Heat Transfer In Rarefied Gas Research Articles

Rarefied Flow Simulations of Heat Transfer Across Evacuated Cryogenic Tank Insulation Structures

The Direct Simulation Monte Carlo Method computations are performed to investigate the heat transfer across highly evacuated cryogenic tank insulation structures. These structures usually consist of one cold and one hot wall with a temperature difference up to 260 K surrounding a rarefied gas which originates from permeating or leaking propellant. To validate the flow solver PICLas for this application, heat transfer results across parallel flat plates with nonflowing gaseous hydrogen and methane are compared to empirical relations of rarefied gas heat transfer and reference computations, showing good agreement with a deviation of less than 11%. Because gas flow usually occurs during and after evacuation, the heat transfer and skin friction coefficient in a symmetrical hydrogen channel flow with a wall distance of 30 mm is compared with literature data, showing a good match with a Nusselt number deviation of less than 20%. Furthermore, honeycomb tank insulation structures are analyzed, which can be used for future cryogenic liquid rocket tanks. Here, rarefied flow simulations are performed for slitted honeycomb structures with and without throughflow of hydrogen gas at a Knudsen number of 1.5 and transitional flow conditions at a Knudsen number of 0.1. The heat transfer results at the honeycomb sandwich are 50 to 70% below empirical relations for heat transfer across flat plates. Throughflow does not affect the heat transfer across the honeycomb because the Peclet number is less than 0.01.

Nanothermometry in rarefied gas using optically levitated nanodiamonds.

Heat transfer in gases in the continuum regime follows Fourier's law and is well understood. However, it has been long understood that in the subcontinuum, rarefied gas regime Fourier's law is no longer valid and various models have been proposed to describe heat transfer in these systems. These models have very limited experimental exploration for spherical geometries due to the difficulties involved. Optically levitated nanoparticles are presented as the ideal experimental system to study heat transfer in rarefied gases due to their isolation from their environment. Nanodiamonds with nitrogen-vacancy centers are used to measure temperature. As the pressure decreases so does the heat transfer to the rarefied gas and the nanodiamond temperature increases by over 200 K. These experiments demonstrate the utility of optically levitated nanoparticles to study heat transfer in any gas across a wide range of pressures. In the future, these measurements can be combined with models to empirically determine the energy accommodation coefficient of any gas.

Correlation of Forced Convection Heat Transfer of Isothermal Plate Under Low Pressure

With the rapid development of vacuum tube transport technology, there is increased interest in understanding the behavior of the heat transfer of rarefied gas in a vacuum tube. Currently, most empirical correlations of forced convection heat transfer are conducted at the standard atmospheric pressure, so many correlations are not applicable to conditions below the atmospheric pressure. To investigate the heat transfer property under low-pressure conditions, the forced convection between isothermal plate and air in a low-pressure environment is numerically simulated. The results show that the traditional correlation of the forced convection heat transfer between the isothermal plate and gases is different from the actual results at low pressure, and the correlation is completely invalid when the pressure is lower than 0.2 kPa. Based on the data of numerical calculation, a modified correlation of forced convection heat transfer between an isothermal plate and gases under low pressure is proposed. The correlation coefficient R is greater than 0.99, and the fitting error is less than 10% at the 95% confidence level. The change of heat transfer depends on the Reynolds number in the pressure range of 0.2–100 kPa, but the effect of Reynolds number is weakened and the effect of pressure is strengthened when the pressure is below 0.2 kPa.

A free convection heat transfer correlation for very thin horizontal wires in rarefied atmospheres

Mars and upper Earth atmosphere missions are booming in recent years increasing the interest in heat transfer in rarefied gases. At these low pressures, the heat transfer problems involving small geometries whose characteristic length is of the order of the mean free path of the gas molecules, raises new difficulties. This being especially severe in the case of free convection, where the velocity of the gas is closely linked to the heat transfer problem. Experiments with horizontal wires with diameters of 12.7 μm and 25 μm were conducted in a tailored vacuum chamber with pressures from 0.03 millibar to ambient pressure, reaching temperature differences of up to 80 K between the wire and the air. Experimental data is comprised of Rayleigh numbers from 10−13 to 10−5 that cover a wide range from free molecular flow to continuum regime. Particularly for the transition regime, with Knudsen numbers ranging between 0.1 and 10, the scattering of the experimental data shows that the free convection heat transfer cannot be represented solely as a function of the Rayleigh number, but a dependence on another parameter, in this case the Knudsen number, must be taken into account for the correlation as well. The presented results for the Nusselt number for Rayleigh numbers below 10−8 exhibit a clear departure from the available correlations in the literature. An empirical correlation for free convection from horizontal thin wires from the transition to continuum regime is presented. The present work sheds light on current thermal engineering problems that involves very thin wires in their systems which interact with a surrounding environment with a significant level of rarefaction. Systems such as temperature sensors based on thermocouple wires for Mars atmosphere, whose measurements are affected by a low free convection heat transfer, could benefit from this study gaining a better performance in modelling with a more accurate estimation of free convection heat transfer. Results in this range of parameters have not been found in published literature.

On the basic concepts of the direct simulation Monte Carlo method

In this paper, the basic ideas underlying the Direct Simulation Monte Carlo (DSMC) method are examined and a novel nonhomogeneous N-particle kinetic equation describing the randomized mathematical model of DSMC is derived. It is shown that different collision-partner selection schemes, including No-Time-Counter (NTC) and Bernoulli-trials schemes, are approximations of the general transition operator of the randomized model. The popular collision-partner selection schemes, represented by the standard NTC and Bernoulli-trials approximations of the general transition operator, represented by Simplified Bernoulli-trials and Generalized Bernoulli-trials schemes, are tested on the one-dimensional rarefied gas heat transfer problem against conditions of two approximation limits: first, leading to the Boltzmann equation and, second, leading to the novel N-particle kinetic one.

Thermal dispersion effects on heat transfer of laminar gas flow in a microtube filled with porous medium

In this paper, dispersion effects on forced convection heat transfer in a gaseous slip flow through a microtube filled with anisotropic porous medium are investigated semi-numerically. Microtube is subjected to constant heat flux and a local thermal non-equilibrium condition is assumed. Rarefaction effects are taken into account by applying first-order velocity slip and temperature jump boundary conditions. Dispersion is proven to have a significant impact on heat transfer in rarefied gases. Temperature distributions for both solid and fluid phases are obtained. Nusselt number variation with respect to porous shape factor and Biot number is illustrated, indicating enhancement up to 10% in predicted heat transfer due to dispersion. The influence of Reynolds number on thermal dispersion is proven to be insignificant. Dispersion plays a significant role as gas becomes more rarefied. It is seen that an increase in shape factor of a porous media can improve Nu for a non-rarefied gas, but as rarefaction effects grow, this can affect heat transfer negatively. Also, effects of dispersion on heat transfer diminishes for higher values of Biot Number due to the overcoming of interstitial heat transfer to thermal dispersion effect.

Impact of mode of application of magnetic field on rate of heat transfer of rarefied gas flows in a microtube

This paper examines theoretically the impact of transverse and radial mode of application of magnetic field on rate of heat transfer of rarefied gas in a micro tube. The momentum and energy governing equations are solved analytically with a uniform wall heat flux (H2 boundary conditions) applied on the heated perimeter of the cross section while the remaining arc length is assumed to be adiabatic. The velocity, temperature and Nusselt number are presented as a function of Knudsen number, azimuth angle and Hartmann number. During the course of numerical and graphical representations, results indicate that the role of magnetic field is to increase rate of heat transfer for both modes of application, while the impact of Knudsen number is to decrease rate of heat transfer for both cases. Furthermore, rate of heat transfer is higher in case of radial magnetic field in comparison with transverse magnetic field for both continuum flow and slip flow regimes.

Analytical solution of the problem of heat transfer in rarefied gas between two coaxial cylinders

The method of characteristics was used within the framework of the kinetic approach to construct an analytical solution of the problem of heat transfer in a channel whose walls were formed by two coaxial cylinders. The main equation was the Williams kinetic equation, and the boundary condition on the channel walls was the diffusion reflection model. The vector field of the heat flux in the channel was determined, and the specific heat flux through the cross section of the channel was calculated. It was shown that the results obtained for a limiting case, in which the cylinder radii were significantly greater than the mean length of free path of gas molecules, were in good agreement with the results obtained for a plane channel with infinite parallel walls.

Analytical Solution of the Problem of Heat Transfer in Rarefied Gas between Two Coaxial cylinders

Analytical Solution of the Problem of Heat Transfer in Rarefied Gas between Two Coaxial cylinders

Conditional maximums of heat fluxes in cylindrically and spherically symmetric problems of heat transfer in rarefied gas for the free molecular and transitional regimes

We consider the heat transfer in gas between surfaces of cylindrical and spherical symmetry for the free molecular and transitional regimes. For the free molecular heat transfer we derive the analytical expressions for the surface temperatures ratios at which the heat fluxes to the surfaces reach the conditional maximums provided that the temperatures of the opposite surfaces remain constant. For the transitional regime we study conditional maximums of the heat fluxes at different Knudsen numbers by the Direct Simulation Monte Carlo method.

Conjugate heat transfer in rarefied gas in enclosed cavities

The heat transfer in buoyancy driven rarefied gas in a conjugate cavity has been investigated in this paper. The governing equations along with the slip flow and temperature jump boundary conditions are solved using finite-volume technique. The simulations are carried by varying cavity aspect ratios, conductivity ratios and cavity tilt angles. The Nusselt number values are calculated for different Knudsen, Rayleigh and Prandtl numbers. It was found that Kn number is the most influential parameter on the heat transfer; as it increases the heat transfer in the cavity decreases. The effect of all other investigated factors was found and documented; however, it is found that, in general, at high Kn Numbers their effect on the heat transfer is marginal. It is also found that cavity walls with good conducting materials will have minor effect on heat transfer while insulation material will have moderate effect on heat transfer. Two correlations for average Nusselt number are proposed: one for horizontal cavities; Nu=0.149kr0.0101Ra0.135Kn−0.393Pr0.178 and the second correlation equation introduces the effect of the cavity tilt angle along with Ra and Kn; Nu = 0.158Ra0.130, Kn−0.396, cos(θ)0.216.

Couette flow regimes with heat transfer in rarefied gas

Based on numerical solution of the Boltzmann equation by direct statistic simulation, the Couette flow with heat transfer is studied in a broad range of ratios of plate temperatures and Mach numbers of a moving plate. Flow regime classification by the form of the dependences of the energy flux and friction stress on the Knudsen number Kn is proposed. These dependences can be simultaneously monotonic and nonmonotonic and have maxima. Situations are possible in which the dependence of the energy flux transferred to a plate on Kn has a minimum, while the dependence of the friction stress is monotonic or even has a maximum. Also, regimes exist in which the dependence of the energy flux on Kn has a maximum, while the dependence of the friction stress is monotonic, and vice versa.

Effect of surface roughness on rarefied-gas heat transfer in microbearings

In this Letter, the rarefaction and roughness effects on the heat transfer process in gas microbearings are investigated. A heat transfer model is developed by introducing two-variable Weierstrass–Mandelbrot (W–M) function with fractal geometry. The heat transfer problem in the multiscale self-affine rough microbearings at slip flow regime is analyzed and discussed. The results show that rarefaction has more significant effect on heat transfer in rough microbearings with lower fractal dimension. The negative influence of roughness on heat transfer found to be the Nusselt number reduction. The heat transfer performance can be optimized with increasing fractal dimension of the rough surface.

Rarefied-gas heat transfer in micro- and nanoscale Couette flows

The physics of the heat conduction and viscous dissipation in rarefied gases is analyzed and discussed. A heat transfer model valid for arbitrary Knudsen numbers, defined as the ratio of the molecular mean free path to the characteristic length of channels, is derived by treating the heat transfer behavior in the slip and transition regimes as an intermediate function of continuum heat transfer model and free molecular heat transfer model. Comparison studies reveal that this model not only shows good agreement with the numerical results based on the direct simulation Monte Carlo method, but also has some unique features that can overcome the deficiencies existing in the previous models. Therefore, this model is capable to study the heat transport phenomena in very dilute gas Couette flows through micro/nanochannels more accurately.

Numerical Studies of Heat Transfer in Rarefied Gases at Head-Disk Interface

In this article we derived a new heat transfer model by treating the heat conduction and viscous dissipation in the slip and transition flow regimes as an intermediate function of continuum heat transfer model and free molecular heat transfer model. We also employed this heat transfer model, together with our self-developed air bearing simulation code called ABSolution to analyze heat transfer behaviors at the head-disk interface (HDI) of two thermal flying height control (TFC) sliders. We found that slider design has a significant effect on the net heat flux from the slider to the disk. A properly designed TFC slider, which uses low pressure distribution around the reader/writer elements, can reduce air bearing cooling and compensation effects in this area and increase the thermal actuation efficiency of the slider. The thermal accommodation coefficient between the slider and the disk is also an important parameter to affect the heat flux at the HDI. Therefore, its effect should be considered carefully to improve the accuracy in simulating TFC sliders.

Heat transfer in the transition regime: solution of boundary value problems for Grad's moment equations via kinetic schemes.

This paper presents a systematic approach to the calculation of heat transfer in rarefied gases (Knudsen numbers between 0.01 and 1) by means of Grad's moment method with high moment numbers, based on the Boltzmann equation with linearized collision term. The problem of describing boundary conditions for the moments is solved by the use of the so-called kinetic schemes that allow the implementation of the boundary condition for the Boltzmann equation. The results, obtained with up to 48 one-dimensional moment equations, exhibit temperature jumps at the walls with adjacent Knudsen boundary layers. For given wall temperatures and Knudsen number, the results change with the number of moments, and converge if the number of moments is increased.

96/02239 Heat transfer in rarefied gas at a gas-solid interface

96/02239 Heat transfer in rarefied gas at a gas-solid interface

Heat transfer in rarefied gas at a gas-solid interface

Modified expressions for the heat-transfer fluxes at the interface of a solid surface and a gas are given for different Knudsen-number regimes. These expressions for diatomic gases contain both a gas-reflection and a thermal accommodation coefficient. Parallel-plate, coaxial-cylindrical and concentric-spherical surfaces are considered. A general expression for the thermal accommodation coefficient is based on experimental data. Sample numerical calculations of heat flux in different heat-transfer regimes are presented in terms of the reciprocal Knudsen number.

Heat transfer in rarefied gases: Critical assessments of thermal conductance and accommodation of argon in the transition regime

Heat transfer measurements from thin filaments to argon gas in cells of cylindrical symmetry are made under extreme clean surface conditions so that known constant values of α, the thermal accommodation coefficient, on the filament pertain over the full range of pressures, 0.01–40 Torr. The results are used in an attempt to assess merit of principal theoretical treatments of heat transfer in the transition regime by extracting α according to each treatment and comparing results with the presumed known value. Before relative merit of the theories can be assigned with confidence, a wider differentiation in the α values obtained is needed. It is expected that this may result when similar experiments for the higher α gases, krypton and xenon, can be completed and critically examined.

Investigation of heat transfer in rarefied gases over a wide range of Knudsen numbers

The paper presents experimental results on heat exchange of fine metallic filaments with a rarefied gas at different pressures. The investigations were carried out using the transient hot-wire technique in the case of small temperature perturbations. The heat fluxes for a number of inert and some polyatomic gases have been measured under different heat transfer conditions ranging from a molecular to a continuum regime. The experimental results showing the dependence of heat fluxes on the gas rarefaction degree have been compared with the theoretical ones obtained from the solution of the BGK model by the variational method. Under the conditions of molecular heat transfer, the dependence of the energy accommodation coefficients on the kind of material and the state of the filament surface, kind of gas and mean temperature of the system is found. The filaments were made of platinum, nickel, tungsten and tantalum. The surface was cleaned by annealing in high vacuum and in a weak hydrogen atmosphere. Control of the surface state was accomplished by the thermal flash method and by checking a change in the surface emissivity. The degree of filament recrystallization in the process of thermal refining was determined by X-ray structural analysis.