Abstract
The transient heat transfer process is studied in rarefied gas confined between two stationary concentric cylinders. The inner cylinder (filament) is subjected to a periodically heating-cooling cycle. The energy transfer is modeled with continuous model based on Navier-Sockes Fourier equations of motion and energy transfer and with a statistical DSMC model. Numerical results for the temperature, thermodynamic pressure and pressure difference between thermodynamic pressure and radial stress tensor component are obtained for different circular frequencies of heating cooling cycle of filament and for different filament radii. The pressure variation at the end of any local heating stage of heating-cooling cycle is close to the value of equilibrium thermodynamic pressure. The results are applicable in designing the pulsed Pirani sensors.
Highlights
Pirani vacuum gauges usually consist of an electrically heated filament suspended in a cylindrical tube
The differences in numerical results between the two models appear visually large but as values are below 0.5%
This means that there were no significant differences in numerical results obtained by two methods – NSF and Direct Simulation Monte Carlo (DSMC)
Summary
Pirani vacuum gauges usually consist of an electrically heated filament suspended in a cylindrical tube. G. Boundary conditions are: diffusive at the outer cylinder wall; diffusive or adiabatic at the inner cylinder wall depending on the time t; periodic along axis Oz. We denote the particle velocity before collision with wall with z , r , and after with. We denote the particle velocity before collision with wall with z , r , and after with This gas-surface interaction model can be described by keeping the particle velocity magnitude invariant and the velocity direction of the reflected particle set based on isotropic scattering boundary conditions in the half unite sphere. We discuss this problem first in the spherical coordinate system c, 1, 2. 2kBT1 m depends on the wall temperature T1 and the particle mass m , while at the adiabatic reflection the coefficient c is the particle velocity magnitude before collision on the particle with the wall
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