Analysis of Fractional Thin Film Flow of Third Grade Fluid in Lifting and Drainage via Homotopy Perturbation Procedure

Abstract

Analysis of thin film flows is an important topic in fluid dynamics due to the large number of industrial applications such as food processing, chip manufacturing, irrigation, oil refining process, painting finishing, etc. Analysis involves studying the effects of various parameters in absolute conditions. These parameters may be film thickness, volumetric flux, liquid velocity profile, viscosity, shear stress, gravity, density, and different boundary formations. We have expanded the formulations of non-Newtonian third grade fluid for lifting and draining in fractional space. Fractional calculus along with Homotopy Perturbation Method is used for the solution and analysis purposes. The suitability and consistency of the solutions is determined by detecting residuals in each case. Velocity profile, average velocity, and volume flow for lifting and drainage cases are calculated. To the best of authors knowledge, thin film flow of fractional third grade fluid is not attempted before in lifting and drainage. Investigation shows increase in value of fractional parameter that decreases the velocity profile in lifting while increases the velocity in drainage scenario. Also, the frictional parameter and the gravitational parameter have opposite, while material constant has direct relationship with the velocity profile in lifting case. All the parameters showed inverse effect on the velocity in drainage case.