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

Abstract

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.

Bioconvection in a squeezing flow of a micropolar fluid in a horizontal channel

“…The system of nonlinear coupled differential equations (10)(11)(12)(13)(14) is reduced to a system of linear differential equations using the successive linearization method (SLM). 35 The resulting system of linearized ordinary differential equations is solved by the Chebyshev pseudo-spectral method.…”

“…are unknown functions and η ( ) k  ≤ ≤ k r (0 ( − 1)) are approximations from the previous iterations. Substituting Equation (17) in the governing equations (10)(11)(12)(13)(14) and retaining the linear terms of η ( ) r  , we get the following system of ordinary differential equations.…”

“…Gupta and Gupta identified that the unsteady squeezing channel flow problem could be simplified to the remarkable extent through similarity transformation in the case that the parallel plates are kept at a distance, which varies as the square root of a linear function of time. The unsteady squeezing flow problems were investigated by several researchers, eg, Verma, Singh et al, Hamza, Duwairi et al, Mustafa et al, Umar Khan and coworkers, Khan et al, Mohyud‐Din et al, Adnan et al, Adesanya et al, Saba et al, Khan et al, and Sultan et al with consideration of various physical properties and computational techniques.…”

Pulsating flow of Casson fluid in a porous channel with thermal radiation, chemical reaction and applied magnetic field

“…Ali et al [3] analyzed the hydromagnetic effects on blood flow in a horizontal circular tube by considering blood as Casson fluid. Khan et al [15] examined the unsteady squeezing hydromagnetic flow of a Casson fluid between parallel plates. Vajravelu et al [45] studied the mixed convective flow of a Casson fluid over a vertical stretching sheet by using optimal homotopy analysis method.…”

Squeezing Flow Analysis of Nanofluid Under the Effects of Magnetic Field and Slip Boundary Conditions Using Chebychev Spectral Collocation Method

“…Consequently, in recent times, there have been several attempts and renewed research interests by different researchers to properly analyze and understand the squeezing flows using different analytical and numerical methods . Also, effects of magnetic field, flow characteristics and fluid properties on the squeezing flow have been widely studied under no slip conditions [27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42]. However, in polymeric liquids, there is slip at the boundary when the weight of molecule is high.…”