Rarefaction and thermal creep effects in square cross-section microchannels

This paper was presented at the 3rd Micro and Nano Flows Conference (MNF2011), which was held at the Makedonia Palace Hotel, Thessaloniki in Greece. The conference was organised by Brunel University and supported by the Italian Union of Thermofluiddynamics, Aristotle University of Thessaloniki, University of Thessaly, IPEM, the Process Intensification Network, the Institution of Mechanical Engineers, the Heat Transfer Society, HEXAG - the Heat Exchange Action Group, and the Energy Institute.Fluid flow and heat transfer in MEMS systems are numerically investigated in this study for potential rarefaction and thermal creep effects using our recently developed implicit, incompressible, hybrid (finite volume/finite element) flow solver. Rarefied flows characterized by the Knudsen number in the range of 0 ≤ Kn ≤ 0.1 are analyzed in detail for thermal creep effects in square cross-section microchannels with constant wall temperature boundary condition. Axial conduction becomes important for very low Reynolds number flows thereby enhancing the thermal creep effect. Three dimensional numerical simulations are conducted for simultaneously developing flows at very low Reynolds numbers in the range of 0.2 ≤ Re ≤ 5. Extended inlet boundary conditions are used to avoid entrance region singularity and also to account for axial heat conduction near the entrance. Friction coefficients are reduced with rarefaction in the slip flow regime. The reduction in friction coefficients was more pronounced due to thermal creep in the entrance region. Effects of rarefaction and thermal creep on heat transfer are studied for different gas-wall surface combinations as defined by the choice of momentum and thermal accommodation coefficients. It was found that heat transfer can increase or decrease with rarefaction. For very small values of gas-wall surface interaction parameter (β), it was observed that velocity slip dominates the temperature jump and heat transfer is enhanced with rarefaction. The opposite effect is observed for higher values of β. Nusselt number values increased slightly with thermal creep as Reynolds number was decreased

Weyssenhoff fluid dynamics in general relativity using a 1+3 covariant approach

The Weyssenhoff fluid is a perfect fluid with spin where the spin of the matter fields is the source of torsion in an Einstein-Cartan framework. Obukhov and Korotky showed that this fluid can be described as an effective fluid with spin in general relativity. A dynamical analysis of such a fluid is performed in a gauge invariant manner using the 1+3 covariant approach. This yields the propagation and constraint equations for the set of dynamical variables. A verification of these equations is performed for the special case of irrotational flow with zero peculiar acceleration by evolving the constraints.Comment: 20 page