Electronic Thesis and Dissertation Repository

Degree

Doctor of Philosophy

Program

Mechanical and Materials Engineering

Supervisor

Prof. Roger E. Khayat

Abstract

This thesis examines different conditions for which non-Fourier effects can be significant in the flow of fluids. Non-Fourier fluids of dual-phase-lagging type (DPL) possess a relaxation time and a retardation time, reflecting the delay in the response of the heat flux and the temperature gradient with respect to one another. For non-Fourier fluids of single-phase-lagging type (SPL) the retardation time is zero. Non-Fourier fluids span a wide range of applications, including liquid helium, nanofluids and rarefied gases. The parallels between non-Fourier fluids and polymeric solutions are established.

The instability of steady natural convection of a thin layer of non-Fourier fluid (SPL) between two horizontal (and vertical) surfaces maintained at different temperatures is studied. The SPL model is particularly relevant to liquid helium II, and nanofluids with high nanoparticle concentration. Linear stability analysis is employed to obtain the critical state parameters such as critical Rayleigh (Grashof) numbers. In both cases, as the fluid becomes more non-Fourier, oscillatory convection increasingly becomes the mode of preference, compared to both conduction and stationary convection. Critical Rayleigh (Grashof) number decreases for fluids with higher non-Fourier levels.

By invoking the role of the eigenvectors to detect and quantify short-time behavior, transient growth of energy of disturbances in is studied. The energy of the perturbations is introduced in terms of the primary variables as a disturbance measure in order to quantify the size of the disturbance. It is found that nonlinearities are not required for the energy growth, and a significant energy growth can be observed even if the flow is stable.

The post-critical convective state for Rayleigh-Benard convection is studied using a nonlinear spectral-amplitude-perturbation approach in a fluid layer heated from below. In the spectral method the flow and temperature fields are expanded periodically along the layer and orthonormal shape functions are used in the transverse direction. A combined amplitude-perturbation approach is developed to solve the nonlinear spectral system in the post critical range, even far from the linear stability threshold. Also, to leading order, the Lorenz model is recovered. Comparison with experimental results is made and a very good qualitative agreement is obtained.


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