Investigation of cold-to-hot transfer and thermal separation zone through nano step geometries

Abstract

Nanosteps form once nanochannels of various diameters connect to each other. The focus of this paper is to investigate the heat transfer and hydro/thermal field behavior in nanostep geometries using direct simulation Monte Carlo. The effects of the hydrodynamics separation on the pressure field and heat lines are reported, i.e., we show that the length of the hydrodynamics separation zone is different from the positive pressure gradient and thermal separation zones. Interestingly, cold to hot transfer is observed when the wall temperatures and inlet temperature are close to each other. We show that cold to hot heat transfer appears due to the interplay between the higher order term of the heat flux formula, which is a function of the second derivate of the velocity, with the Fourier term; the cold to hot transfer effect is omitted as the wall temperature or Knudsen number increases. In addition, the impact of different parameters, such as pressure ratio, Knudsen number, and wall temperature adjacent to the separation zone, are investigated. The dependence of the mass flow rate and the length of the separation zone on the wall temperature and the channel pressure ratio is considered. We show that Knudsen minimum is not observed in the step geometry for both isothermal and non-isothermal wall conditions.

A Comparative Study on the Molecular- and Continuum-Based Simulation Methods for Gas Flow and Mixing in Micro/Nanochannels

“…It seems that using the higher-order constitutive laws is inevitable if one is going to use Eqs. 168-7 mention that a similar phenomenon called "cold-to-hot" transfer was observed in studying the heat transfer in rarefied conditions, which could be described by including the higher order terms in the heat flux expression [15].…”

Free-molecular and near-free-molecular gas flows over backward facing steps

“…Reviewing existing studies on rarefied gas flows over micro-steps (Beskok 2001;Baysal et al 2004;Xue et al 2005;Hsieh et al 2010;Bao & Lin 2011;Darbandi & Roohi 2011;Mahdavi et al 2014;Mahdavi & Roohi 2015;Gavasane et al 2018), the current work presents several new findings that are of fundamental and practical significance. In contrast to the common view, it is first demonstrated that step detachment may occur at free-molecular conditions, identified by a unique velocity profile.…”

“…To this end, Xue et al (2005) applied DSMC calculations to characterize the effect of gas rarefaction on the flow regime, and reported on sudden 'jumps' in the hydrodynamic fields at the step section at large Kn conditions. Roohi, Mahdavi and co-workers (Darbandi & Roohi 2011;Mahdavi et al 2014;Mahdavi & Roohi 2015) conducted numerical simulations to analyse the effects of step temperature and gas heat transfer on the flow field. More recently, Gavasane, Agrawal & Bhandarkar (2018) demonstrated the occurrence of the Knudsen paradox in a micro-step channel geometry.…”

“…The channel solid boundaries are assumed isothermal and with the common inlet reservoir temperature T * in . Consideration of different wall temperatures, as studied in Mahdavi et al (2014) and Mahdavi & Roohi (2015), may be readily carried out, but is not followed here to simplify presentation (see § 6).…”

“…It is in this limit where the analytic solution becomes of particular value to study the free-molecular flow field, as described below. Based on previous DSMC investigations (Xue et al 2005;Darbandi & Roohi 2011;Mahdavi et al 2014;Mahdavi & Roohi 2015;Gavasane et al 2018), it is expected that no flow detachment (in the form of step separation and recirculation) occurs at free-molecular conditions. This is supported by the results in figure 6, showing fully attached streamline profiles at the step in set-ups with high density and temperature drops.…”