There is evidence in the literature as well as experimental data from our lab suggesting that the Navier-Stokes-Fourier equations are inadequate to explain several observations with low-pressure gas flows. There seems to be no satisfactory alternative to theoretically describe the flow when the mean free path of the gas is of the order of the characteristic length scale. The two well established approaches of solving the Boltzmann equation yields the Burnett and Grad 13-moments equations. However, several shortcomings of these equations are known by now. This motivated us to explore alternate ways to derive higher-order continuum transport equations. We have employed distribution function consistent with Onsager’s reciprocity principle to capture non-equilibrium thermodynamics effects, and derived higher-order continuum transport equations in Refs. [1, 2].
We have also derived the first analytical solution of the Burnett equations for any configuration. The solution for pipe flow, channel flow, and Couette flow are provided in Refs. [3-5] respectively. The connection between Grad’s equation and Cattaneo’s equation (a non-Fourier model) is shown in Ref. [6]. The applicability of the Navier-Stokes equations to high Knudsen number flows is explored in Refs. [7-10].
Singh, N., Agrawal, A., "Onsager’s principle consistent 13 moments transport equations," Physical Review E, Vol 93, 063111 (10 pp), 2016.
Singh, N., Agrawal, A., "Derivation of stable Burnett equations for rarefied gas flows," Physical Review E (under review).
Singh, N., Agrawal, A., "The Burnett Equations in Cylindrical Coordinates and Their Solution for Flow in a Microtube," Journal of Fluid Mechanics, Vol. 751, pp. 121-141, 2014.
Tripathi, S., Kumar, Y.V.B., Prabhakar, A., Joshi, S.S., Agrawal, A., "Performance Study of Microfluidic Device for Blood Plasma Separation – A Designer’s Perspective," Journal of Micromechanics and Microengineering, Vol. 25, 084004 (15 pp), 2015. " Journal of Micromechanics and Microengineering, Vol. 25, 083001 (24 pp), 2015 (invited review article)." Annals of INAE (to appear).
Singh, N., Dongari, N., and Agrawal, A., "Analytical solution of plane Poiseuille flow within Burnett hydrodynamics," Microfluidics and Nanofluidics, Vol. 16, pp. 403-412, 2014.
Singh, N., Gavasane, A., Agrawal, A., "Analytical Solution of Plane Couette Flow in the Transition Regime and Comparison with Direct Simulation Monte Carlo Data," Computers & Fluids, Vol. 97, pp. 177-187, 2014.
Agrawal, A., "Higher-order continuum equation based heat conduction law," INAE Letters, Vol 1, pp. 35-39, 2016.
Dongari, N., and Agrawal, A., "Modeling of Navier-Stokes equations for high Knudsen number gas flows," International Journal of Heat and Mass Transfer, Vol. 55, pp. 4352-4358, 2012.
Agrawal, A., and Dongari, N., "Application of Navier-Stokes equations to high Knudsen number flow in a fine capillary," International Journal of Microscale and Nanoscale Thermal and Fluid Transport Phenomena, Vol. 3 (2), pp. 125-130, 2012.
Agrawal, A., and Prabhu, S.V., "Deduction of slip coefficient in slip and transition regimes from existing cylindrical Couette flow data," Experimental Thermal and Fluid Science, Vol. 32, pp. 991-996, 2008.
Dongari, N., Agrawal, A., and Agrawal, A., "Analytical solution of gaseous slip flow in long microchannels," International Journal of Heat and Mass Transfer, Vol. 50, pp. 3411-3421, 2007.