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Title Mathematical Analysis of Burgers Fluid Flow Induced by an Unsteady Motion

Author(s) Nimra Umbreen

Abstract The aim of this work is to analyze two unsteady motions of incompressible non-Newtonian fluids through a plate channel. Exactly, we examine exact analytical expressions for unsteady, laminar flows of an incompressible Burgers fluid. The porous effects are taken into consideration. Also, we use the assumption that pressure is constant and there is no body force along the direction of the flow. The fluid motion is generated by one of the plates which is either moving in its plane or oscillates in its own plane, and the obtained solutions satisfy all imposed initial and boundary conditions. The exact analytical solutions for dimensionless velocity and associated shear stress are acquired by means of the Finite Fourier Sine Transform (FFST). The starting solutions corresponding to the oscillatory motion of the boundary are presented as a sum of permanent (steady-state) and transient components. These solutions can be useful for those who want to eliminate the transients from their experiments. For a check of the obtained results, their steady-state components are presented in different forms whose equivalence is graphically illustrated. Analytical solutions for incompressible Oldoryd-B, Maxwell and Newtonian fluids performing the same motions are recovered as limiting cases of the presented results. To shed light on some relevant physical aspects of the obtained results, the influence of the material parameters of the fluid motion as well as comparison amongst various models are underlined by graphical illustrations. It is found that the Burgers fluids flow slower as compared to Newtonian fluids. The required time to reach the steady-state is also presented. It is found that the presence of porous medium delays the appearance of the steady-state. It has been observed that the velocity is an increasing function of Burgers fluid parameter and by increasing time the magnitude of velocity is larger for both cases. Moreover, the amplitude of oscillations is larger for the velocity profile without porous medium, but we have seen the opposite effect for the steady state shear stress, for different values of Burgers parameter.

Type Thesis/Dissertation MS

Faculty Engineering and Computer Science

Department Mathematics

Language English

Publication Date 2024-06-06

Subject Mathematics

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