectives of this article, specifically, to discuss the heat characteristics of flow, to find multiple solutions on both surfaces, and to do stability analyses. The main equations of flow are governed by the Brownian motion, the Prandtl number, and the thermophoresis parameters, the Schmid and Biot numbers. The shooting method and three-stage Lobatto IIIa formula have been employed to solve the equations. The ranges of the dual solutions are f w c 1 ≤ f w and λ c ≤ λ , while the no solution ranges are f w c 1 > f w and λ c > λ . The results reveal that the temperature of the fluid increases with the extended values of the thermophoresis parameter, the Brownian motion parameter, and the Hartmann and Biot numbers, for both solutions. The presence of dual solutions depends on the suction parameter. In order to indicate that the first solution is physically relevant and stable, a stability analysis has been performed.

show abstract

Section: Resultsmentioning

confidence: 99%

Stability Analysis of the Magnetized Casson Nanofluid Propagating through an Exponentially Shrinking/Stretching Plate: Dual Solutions

et al. 2020

View full text Add to dashboard Cite

show abstract

“…e affirmation of slip has been confirmed experimentally through indirect approaches [20]. Considering slip results in increasing error and computational time, which is why it is ignored in many theoretical analyses [21,22].…”

Section: Introductionmentioning

confidence: 87%

“…After computing J(c 3 , c 4 , c 5 , c 6 ) � ′ s can be obtained from zJ/zc i � 0. e same procedure is applied to (22) and (24) to calculate the second-order solution in case of slip at the boundary.…”

Section: Application Of Lshpm To Squeezing Flowmentioning

confidence: 99%

Exploration of Unsteady Squeezing Flow through Least Squares Homotopy Perturbation Method

Qayyum

Oscar

2021

Journal of Mathematics

Self Cite

View full text Add to dashboard Cite

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.

show abstract

“…is method combines homotopy concepts with perturbation theory and does not rely on small or large parameter like other traditional perturbation techniques [6]. Wide range of problems has been solved using HPM [7][8][9][10].…”

Section: Introductionmentioning

confidence: 99%

Least Square Homotopy Perturbation Method for Ordinary Differential Equations

Qayyum

Oscar

2021

Journal of Mathematics

Self Cite

View full text Add to dashboard Cite

In this study, a new modification of the homotopy perturbation method (HPM) is introduced for various order boundary value problems (BVPs). In this modification, HPM is hybrid with least square optimizer and named as the least square homotopy perturbation method (LSHPM). The proposed scheme is tested against various linear and nonlinear BVPs (second to seventh order DEs). Validity of the obtained solutions is confirmed by finding absolute errors. To analyze the efficiency of the proposed scheme, tested problems have also been solved through HPM and results are compared with LSHPM. Furthermore, obtained results are also compared with other numerical schemes available in literature. Analysis reveals that LSHPM is a consistent and effective scheme which can be used for more complex BVPs in science and engineering.

show abstract

Slip Analysis at Fluid-Solid Interface in MHD Squeezing Flow of Casson Fluid through Porous Medium

Cited by 34 publications

References 31 publications

Stability Analysis of the Magnetized Casson Nanofluid Propagating through an Exponentially Shrinking/Stretching Plate: Dual Solutions

Stability Analysis of the Magnetized Casson Nanofluid Propagating through an Exponentially Shrinking/Stretching Plate: Dual Solutions

Exploration of Unsteady Squeezing Flow through Least Squares Homotopy Perturbation Method

Least Square Homotopy Perturbation Method for Ordinary Differential Equations

Contact Info

Product

Resources

About