Application of Shooting Method and Nonlinear Dynamical Techniques to Coupled Boundary Value Problems In Fluid Mechanics and Heat Transfer
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Date
2021-05-21
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Addis Ababa University
Abstract
This thesis focused on a dynamical and numerical study of non-linear dynamics system of coupled boundary value problems for fluid mechanics and heat transfer. The study of heat transfer is a class of boundary layer theory and an integral part of natural convection flow. We used Runge-Kutta fourth order method with the help of a shooting-secant technique to solve numerically. We investigated the numerical solution of non-linear dynamics system of coupled boundary value problems for fluid mechanics and heat transfer and observed the Shooting- secant method results were accurate and generates numerical solutions that are stable and numerically acceptable. We also studied the dynamical solution of non-linear heat transfer equation. To this end, the study investigates coupled boundary value problems for fluid mechanics and heat transfer, which have different forms of non-linearity. And Falkner-Skan boundary layer viscous flow over a wedge was investigated including a nonslip and slip boundary condition and the result of Shooting-secant method was accurate and generates numerical solutions that are stable and physically reasonable. We also consider the magnetohydrodynamics viscous flow over a shrinking sheet for a closed form exact solution. The flow of magnetohaydrodynamics (MHD) over a shrinking sheet often varies significantly from the flow of MHD over a stretching sheet for Newtonian and non-Newtonian fluids and observed that the opposite value sign of the exact solution occurs only for mass suction and as the mass suction parameter increases, the wall shear stress for M= 1 increases. We also consider the two-dimensional magnitohydrodynamics (MHD) of the numerical and analytic solution boundary layer flow and heat transfer along an infinity porous hot horizontal continuous moving plate and observed the velocity profile in the flow region decreases as the magnetic parameters increase. Moreover, we investigate magnitohydrodynamics (MHD) convectional flow and entropy generation over an inclined stretching sheet. Increasing the magnetic parameter and Eckert number, increases entropy generation, while increasing the thermal convective parameter and dimensionless temperature function decreases entropy generation. A comparison with published results is presented.
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Falkner-Skan Equation, Shooting-Secant Method, Viscous, Velocity Slip, Magnitohydrodynamics(Mhd), Entropy, Dynamics System, Phase Plane Analysis, Eigenvalues