It is well established that rarefied flows cannot be properly described by traditional hydrodynamics, namely the Navier-Stokes equations for gas flows, and the Fourier’s law
for heat transfer. Considering the significant advancement in miniaturization of electronic devices, where dimensions become comparable with the mean free path of the flow, the It is well established that rarefied flows cannot be properly
described by traditional hydrodynamics, namely the Navier-Stokes equations for gas flows, and the Fourier's law for heat transfer. Considering the significant
advancement in miniaturization of electronic devices, where dimensions become
comparable with the mean free path of the flow, the study of
rarefied flows is extremely important. This dissertation includes two main parts.
First, we look into the heat transport in solids when the mean free path for phonons are comparable with the length scale of the flow. A set of macroscopic moment equations for heat transport in solids are derived to extend the validity of Fourier's law beyond the
hydrodynamics regime. These equations are derived such that they remain
valid at room temperature, where the MEMS devices usually work. The system of moment equations for heat transport is then employed to model
the thermal grating experiment, recently conducted on a silicon wafer. It turns out that at
room temperature, where the experiment was conducted, phonons with high mean
free path significantly contribute to the heat transport. These low
frequency phonons are not considered in the classical theory, which
leads to failure of the Fourier's law in describing the thermal
grating experiment. In contrast, the system of moment equations successfully
predict the deviation from the classical theory in the experiment, and suggest
the importance of considering both low and high frequency phonons at room
temperature to capture the experimental results.
In the second part of this study, we look into the gas-surface interactions for conventional gas dynamics when the gas flow is rarefied.
An extension to the well-known Maxwell boundary conditions for gas-surface
interactions are obtained by considering velocity dependency in the
reflection kernel from the surface. This extension improves the Maxwell boundary conditions
by providing an extra free parameter that can be fitted to the experimental data
for thermal transpiration effect in non-equilibrium flows. The velocity dependent Maxwell boundary conditions are derived for the Direct Simulation Monte Carlo (DSMC) method and the
regularized 13-moment (R13) equations for conventional gas dynamics. Then, a
thermal cavity is considered to test and study the effect of these boundary
conditions on the flow formation in the slip and early transition regime. It
turns out that using velocity dependent boundary conditions allows us to change the size and
direction of the thermal transpiration force, which leads to marked changes
in the balance of transpiration forces and thermal stresses in the flow. / Graduate
| Identifer | oai:union.ndltd.org:uvic.ca/oai:dspace.library.uvic.ca:1828/7626 |
| Date | 17 November 2016 |
| Creators | Mohammadzadeh, Alireza |
| Contributors | Struchtrup, Henning |
| Source Sets | University of Victoria |
| Language | English, English |
| Detected Language | English |
| Type | Thesis |
| Rights | Available to the World Wide Web |
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