In this paper Cu(II), Mn(II) and Zn(II) complexes with N,N,N-trimethyl-2-oxo-2-(2-(1-(thiazol-2-yl)ethylidene)hydrazinyl)ethan-1-aminium chloride (HL1Cl) were synthesized and characterized by single-crystal X-ray diffraction, IR spectroscopy, elemental analysis and DFT calculations. In all three...
The analytical solution for steady viscous pressure-driven compressible isothermal gas flow through the micro and nanochannels with variable cross section for all Knudsen and all Mach number values is presented in this paper. The continuum one-dimensional governing equations are solved using the friction factor that is established in a special way to provide solutions for mass flow rate, pressure and velocity distribution through the microchannels and nanochannels in the entire rarefaction regime. The friction factor, defined by the general boundary condition and generalized diffusion coefficient proposed by Beskok and Karniadakis [1], spreads the solution application to all rarefaction regimes from continuum to free molecular flow. The correlation between product of friction factor and Reynolds number (Poiseuille number) and Knudsen number is established explicitly in the paper. Moreover, the obtained solution includes the inertia effect, which allows solution application beside on subsonic also on supersonic gas flow, which was not shown earlier. Presented solution confirms the existence of the Knudsen minimum in the diverging, converging and microchannels and nanochannels with constant cross section. The proposed solution is verified by comparison with experimental, analytical and numerical results available in literature.
number, axisymmetric, isothermal, compressible, slip gas flow in microtubes is investigated in this paper. The problem is solved by the continuum equations, continuity and Navier-Stokes, along with Maxwell first order boundary condition. The analytical results are obtained by perturbation method. The solutions show a good agreement with experimental results.
The paper presents an analytical solution for the non-isothermal compressible gas flow in a slide microbearing with different temperatures of walls. The gas flow is defined by the Navier-Stokes-Fourier system of the continuum equations and first order boundary conditions. Knudsen number corresponds to the slip and continuum flow (Kn ≤ 10−1) and Reynolds number is moderately high, so inertia needs to be included. The solution is obtained by perturbations with the first approximation that relates to the continuum flow and the second one that involves second-order effects: the rarefaction, inertia, convection, dissipation, and rate at which work is done in compressing the element of fluid. The presented model analyzes the influence of the dependence of transport coefficients on temperature. The obtained analytical solution for the pressure, velocity, and temperature is approved by a comparison with the results of other authors. The microbearings can often be a part of MEMS, so the presented method and the obtained analytical solution can serve for solving similar non-isothermal shear-driven or pressure-driven problems. The paper gives an estimation about the error in values for microbearing mass flow and load capacity if the dependence of transport coefficients on temperature are neglected.
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