Analysis of unsteady flow of a Burgers’ fluid with Caputo time fractional derivatives
Loading...
Date
2021
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
UMT Lahore
Abstract
This dissertation deals with the applications of a new hybrid scheme to find the approximate solutions of non-Newtonian fluids under different circumstances involving fractional derivatives. using hybrid approach, we have less calculating efforts and time consumption as compared to other methods present in the literature to find the solutions of problems. in starting, some preliminaries and basic concepts related to Newtonian and non-Newtonian fluids, constitutive equations, fractional calculus and hybrid scheme have been presented. then in the next chaptes the mongrel scheme has been successfully applied to find the approximate solutions of unsteady longitudinal flow of burger’s fluid with non-integer caputo time fractional derivative through a circular cylinder. the flow of fluid is generated due to hyperbolic stress applied on the surface of cylinder. the laplace inversion numerical algorithms methodology is adopted to solve the governing equations. the inverse laplace transformation has been procured through stehfest’s’ algorithm using MATHCAD software. the affirmation of the numerical results in inverse laplace transform is executed by using the four other numerical inverse laplace algorithms namely, tzou’s algorithm, honig and hirdes algorithm, fourier series algorithm and talbot’s algorithm. towards the end, the velocity field and shear stress graphs are depicted to understand the response of physical parameters.