An Application of Homotopy Perturbation Method to Fractional-Order Thin Film Flow of the Johnson-Segalman Fluid Model

Thin film flow is an important theme in fluid mechanics and has many industrial applications. These flows can be observed in oil refinement process, laser cutting, and nuclear reactors. In this theoretical study, we explore thin film flow of non-Newtonian Johnson-Segalman fluid on a vertical belt in fractional space in lifting and drainage scenarios. Modelled fractional-order boundary value problems are solved numerically using the homotopy perturbation method along with Caputo definition of fractional derivative. In this study, instantaneous and average velocities and volumetric flux are computed in lifting and drainage cases. Validity and convergence of homotopy-based solutions are confirmed by finding residual errors in each case. Moreover, the consequences of different fractional and fluid parameters are graphically studied on the velocity profile. Analysis shows that fractional parameters have opposite effects of the fluid velocity.