Approximate solutions of the flow models for non-newtonian fluids using hybrid techniques
Loading...
Date
2021
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
UMT Lahore
Abstract
This thesis deals with the applications of a novel hybrid scheme to find the approximate solutions of non-newtonian fluids under different circumstances involving fractional derivatives. Using mongrel 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 mongrel scheme have been presented. Then in the next chapters the mongrel scheme has been successfully applied to find the approximate solutions of second grade and maxwell fluids with non-integer order derivatives. In chapter 2, approximate solution of unsteady rotational flow of second grade fluid with non-integer caputo time fractional derivative through a circular cylinder has been procured. The flow of the 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 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. The aim of chapter 3 is to examine the flow of maxwell fluid involving fractional time derivatives in an infinite long circular cylinder. A mongrel scheme is used to achieve semi-analytical solutions. The fluid is lying inside the cylinder. The approximate results for the velocity field and the time dependent hyperbolic shear stress have been created. The approximate solutions are procured by employing laplace inversion stehfest’s algorithm using mathcad software. The affirmation of the numerical results in inverse laplace transform is executed by employing several other numerical inverse algorithms namely as tzou’s algorithm, honig and hirdes algorithm, fourier series algorithm and talbot’s algorithm. At the end, velocity field and time dependent shear stress graphs are plotted to see the insight behavior of physical parameters and discussed in detail.