The regularized 13-moment equations for rarefied gas flows are considered for planar microchannel flows. The governing equations and corresponding kinetic boundary conditions are partly linearized, such that analytical solutions become feasible. The nonlinear terms include contributions of the shear stress and shear rate, which describe the coupling between velocity and temperature fields. Solutions for Couette and force-driven Poiseuille flows show good agreement with direct simulation Monte Carlo data. Typical rarefaction effects, e.g., heat flux parallel to the wall and the characteristic dip in the temperature profile in Poiseuille flow, are reproduced accurately. Furthermore, boundary effects such as velocity slip, temperature jump, and Knudsen boundary layers are predicted correctly.

Efficient modelling of gas microflows requires accurate, yet fast to solve, models. For finite but moderate Knudsen numbers, extended macroscopic transport equations offer an alternative to the Boltzmann equation, from which they are derived. Classical and modern approaches for the derivation of these models are reviewed, and the resulting equations are compared for their ability to describe the multitude of known rarefaction phenomena. Among the equations discussed are the Burnett and super-Burnett equations, Grad's 13 moment equations, and the regularized 13 and 26 moment equations.

A rigorous three-dimensional analytical model is proposed to investigate thermal response of batteries to transient heat generation during their operation. The modeling is based on integral-transform technique that gives a closed-form solution for the fundamental problem of heat conduction in battery cores with orthotropic thermal conductivities. The method is examined to describe spatial and temporal temperature evolution in a sample prismatic lithium-ion battery (EiG ePLB C020), subjected to transient heat generation in its bulk, and various convective cooling boundary conditions at its surfaces (the most practical case is considered, when surrounding medium is at a constant ambient temperature). The full-field solutions take the form of a rapidly converging triple infinite sum whose leading terms provide a very simple and accurate approximation of the battery thermal behavior. A surface-averaged Biot number has been proposed that can simplify the thermal solutions under certain conditions. The presented analytical model provides a fast yet accurate tool for battery thermal management system designs.

No abstract

In the present study, a compact analytical model is developed to determine the pressure drop of fully-developed, incompressible, and constant properties slip-flow through arbitrary cross section microchannels. An averaged first-order Maxwell slip boundary condition is considered. Introducing a relative velocity, the difference between the bulk flow and the boundary velocities, the axial momentum reduces to Poisson’s equation with homogeneous boundary condition. Square root of area is selected as the characteristic length scale. The model of Bahrami et al. (2006, “Pressure Drop of Laminar, Fully Developed Flow in Microchannels of Arbitrary Cross Section,” ASME J. Fluids Eng., 128, pp. 1036–1044), which was developed for no-slip boundary condition, is extended to cover the slip-flow regime in this study. The proposed model for pressure drop is a function of geometrical parameters of the channel: cross sectional area, perimeter, polar moment of inertia, and the Knudsen number. The model is successfully validated against existing numerical and experimental data collected from different sources in literature for several shapes, including circular, rectangular, trapezoidal, and double-trapezoidal cross sections and a variety of gases such as nitrogen, argon, and helium.