Fractional analysis of unsteady squeezing flow of Casson fluid via homotopy perturbation method

The objective of this article is to model and analyze unsteady squeezing flow of fractional MHD Casson fluid through a porous channel. Casson fluid model is significant in understanding the properties of non-Newtonian fluids such as blood flows, printing inks, sauces and toothpaste etc. This study provides important results as unsteady flow of Casson fluid in fractional sense with aforementioned effects has not been captured in existing literature. After applying similarity transformations along with fractional calculus a highly non-linear fractional-order differential equation is obtained. Modeled equation is then solved along with no-slip boundary conditions through a hybrid of Laplace transform with homotopy perturbation algorithm. For validity purposes, solution and errors at various values in fractional domain are compared with existing results. LHPM results are better in terms of accuracy than other available results in literature. Effects of fractional parameter on the velocity profile, skin friction and behaviors of involved fluid parameters is the focal point of this study. Comprehensive, quantitative and graphical analysis is performed for investigating the effects of pertinent fluid parameters on the velocity profile and skin friction. Analysis revealed that fractional parameter depicts similar effect in case of positive and negative squeeze number. Also, skin friction decreases with an increasing fractional parameter. Moreover, in fractional environment Casson parameter has shown similar effect on the velocity profile in case of positive and negative squeeze number.