Introduction to Microscale Flows and Mathematical Modelling
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The purpose of this book is to understand fluid flow and heat transfer at the microscale. The focus is on gases, as the mean free path of the gas can become comparable to the passage dimensions, and an additional non-dimensional number (Knudsen number) starts affecting the dynamics of the flow and heat transfer behavior. The effect of Knudsen number turns out to be non-trivial, as it not only leads to several new physical phenomena, but also exposes the limitations of the celebrated Navier–Stokes equations in modelling such flows. The second major purpose of this book is therefore to examine equations which can model such high Knudsen number flows. Again, we first show that simple modifications to the Navier–Stokes equations and boundary conditions are not sufficient to fulfill this objective. There is perhaps no alternative but to shun the conventional way of deriving transport equations, and resort to the Boltzmann equation for derivation of “higher-order continuum transport equations.” The book presents a clear derivation of the Burnett and Grad equations starting from the Boltzmann equation, a discussion on the variants of the Burnett and Grad equations, and some known solutions of these higher-order continuum transport equations.
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