No abstract

We present a phenomenological description of the hydrodynamics in terms of the Fokker-Planck (FP) equation for one-particle distribution function. Similar to the Boltzmann equation or the Bhatnager-Gross-Krook (BGK) model, this approach is thermodynamically consistent and has the H theorem. In this model, transport coefficients as well as the equation of state can be provided independently. This approach can be used as an alternate to BGK-based methods as well as the direct simulation Monte Carlo method for the gaseous flows.

ZnO is a promising candidate as an environment friendly thermoelectric (TE) material. However, the poor TE figure of merit (zT) needs to be addressed to achieve significant TE efficiency for commercial applications. Here we demonstrate that selective enhancement in phonon scattering leads to increase in zT of RGO encapsulated Al-doped ZnO core shell nanohybrids, synthesized via a facile and scalable method. The incorporation of 1 at% Al with 1.5 wt% RGO into ZnO (AGZO) has been found to show significant enhancement in zT (=0.52 at 1100 K) which is an order of magnitude larger compared to that of bare undoped ZnO. Photoluminescence and X-ray photoelectron spectroscopy measurements confirm that RGO encapsulation significantly quenches surface oxygen vacancies in ZnO along with nucleation of new interstitial Zn donor states. Tunneling spectroscopy reveals that the band gap of ~ 3.4 eV for bare ZnO reduces effectively to ~ 0.5 eV upon RGO encapsulation, facilitating charge transport. The electrical conductivity enhancement also benefits from the more than 95% densification achieved, using the spark plasma sintering method, which aids reduction of GO into RGO. The same Al doping and RGO capping synergistically brings about drastic reduction of thermal conductivity, through enhanced phonon-phonon and point defect-phonon scatterings. These opposing effects on electrical and thermal conductivities enhances the power factors as well as the zT value. Overall, a practically viable route for synthesis of oxide -RGO TE material which could find its practical applications for the hightemperature TE power generation.

No abstract

We present a comparative study of gaseous microflow systems using the recently introduced Fokker-Planck approach and other methods such as: direct simulation Monte Carlo, lattice Boltzmann, and variational solution of Boltzmann-BGK. We show that this Fokker-Plank approach performs efficiently at intermediate values of Knudsen number, a region where direct simulation Monte Carlo becomes expensive and lattice Boltzmann becomes inaccurate. We also investigate the effectiveness of a recently proposed Fokker-Planck model in simulations of heat transfer, as a function of relevant parameters such as the Prandtl, Knudsen numbers. Furthermore, we present simulation of shock wave as a function of Mach number in transonic regime. Our results suggest that the performance of the Fokker-Planck approach is superior to that of the other methods in transition regime for rarefied gas flow and transonic regime for shock wave.