Session 1B: Inaugural Lectures by Fellows/Associates

Kalidas Sen

Higher order transport equations: Why do we need them?

The Navier–Stokes equations are well-known fluid equations and have been employed for more than a century to describe flows. However, there is growing evidence in literature as well as from experimental data from labs suggesting that these equations are inadequate to explain several observations with low-pressure gas flows. There seems to be no satisfactory alternative to theoretically describe gas flow when the mean free path of the gas is of the order of the characteristic length scale. The two known approaches of solving the Boltzmann equation yield the Burnett and Grad 13-moments equations, which are higher-order transport equations. However, several shortcomings of these equations are known by now. This motivated the speaker’s group to explore alternate ways to study and derive higher-order transport equations. A novel approach of employing a distribution function consistent with Onsager’s reciprocity principle to capture non-equilibrium thermodynamics effects, and present the new equations derived by the speaker’s group will be discussed. The attractive features of these newly derived OBurnett and O13 equations and some novel solutions of these equations will be highlighted. The talk will describe the conditions under which the celebrated Navier–Stokes equations fail, and the way to model fluid flow under such extreme circumstances.