Some Approximate Solutions of Non-Newtonian Fluid Flows in Channel

Abstract

This thesis presents the comparative study of the steady flow of an incompressible couple stress fluid of both Reynolds and Vogel’s temperature-dependent Viscosity models. Considering the steady flow of an incompressible couple stress fluid between two infinite parallel plates distant 2d apart, temperatures of lower and upper plates are supposed to be 0 and 1 respectively. Depending upon the relative motion of the plates three different problems namely Couette, Poiseuille, and Generalized Couette flow have been studied in this thesis for temperature dependent viscosity models i.e. Reynolds and Vogel’s viscosity models, solutions for velocity, temperature profiles, volume flux and share stress have been obtained using the Optimal Homotopy Asymptotic Method (OHAM), New Iterative Method (NIM), the Asymptotic Homotopy Perturbation Method (AHPM) and Optimal Homotopy Asymptotic Method with DJ Polynomials (OHAM-DJ). The main difficulty for finding the exact and numerical solutions of coupled systems is a strong nonlinearity. Our aim of the study is to find the approximate solutions of these systems. Coupled systems are solved by many researchers to obtain approximate results with numerical and analytical solutions. All these techniques have thesir worth and limitations in terms of convergence, accuracy, robustness and applicability in different applications over one and other. However, OHAM and NIM also OHAM-DJ and AHPM have not been applied exhaustively for solving these coupled systems of differential equations. This thesis has two parts, in first part the time-independent, non-isothermal Couette, Poiseuille, and Generalized Couette flow of couple stress fluid between two parallel infinite plates has been investigated for Reynolds viscosity model and in the second part of this thesis the time independent, non-isothermal Couette, Poiseuille, and Generalized Couette flow of couple stress fluid between two parallel infinite plates has been investigated for Vogel’s viscosity model, In doing so, the governing continuity and momentum equations are reduced to ordinary differential equations. The coupled system of differential equations is then solved using the Optimal Homotopy Asymptotic Method (OHAM), New Iterative Method (NIM), the Asymptotic Homotopy Perturbation Method (AHPM) and Optimal Homotopy Asymptotic Method with DJ Polynomials (OHAM-DJ). The expressions for velocity profile, temperature distribution, volume xxv flux, average velocity and shear stress are obtained. The results of OHAM and NIM also of OHAM-DJ and AHPM are compared numerically as well as graphically and an excellent agreement is achieved.