Modeling and Analysis of Unsteady Axisymmetric Squeezing Fluid Flow through Porous Medium Channel with Slip Boundary

Abstract

The aim of this article is to model and analyze an unsteady axisymmetric flow of non-conducting, Newtonian fluid squeezed between two circular plates passing through porous medium channel with slip boundary condition. A single fourth order nonlinear ordinary differential equation is obtained using similarity transformation. The resulting boundary value problem is solved using Homotopy Perturbation Method (HPM) and fourth order Explicit Runge Kutta Method (RK4). Convergence of HPM solution is verified by obtaining various order approximate solutions along with absolute residuals. Validity of HPM solution is confirmed by comparing analytical and numerical solutions. Furthermore, the effects of various dimensionless parameters on the longitudinal and normal velocity profiles are studied graphically.

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

“…The longitudinal and normal velocity components in radial and axial directions are ( , , ) and ( , , ), respectively. For more physical explanation, see [14][15][16].…”

“…The optimal homotopy asymptotic method (OHAM) has been used by Qayyum et al [14] to analyze the unsteady axisymmetric 2 Mathematical Problems in Engineering flow of nonconducting Newtonian fluid squeezed between two circular plates with slip and no-slip boundaries. Also, the homotopy perturbation method (HPM) has been developed by Qayyum et al [15], to model and analyze the unsteady axisymmetric flow of nonconducting, Newtonian fluid squeezed between two circular plates passing through a porous medium channel with slip boundary condition. The new iterative and Picard methods had been used by Hemeda and Eladdad in [16] for solving the fractional form of unsteady axisymmetric flow of a nonconducting, Newtonian fluid squeezed between two circular plates with slip and no-slip boundaries.…”

Iterative Methods for Solving the Fractional Form of Unsteady Axisymmetric Squeezing Fluid Flow with Slip and No-Slip Boundaries

“…The longitudinal and normal velocity components in radial and axial directions are ( , , ) and ( , , ), respectively. For more physical explanation and details, see [7,8].…”

“…Leider and Byron Bird performed theoretical analysis of power-law fluid between parallel disks [6]. Qayyum et al present in [7] analysis of unsteady axisymmetric flow of nonconducting, Newtonian fluid squeezed between two circular plates with slip and no-slip boundaries using OHAM and in [8] the authors model and analyse the unsteady axisymmetric flow of nonconducting Newtonian fluid squeezed between two circular plates passing through porous medium channel with slip boundary condition using HPM. Furthermore, in [9] analytical solutions for squeeze flow with partial wall slip are introduced by Laun et al, while in [10] Ullah et al present approximation of first-grade MHD squeezing fluid flow with slip boundary condition using DTM and OHAM.…”

The Effects of Thermal Radiation on an Unsteady MHD Axisymmetric Stagnation-Point Flow over a Shrinking Sheet in Presence of Temperature Dependent Thermal Conductivity with Navier Slip

“…Recently, Mahapatra and Nanday [17] studied heat transfer in an axisymmetric stagnation-point flow in the presence of a magnetic field. Qayyum et al [18] presented an analysis of unsteady axisymmetric squeezing fluid flow with slip boundary conditions through a porous channel. Some recent studies of boundary layer flow in presence of a magnetic field include those of Mabood and his group [19–21].…”