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Title: Mathematical Modeling and Exact Solutions for the Magnetohdrodynamics Flow of Non-Newtonian Fluids in a Channel
Authors: Khan, Zar Ali
Keywords: Physical Sciences
Issue Date: 2020
Publisher: University of Peshawar, Peshawar.
Abstract: This work in the present thesis deals with new results regarding the nature of some nonNewtonian fluids in the presence of magnetohydrodynamics between two parallel side walls perpendicular to an infinite bottom plate. In chapter 1, the related basic concepts and applicable literature review are discussed, which present the basic concepts regarding Modeling, Newtonian and non-Newtonian fluids, magnetohydrodynamics, constitutive equations, porous medium, continuity equation, equations of motion, fractional calculus and integral transforms. The exact solutions have been established for the velocity field as well as shear stress corresponding to some non-Newtonian fluids flow of classical Brinkman, classical Jeffrey and fractional Brinkman type fluids. In chapter 2, mathematical model for the classical Brinkman type fluid has been developed. Then the obtained governing equation is reduced to dimensionless form by using suitable dimensions. The exact solutions have been established by using Fourier transform technique corresponding to the Brinkman type fluid in the presence of magnetohydrodynamics in a channel. Graphical illustrations are made by using Mathcad software. Moreover, special cases have been discussed that link our solutions to the published papers as limiting cases. In chapter 3, the exact solutions for velocity and shear stress are established for Jeffrey MHD type fluid set in porous medium between two parallel side walls over an infinite bottom plate. The dimensionless criteria have been used to reduce the governing equation into dimensionless form. The dimensionless governing partial differential equation has been reduced to ordinary differential equation by using Fourier as well as Laplace transforms techniques. At the end of chapter 3, the effects of various parameters have been discussed graphically. Chapter 4, contains new exact solutions of incompressible generalized Brinkman type fluid in a channel with the effect of MHD with Caputo-Fabrizio fractional derivative. The dimensionless fractional Brinkman model is reduced to simple algebraic form by using integral transform techniques that is Fourier and Laplace transforms, which can be easily solvable. The effects of different parameters for velocity and shear stress have been shown graphically. Moreover, through this recent work, the classical Brinkman type fluid has been recovered through graphs.
Gov't Doc #: 20218
Appears in Collections:PhD Thesis of All Public / Private Sector Universities / DAIs.

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