Kapitza conductance of aluminium and heat transport through subcooled He II

Heat transport measurements in a large diameter tube containing He II are reported. The range of temperatures investigated are from 1.7 K to 2.1 K with applied pressures up to the critical pressure, 0.23 MPa. Temperature gradients established in the liquid are compared with previous experimental work and the theory of mutual friction. The Gorter-Mellink mutual friction constant, A, is observed to increase with applied pressure. At 2.01 K, a 0.1 MPa increase in pressure results in a 13.5 ± 4% enhancement of A. The results are used to predict the pressure and temperature dependence of the peak heat flux. Simultaneous measurements of the surface heat transfer from high purity aluminum to He II are reported. Kapitza conductance, film boiling and recovery heat flux data are analyzed and compared to other results on similar systems. A correlation is observed between the recovery heat flux and the film boiling heat transfer coefficient.     

Time dependent heat transport in subcooled superfluid helium

The authors present an extensive study on the behaviour of time dependent heat transport in subcooled He II under conditions which are closely related to the cooling problem of superconducting magnets. Experimental results on the delay for onset of burnout and on the transient recovery from burnout are discussed. A theoretical model is derived from the assumption that heat diffusion characterized by the Gorter-Mellink equation is the dominant mode of heat transport and that thermal waves play no direct role in this connection. The comparison of experimental and calculated results shows a very satisfactory agreement which fully validates the model.     

Visualization of Bubble Nucleation in Boiling 3He

The heat transfer properties of ³He bubbles in the nucleate boiling state have been investigated in liquid ³He below 1.0 K by using the shadowgraph method. The temperature difference between the copper surface and liquid ³He temperature was also measured as a function of heat flux in steady state. The size and number of bubbles departing from the surface in a specific time were compared using photograph recorded by a high-speed video camera at various heat flux and liquid ³He temperature of 0.5, 0.7 and 1.0 K.     

Studies of heat transport to forced flow He II

Analytical and experimental studies of heat transport to forced flow He II are reported. The work is pertinent to the transfer of He II in space. An analytical model has been developed which establishes a condition for two phase flow to occur in the transfer line. This condition sets an allowable limit to the heat leak into the transfer line. Experimental measurements of pressure drop and flow meter performances indicate that turbulent He II can be analysed in terms of classical pressure drop correlations.     

Recovery heat flux from silent and noisy film boiling states in saturated liquid He II

Heat transfer into saturated He II was investigated in an experiment which simulates the use of He II as coolant for the stabilization of superconducting magnets. One must distinguish two critical values of the recovery heat flux density (ie recovery from film boiling to non-boiling), namely for recovery from silent film boiling and recovery from noisy film boiling. There are also two threshold values of the power of short-time heat pulses which trigger a transition from the non-boiling heat transfer into film-boiling. The increased cooling capacity of He II at about 1.9 K seems to compensate for the reduction of the thermal parameters of the stabilizing material at the low temperature.     

PIV application in He II forced flow research

We report an experimental approach for applying the PIV technique to measurements in He II forced flow. The forced flow of He II is created in a 3.5 m long experimental channel within the Liquid Helium Forced Flow Visualization Facility (LHFVF). We demonstrate that micron size solid hydrogen isotope particles are the best choice for tracing He II forced flow. A novel particle seeding device has been developed to form and seed such solid hydrogen isotope particles directly within He II flow. Velocity field measurements of forced flow He II subjected to a constant locally applied heat flux are presented. Results are compared to analysis based on the two-fluid model.     

Criterion for quantum turbulence onset after rectangular heat pulse in superfluid helium

On the basis of transient heat transfer measurements of the film boiling onset time in a He II bath, a criterion correlated to the bath temperature and pressure for quantum turbulence onset after a rectangular heat pulse in superfluid helium is shown. Using the criterion parameter α it is possible to determine the time τ needed to initiate quantum turbulence in the He II bath after a rectangular heat pulse. It is found that the criterion value in a He II bath is much smaller than that for He II confined in small channels. A strong pressure effect is also exhibited.     

Effects of wall thickness and material property on inverse heat conduction analysis of a hollow cylindrical tube

In this study, we examined the effects of a hollow cylindrical tube’s thickness and material properties on estimated time delay and waveform distortion in a one-dimensional inverse heat transfer analysis model using the thermal resistance method and an input estimation algorithm. Results indicated a persistent time delay for various heat flux amounts applied to different tube thicknesses. As the tube thickness increased, the numerically determined temperature data also experienced a time delay, which affected the inverse heat transfer response curve. Results also indicated that the transient heat flux waveform estimated for different material properties showed higher levels of distortion for materials having relatively low thermal conductivity. These materials also exhibited greater time delays. To address these issues, we applied a Fourier number (a dimensionless number representing the tube’s thickness and material properties) and proposed an equation to calculate sharpness, which can subsequently be used to predict probable time delays and heat flux waveform distortion. In conclusion, a correction is required when a low Fourier number is used in inverse heat transfer analysis.     

Microscale bone grinding temperature by dynamic heat flux in nanoparticle jet mist cooling with different particle sizes

Nanoparticle jet mist cooling (NJMC) is an effective solution to prevent heat injuries in clinical neurosurgery bone grinding. A simulation study on temperature field of microscale bone grinding was performed to discuss the effect of nanoparticle size on heat convection during this cooling method by the dynamic heat flux density model. Such dynamic heat flux density model was established through real-time acquisition of grinding force signals. Results showed that given the real-time dynamic heat flux, workpiece surface temperature changes with time. Nanofluids using 30?nm nanoparticles show the largest heat convection coefficient (1.8723?W/mm²?·?K) and the lowest average surface temperature followed by nanofluids of 50, 70, and 90?nm nanoparticles successively. An experimental verification using fresh bovine femur was conducted with 2% (volume fraction) of different sizes of Al₂O₃ nanoparticles. The simulated temperature under dynamic heat flux comes close to the actual measured temperature. Under testing conditions, temperature under mist cooling is 33.6°C, temperatures under NJMC using nanofluids (30, 50, 70, and 90?nm) are 21.4, 17.6, 16.1, and 8.3% lower, respectively. This result confirmed the positive correlation between the average workpiece surface temperature and nanoparticle size. Experimental results agreed with theoretical analysis, verifying the validity of theoretical modeling.     

Effect of superheating on heat transfer from a good thermal conductor in a two-dimensional channel to He II below the λ-point pressure

Heat transfer characteristics in He II have been investigated in relation to superheating. When a good thermal conductor in a narrow two-dimensional channel is heated above the critical heat flux of the λ-transition, superheated He I nucleates in the hottest area of the conductor covered with superheated He II. The spread of superheated He I, which has a low thermal conductivity, forms an intermediate state in which superheated He I coexists with superheated He II. Superheated He I together with superheated He II is apparently stabilized since part of the heat cut off by superheated He I tends to flow in the conductor. Higher heat input turns the intermediate state into a mixed state where superheating and boiling alternate irregularly.     

Experimental measurements and modeling of transient heat transfer in forced flow of He II at high velocities

An experiment has been built to study heat transfer in forced flow of He II at flow velocities up to 22 m/s. The main part of this experiment is a 10 mm ID, 0.86 m long straight test section instrumented with a heater, thermometers and pressure transducers. The high flow velocities allow clear observation of the effects of the forced convection, counterflow heat transfer and the Joule–Thomson effect. A numerical model based on the He II energy conservation equation and including pressure effects has been developed to compare with the experimental results. The model works well for low flow velocities where the heat flux is primarily driven by the temperature gradient and for high flow velocities where the heat flux is primarily driven by the pressure gradients. In the intermediate velocity region, discrepancies between the model and experiment may result from an inappropriate representation of the heat flux by counterflow when the temperature and pressure gradients have an effect of similar magnitude on the heat flux.     

Effect of channel restrictions on the axial heat transport in subcooled superfluid helium

The present study investigates the influence of partial restrictions on the axial heat transport and critical heat flux limits in subcooled superfluid helium (helium II) channels. Different size orifices are used to simulate partial plugging of superconducting magnets cooling channels by frozen oxygen, nitrogen, hydrogen, neon or moisture during the cool down process. Thin stainless steel sharp edged orifices of sizes 0.5, 1, 2 and 5 mm id are mounted between stainless steel flanges attached to 9 mm diameter (helium II) channel. The helium II channel is heated at one end with a copper block heater while the other end heat sinks to an atmospheric superfluid helium heat exchange. Temperature drop across the restriction is measured by two calibrated carbon resistors. Measurements are carried out at both temperatures ranging from 1.8 to 2.2 K.As the orifice/channel area ratio decreases, data show a considerable decrease in the axial heat transported by internal convection process resulting in lower critical heat flux at the phase transition from helium II to helium I by the destruction of superfluidity and inititation of boiling. A linear correlation between critical channel heat flux and orificeI channel area ratio gives a good fit to the experimental data. For heat fluxes higher than the critical heat flux, transient temperature measurements for a step heat input are correlated with the time required to reach the phase transition.     

Numerical analysis for two-dimensional transient heat transfer from a flat plate at one-side of a duct containing pressurized He II

A numerical analysis of two-dimensional transient heat transfer produced by step heat inputs to a flat plate located at one end of a rectangular duct containing pressurized He II was performed. The computer code, SUPER-2D, that is the two-dimensional heat transfer code for He II developed by Tatsumoto et al. [1] based on the two fluid model and the theory of the mutual friction was used for the calculation. The time lag from the application of the step heat input to the occurrence of the λ transition, which is called a lifetime, was obtained for various values of step heat flux for bulk liquid temperatures ranging from 1.8 to 2.0 K. The calculations were made for three rectangular ducts having different cross-sectional area. The ratios of the cross-sectional area of the duct to the heated surface area, A_d/A_h, were 1.0, 1.6 and 2.0. Effect of the A_d/A_h on the lifetime was clarified. The solutions agreed with the experimental data by Shiotsu et al. [2] for the ducts with the same structures and the corresponding conditions. It was confirmed that the computer code, SUPER-2D, can describe transient heat transport in He II as well as steady-state one [1].     

Theoretical prediction of piloted ignition of polymeric fuels in microgravity at low velocity flows

A numerical model developed for the prediction of the piloted ignition delay of solid polymeric materials exposed to an external radiant heat flux is used to predict the ignition delay and critical heat flux for ignition of solid fuels in microgravity at low velocity flows. The model considers the coupled thermochemical processes that take place in the condensed phase, including oxidative and thermal pyrolysis, phase change, radiation absorption, and heat and mass transfer in a multi-phase and multi-composition medium. Ignition is considered to occur when a critical pyrolysate mass flow rate is reached at the sample surface. Microgravity experimental surface temperature and ignition delay data previously obtained in a KC-135 aircraft are used to infer, in conjunction with the theoretical analysis, the critical mass flow rate for ignition. This value is then used to predict the ignition delay as a function of the external radiant heat flux, and the critical heat flux for ignition. Calculations are made for Polymethylmethacrylate (PMMA) and a Polypropylene/Fiberglass composite at airflows of 0.09 and 0.15 m/s under microgravity conditions and at 1.0, 1.75 and 2.5 m/s under normal gravity. The experiments and theoretical predictions show that the ignition delay and critical heat flux for ignition decrease as the forced airflow velocity decreases. It is predicted that at the tested lower velocities, the critical heat flux for ignition is close to half the value measured in normal gravity. The results have important implications since they indicate that materials could ignite easier under the conditions expected in spacecraft, and consequently stricter design specifications may be needed for fire safety.     

Visualization study of the interface between superheated He II and superheated He I in a two-dimensional narrow channel by using the shadowgraph method

Dynamic behavior of superheated He II-superheated He I interface as a result of heating in a narrow channel between parallel walls that simulates cooling channels of superconducting magnets was investigated using a shadowgraph visualization method. It was confirmed that a superheated state could be created in the narrow channel without preparing a special calm environment. A superheated He II-superheated He I interface transiently appeared between 2.0 K and lambda temperature when applying a small heat flux. The boiling state accompanying the superheated He II-superheated He I interface was repeatedly generated and collapsed. This boiling mode was anticipated to have a high heat transfer coefficient.     

Influence of dislocations on the Kapitza conductance of copper at temperatures between 1 and 2 K

An experiment is described in which the dependence of the Kapitza conductance of copper to He II on the dislocation density near the interface is investigated in the temperature range of 1–2 K. A dependence is found, which has not been reported before, giving support to the dislocation -based theoretical models. The Kapitza conductance for a low-dislocation-density sample is shown to be an order of magnitude below the usual values, and within the range of validity of these theories.Supported by the Science Research Council.     

Numerical analysis of two-dimensional steady-state and transient heat transfer in a parallel duct filled with pressurized He II

Analysis on steady-state and transient heat transfer on a flat plate at the middle of a parallel duct immersed in He II was performed for bath temperatures from 1.8 to 2.1 K at 101.3 kPa. Two-dimensional computer code named SUPER-2D developed by the authors based on the two-fluid model and the theory of mutual friction was used. Steady-state critical heat flux (CHF) and the time lag from the application of a step heat input to λ transition, that is called a lifetime, were obtained numerically for various step heat fluxes and for the channel gaps from 2 to 20 mm. Effect of the gap restriction on the CHF and the lifetime were clarified. The solutions were compared with the experimental data for the ducts with the same structures and the corresponding conditions. They agreed well with the experimental data. The heat transport mechanism in the parallel duct was clarified.