Exploration of Unsteady Squeezing Flow through Least Squares Homotopy Perturbation Method

Abstract

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.

Exploration of No-Slip and Slip of Unsteady Squeezing Flow Fluid Through a Derivatives Series Algorithm

“…The acting of the uniform magnetic field = 𝜂(0, 𝜂 0 , 0 ) along 𝑦 ̌-Axis. The properties of the magnetic field [5] can be outlined as follows i. A very small magnetic Reynolds number causes the induced magnetic field to be small so it is considered [35][36][37][38][39].…”

“…The use of magneto-hydrodynamic fluid as a lubricant is highly increased because of any unexpected change in the viscosity of this lubricant can be avoided under certain extreme conditions. Various authors have studied the impact of magnetic field on fluid flow [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. In [20] by the presence of a magnetic field squeezing flow between two disks together was examined and between the rotating disks was investigated in [21,22].…”

Squeezing unsteady nanofluid flow among two parallel plates with first‐order chemical reaction and velocity slip

“…Krishna and Chamkha 11 considered squeezing nanofluid flow in which liquid passed through two parallel disks and analyzed the effect of the magnetic field and Hall effect on the fluid flow. Qayyum and Oscar 12 modeled the flow of viscous liquid amid two parallel surfaces compressed to “each other” in the presence of a “magnetic field.” They analyzed the slip consequences on various fluid properties. Jeffrey fluid was considered by Mat Noor et al 13 for squeezing flow in attendance of a “magnetic field.” Soret and Dufour effects and “thermal radiation” effects were also studied by them.…”

The 2-D Cu-water nanofluid-flow and heat transfer over an inclined wall and between two inclined walls: The numerical solution of PDE and ODE

“…The majority of problems in fluid mechanics including viscous nanofluid-flow over a stretching wall and or between two inclined walls are non-linear in nature and are characterized by non-linear differential equations. Consequently, these equations are usually solved using numerical and analytical methods such as the Hermite wavelet method [11], homotopy perturbation method (HPM) [12], reconstruction of variational iteration method [13], and Galerkin optimal homotopy asymptotic method [14]. In this paper, we presented the results of the numerical solutions for nanofluid-flow between two inclined walls and over an inclined wall.…”