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.
Highlights
Squeezing flow between parallel plates is an important problem in the area of fluid dynamics
Mathematical Problems in Engineering (MHD) aspect of the flow needs to be considered. We investigate this particular case for a porous medium channel and present a comprehensive analysis
Other approximation techniques that have been used for the case of fluid dynamics include the Homotopy Analysis Method (HAM) [26], Optimal Homotopy Asymptotic Method (OHAM) [27], Adomian Decomposition Method (ADM) [28], and Variational Iteration Method (VIM) [29]
Summary
Squeezing flow between parallel plates is an important problem in the area of fluid dynamics. The model has to deal with conducting fluids which exhibit different behaviors under the influence of a magnetic field Other approximation techniques that have been used for the case of fluid dynamics include the Homotopy Analysis Method (HAM) [26], Optimal Homotopy Asymptotic Method (OHAM) [27], Adomian Decomposition Method (ADM) [28], and Variational Iteration Method (VIM) [29]. In addition to these analytical approaches, various numerical schemes can be used to solve these problems.
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