Fractional modeling and analysis of unsteady squeezing flow of Casson nanofluid via extended He-Laplace algorithm in Liouville-Caputo sense

Abstract

The objective of this manuscript is to model the fully fractional unsteady Casson nanofluid flow between two parallel plates influenced by magneto hydrodynamic forces and Darcian effects in both slip and no-slip case. Casson nanofluid model is fractionally transformed through mixed similarity transformations into a non-dimensional fully fractional model. In modeled fluid problem the continuity equation is identically satisfied and fractional order highly non-linear momentum equation is obtained. The obtained fractional model is further validated by putting α=1 and obtaining the integer order Casson fluid model already existing in literature. In order to solve the flow problem, a hybrid of homotopy perturbation method and Laplace transform, namely He-Laplace method (HLM) is utilized. The obtained results are validated with existing results in literature and through residual errors and average error plots with increasing order of approximation. It is observed that results obtained through HLM are better in terms of accuracy than existing results. Moreover, the errors reduce substantially as order of approximation in HLM increases, depicting the convergence of proposed scheme. Graphical analysis is also performed to analyze the behavior of normal and radial velocity. Furthermore, contour plots are presented for flow rate and skin friction of Casson nanofluid. It is observed that fluid parameters present different behavior incase of fractional environment when compared with existing integer order results. Also, the behavior of velocity profile in no-slip case is in contrast to the behavior noted in slip case of Casson nanofluid. These finding confirm the importance of fractional modeling in terms of capturing more generalized physical phenomena.