Imposed Heat Flux Research Articles

Coupling of heat flux and vortex polarization in superfluid helium

We consider a macroscopic description of the mutual influence between heat flux and vortex polarization in superfluid helium, in which the vortices produce a lateral deviation of the heat flux, and the heat flux produces a lateral drift of vortices. This coupling is a consequence of a microscopic Magnus force and mutual friction force between the vortices and the flow of excitations carrying the heat. We keep track of these effects with simplified macroscopic equations, and we apply them to second sound propagation between rotating concentric cylinders and to spatial distribution of polarization across a rectangular channel with vortices polarized orthogonally to the channel in the presence of an imposed heat flux.

Experimental analysis on the hysteresis phenomenon during flow boiling heat transfer in a horizontal stainless-steel tube

This paper presents an experimental analysis on the hysteresis phenomenon occurring during flow boiling heat transfer in a horizontal stainless-steel tube having an internal diameter of 6.0 mm. Pure R134a is the working fluid employed, working at a saturation temperature and a vapor quality fixed to 40°C and 0.30, respectively, whereas two different mass velocities of 400 and 800 kg/m2s are studied. A dedicated experimental procedure has been carried-out to highlight the variation of the two-phase heat transfer performance due to the hysteresis effect. Specifically, tests performed at the same operating conditions but having a different thermal history (a higher imposed heat flux in the transient phase) were seen to provide lower wall superheat values and therefore higher heat transfer performances.The nucleate boiling contribution is isolated from the overall heat transfer and the parameters affecting the boiling curve behavior are highlighted and discussed, pointing out the differences when increasing and decreasing the imposed heat flux once a peak value is reached. The experimental trends are finally upheld by the boiling theory, considering the hysteresis effect as the activation of the surface cavities undergone a higher given thermal boundary condition.

Extension to various thermal boundary conditions of the elliptic blending model for the turbulent heat flux and the temperature variance

Abstract

Asymmetric reverse transition phenomenon in internal turbulent channel flows due to temperature gradients

Laminarization of a turbulent flow due to wall heating has been known for more than 50 years, to the point that it is sometimes used as means of reducing friction. However this phenomenon has been mainly studied for cylindrical pipes and with imposed heat flux but not for channel flows and with imposed temperature boundary conditions, especially with asymmetric ones (that is to say in presence of a transverse thermal gradient). Based on the recent success of some Reynolds-averaged Navier-Stokes (RANS) models to correctly describe the influence of a strong transverse temperature gradient on turbulent Poiseuille flows, when compared to similar direct numerical simulations (DNS) or large eddy simulations (LES) results, these approaches are used here to investigate reverse transition. Since the choice of the turbulence model has a non-negligible influence on the results, however, it is necessary to use different models to get an indication of the uncertainty associated with them. The proposed methodology is based on the use of RANS closures that do not involve any wall functions due to the strong gradient in the wall layer that has to be modeled. Thus, two first-moment closures and a second-moment closure are considered: the k−ω−SST and the k−ε−v2¯/k, and the EB-RSM. The latter two rely on an elliptic blending. The turbulent heat flux is modeled with a simple gradient diffusion hypothesis (SGDH) and a generalized gradient diffusion hypothesis (GGDH) for the first-moment and second-moment closures respectively. In summary, more than 800 calculations are performed for the above three models in order to analyze the reverse transition, and to open room for debate on the possibility for such approaches to correctly reproduce the experimentally observed behavior.

Linear frequency modulated thermal wave imaging for estimation of osteoporosis: an analytical approach

Active infrared thermography or thermal wave imaging is one of the promising non-contact, non-invasive, remote, patient friendly and safe imaging modality for the testing and evaluation of various bio-materials. Among various thermal wave imaging modalities recently proposed, frequency modulated thermal wave imaging gained its acceptance due to its high depth resolvability for visualising the surface and sub-surface features of the test sample. This is due to its continuous depth scanning capabilities with the imposed continuous band of thermal waves with significant and equal magnitudes into the test sample with moderate peak power imposed heat flux in a limited span of experimentation time. This Letter highlights a novel analytical approach for examination of the severity of the osteoporosis. Further, the proposed analytical treatment is validated with the results obtained from the commercially available finite-element based modelling and simulation.

Effects of material thickness on ignition times and creeping flame spread in the thermal regime: Theory, analytical solution and experimental justification

Although there has been a lot of work on ignition times at constant imposed heat flux and on steady creeping flame spread, no definite results exist for the effect of material thickness on these phenomena, specifically away from purely thermally thick or thermally thin conditions. In this work, we first demonstrate, concentrating on the thermal ignition regime, that creeping flame spread can be cast in the form of ignition time at constant heat flux if surface heat losses are neglected. Subsequently, we review relations for ignition time for thermally thick, intermediate and thermally thin conditions including the effects of critical heat flux and heat losses. Finally based on these analyses we present for the first time, new nondimensional correlations and a theoretical way to include the effects of material thickness on creeping flame spread in a practical way as derived from exact equations in the ignition analysis. Then, we compare and validate the new relations using an earlier semi-empirical correlation developed by the author based on numerical and experimental data as well as with recent data.

Influencing factors on flow boiling of carbon dioxide in enhanced tubes and comparison with correlations

Carbon dioxide two-phase flow characteristics are different from those of conventional refrigerants, due to the CO2 particular thermodynamic and transport properties obtained by working at high reduced pressures. Moreover, the use of peculiar heat transfer surfaces such as grooves and internal fins are often preferred to enhance the boiling heat transfer performance. This paper collects CO2 flow boiling heat transfer coefficient data from different independent databases available in scientific literature, regarding both smooth and enhanced geometries and a wide range of operative conditions, that are typical of refrigeration systems and heat pumps. The database for enhanced tubes covers internal diameters from 0.8 to 8.92 mm, saturation temperatures from -30 to +20 °C, imposed heat fluxes from 1.67 to 60 kW/m2 and mass velocities from 75 to 800 kg/m2s, collecting more than 800 points. Heat transfer data for smooth and enhanced surfaces under the same conditions are collected, in order to measure the enhancement and to correlate it to the geometry augmentation. The assessment of quoted prediction methods explicitly developed for carbon dioxide is finally carried out, with a proposal for a correction factor.

Flow boiling of azeotropic and non-azeotropic mixtures. Effect of the glide temperature difference on the nucleate boiling contribution: assessment of methods

Due to the increasing concern about the global warming caused by the use of conventional refrigerants, new HFC/HFO blends are currently proposed to replace high-GWP substances. Most of them, however, present a considerable temperature glide that may negatively affect the nucleate boiling contribution to the heat transfer during evaporation. In this paper, flow boiling data of the new non-azeotropic mixtures R452A and R448A (carrying a high temperature glide of almost 5 °C) and of the conventional quasi-azeotropic blend R404A are provided in a horizontal stainless-steel tube having an internal diameter of 6.0 mm. For all the investigated fluids, the operating conditions explore mass fluxes from 150 to 600 kg/m2s, saturation temperatures from 25 to 55 °C and imposed heat fluxes from 10 to 40 kW/m2, in the whole range of vapor qualities. The nucleative boiling contribution is then isolated from the overall heat transfer coefficient data at disposal and the effect of the heat flux is discussed for both types of blends. Finally, the experimental values and trends are compared to different nucleate boiling correlations taken from literature and conceived for pure fluids, by testing some correction factors explicitly developed for high temperature glide substances.

An Analytical Model for Natural Convection in a Rectangular Enclosure with Differentially Heated Vertical Walls

This paper proposes an analytical model for natural convection in a closed rectangular enclosure filled by a fluid, with imposed heat fluxes at the vertical walls and adiabatic horizontal walls. The analytical model offers a simplified, but easy to handle, description of the temperature and velocity fields. The predicted temperature, velocity, and pressure fields are shown to be in agreement with those obtained from a reliable numerical model. The Nusselt numbers for both the analytical and numerical solutions are then calculated and compared, varying both the aspect ratio of the enclosure and the Rayleigh number. Based on the comparisons, it is possible to assess the dependence of the reliability of the analytical model on the aspect ratio of the enclosure, showing that the prediction error rapidly decreases with the increase of the enclosure slenderness.

Experimental study on bubble characteristics of time periodic subcooled flow boiling in annular ducts due to wall heat flux oscillation

The significant effects of imposed wall heat flux oscillation on bubble characteristics of subcooled flow boiling with R-134a in horizontal annular ducts are experimentally performed in details. Specific emphasis has been applied on the bubble dynamics of the time periodic subcooled flow boiling characteristics influenced by the mean levels, amplitudes, and periods of the wall heat flux oscillations. The obtained experimental results have disclosed that the bubble parameters like the departure diameter, frequency and active nucleation site density, do oscillate periodically in time and are at the same frequency as the imposed wall heat flux oscillation. Nevertheless, these parameters also increase at long periods, high amplitudes of imposed heat flux oscillation or high values of mean imposed heat flux. Furthermore, the bubble size reduced after the time lag when the imposed heat flux decreases with time.

Non-linear Non-Iterative transient inverse conjugate heat transfer method applied to microelectronics

Solving for temperature profiles given boundary conditions, geometry, and material properties is relatively straightforward given the wealth of analytical and computational techniques available. However, experimentally we often measure temperatures and seek to understand unknown boundary conditions or material properties. This problem is generally ill-posed. Thus, to get the value of these input parameters, we use inverse methods: knowing the output of the system (i.e., temperature), we can compute the value of the unknown parameters (e.g., thermal conductivity or heat fluxes). In microelectronics, the location and magnitude of the boundary conditions including local heat generation rates are often unknown or difficult to model due to the compactness of the current microchips and active thermal management schemes that distribute computations between different cores causing time-varying heat generation within the chips. This information can be retrieved using inverse heat transfer methodologies by tracking the temperature distributions in space and time. In this work, we develop a new, non-iterative inverse methodology to retrieve the heat flux inside of 3D geometries of stacked microchips. This method not only provides good agreement between the imposed and the retrieved heat flux with a linear form of the heat diffusion equation, but also predicts the imposed heat flux with good accuracy in situations with non-linearities. Here we numerically and experimentally validate our new approach using a microchip with 25 heaters that can be operated independently to create different spatial and temporal heat flux patterns. During testing, the system is in a controlled environmental chamber and the temporal and spatially varying temperature of the top surface of the chip is measured using infrared thermography for input to the inverse method. The system and model include non-linearities through varying convective heat transfer boundary conditions on different parts of a test article and temperature-dependent thermal properties of the constituent materials. The inverse methodology retrieves the local heat generation rates with good agreement in time, space, and magnitude. An uncertainty analysis of the computation and the experiments is also detailed. Our methodology is unique compared to past work because non-linearity is solved without the need of using iterative processes, which makes the algorithm computationally efficient. Ultimately, this method is useful for the determination of the location and magnitude of the heat flux in any 3D system based on external temperature measurements with real heat transfer properties without the need of an iterative procedure.

Buoyancy-driven convection in a horizontal porous layer saturated by a power-law fluid: The effect of an open boundary

An infinitely wide horizontal porous layer saturated by a power-law fluid is heated from below by an imposed heat flux. The basic stationary state is characterised by a horizontal throughflow and a constant temperature gradient along the vertical direction. A linear stability analysis is performed by employing the method of normal modes. The eigenvalue problem obtained is solved by employing two different approaches: a hybrid analytical/numerical technique and a fully numerical technique. The critical values defining the threshold configurations for the onset of thermal convection are presented. These threshold values display a non monotonic dependence on the basic flow rate while they are monotonically increasing functions of the power-law index.

Compressibility and variable inertia effects on heat transfer in turbulent impinging jets

This article shows the importance of flow compressibility on the heat transfer in confined impinging jets, and how it is driven by both the Mach number and the wall heat flux. Hence, we present a collection of cases at several Mach numbers with different heat-flux values applied at the impingement wall. The wall temperature scales linearly with the imposed heat flux and the adiabatic wall temperature is found to be purely governed by the flow compression. Especially for high heat-flux values, the non-constant wall temperature induces considerable differences in the thermal conductivity of the fluid. This phenomenon has to date not been discussed and it strongly modulates the Nusselt number. In contrast, the heat transfer coefficient is independent of the varying thermal properties of the fluid and the wall heat flux. Furthermore, we introduce the impingement efficiency, which highlights the areas of the wall where the temperature is influenced by compressibility effects. This parameter shows how the contribution of the flow compression to raising the wall temperature becomes more dominant as the heat flux decreases. Thus, knowing the adiabatic wall temperature is indispensable for obtaining the correct heat transfer coefficient when low heat-flux values are used, even at low Mach numbers. Lastly, a detailed analysis of the dilatation field also shows how the compressibility effects only affect the heat transfer in the vicinity of the stagnation point. These compressibility effects decay rapidly further away from the flow impingement, and the density changes along the developing boundary layer are caused instead by variable inertia effects.

A molecular dynamics simulation study of thermal conductivity anisotropy in β-octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine (β-HMX)

Molecular dynamics (MD) simulations were used to predict the thermal conductivity of β-octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine (β-HMX) along directions normal to the (011), (110), and (010) crystal planes. These directions were selected based on the measured morphological importance of the corresponding crystal surfaces. A reverse non-equilibrium MD approach was used wherein a constant heat flux is imposed along a prescribed direction and the resulting steady-state temperature gradient determined. The coefficient of thermal conductivity λ is the quotient of heat flux and temperature gradient (i.e. Fourier’s law). Finite-size effects and sensitivity to imposed heat flux were investigated. The results reveal a modest dependence of the conductivity on crystal orientation, significant finite-size effects, and low sensitivity to imposed flux so long as the Fourier’s law analysis is limited to the spatial interval in the simulation cell for which the temperature gradient is constant. Infinite-length thermal conductivities were estimated by linear regression of λ−1(L) versus reciprocal cell length L−1 for each direction. The predicted values are systematically larger, but within a factor of two, than most published experimental determinations, the latter of which were obtained for pressed-powder or composite samples rather than oriented single crystals.

Excitons Diffusion Length, Tree Dimensionless Numbers and Mean Temperature Dependence of Semiconductor Performance Including Excitons

The author, taking into account the non-uniformity of dissociation, the recombination of excitons in the depletion region, as well as the variability of the coefficients as a function of temperature, used dimensional analysis. Thus, by grouping together the physical parameters, dependent and independent variables, he generates dimensionless numbers. Among the latter, we have the ratio between the diffusion time and the lifetime of the charge carriers (Fourier number); the ratio between the imposed heat flux and that thermal conduction (heating factor) and the ratio between the mobility of the excitons and that of the electrons. The motivation of the author is on the one hand to show the influence of these dimensionless numbers on the diffusion lengths of the charge carriers and on the other hand their influence and that of the diffusion lengths on the total photocurrent density of the carriers. Therefore, he studied the effects of the mean temperature and those of the mobility ratio on the total density of the photocurrent. In order to carry out such work, the author opted for the finite volume method combined with an iterative line-by-line relaxation method of the Gauss-Seidel type as a method of solving his physical problem.

Peripheral Heat Transfer Coefficient during Flow Boiling: Comparison between 2-D and 1-D Data Reduction and Discussion about Their Applicability

This paper presents a critical analysis of possible data reduction procedures for the evaluation of local heat transfer coefficient during flow boiling experiments. The benchmark method using one-dimensional (1-D) heat transfer in a heated tube was compared to a new data reduction method in which both radial and circumferential contributions to the conductive heat transfer inside a metal tube are considered. Using published experimental flow boiling data, the circumferential profiles of the wall superheat, inner wall heat flux, and heat transfer coefficients were independently calculated with the two data reduction procedures. The differences between the two methods were then examined according to the different heat transfer behavior observed (symmetric or asymmetric), which in turn was related to the two-phase flow regimes occurring in a channel during evaporation. A statistical analysis using the mean absolute percentage error (MAPE) index was then performed for a database of 417 collected flow boiling data taken under different operating conditions in terms of working fluid, saturation temperature, mass velocity, vapor quality, and imposed heat flux. Results showed that the maximum deviations between the two methods could reach up to 130% in the case of asymmetric heat transfer. Finally, the possible uses of the two data reduction methods are discussed, pointing out that the two-dimensional (2-D) model is the most reliable method to be employed in the case of high-level modeling of two-phase flow or advanced design of heat exchangers and heat spreader systems.

Investigation of the Wall Scalar Fluctuations Effect on Passive Scalar Turbulent Fields at Several Prandtl Numbers by Means of Direct Numerical Simulations

Abstract We investigate the effect of the wall-scalar fluctuations on passive scalar turbulent fields for a moderate Reynolds number Rτ = 395 and for several Prandtl numbers ranging from the very low value Pr = 0.01 to the high value Pr = 10 by means of direct numerical simulation (DNS) simulations. Several cases of plane channel flows are considered. Case I is a channel flow heated on both walls with a constant imposed heat flux qw. We consider for this case two different types of boundary conditions. For the first one, the isoscalar boundary condition θw = 0 is imposed at the wall implying that its fluctuation and therefore its rms scalar fluctuations θrms=⟨θ′θ′⟩ is zero at the wall whereas in the second type, θw is not prescribed to a fixed value so that it is fluctuating in time at the wall leading to nonzero rms fluctuations. In this latter case, as the heat flux is maintained constant in time at the wall, the fluctuating heat flux q′w reduces to zero at the wall. For illustration purpose, in addition to case I, we also consider case II, which is a plane channel heated only from one wall but cooled from the other one at the same rate taking into account of the freestream scalar boundary condition at the wall θ′w≠0 with q′w=0. The distributions of the mean scalar field, root-mean-square fluctuations, turbulent heat flux, correlation coefficient, turbulent Prandtl number, and Nusselt number are examined in detail. Moreover, some insights into the flow structure of the scalar fields are provided. As a result of interest, it is found that the mean scalar field ⟨θ⟩ is not affected by the scalar fluctuations at the wall. But owing to the different boundary conditions applied at the wall, significant differences in the evolution of the rms scalar fluctuations θrms are observed in the immediate vicinity of the wall. Surprisingly, the maximum rms intensity remains almost unchanged in the near wall region whatever the type of boundary condition is applied at the wall. In addition, the turbulent heat fluxes that play a major role in heat transfer are found to be independent of the wall scalar fluctuations. This study demonstrates that the impact of the wall scalar fluctuations is appreciable mainly in the near wall region. This outcome must be taken into account when simulating industrial flows with thermal boundary conditions involving different fluid/solid combinations.

Thermal conductivity and thermal rectification of nanoporous graphene: A molecular dynamics simulation

Using non-equilibrium molecular dynamics (NEMD) simulation, we study thermal properties of the so-called nanoporous graphene (NPG) sheet which contains a series of nanoporous in an ordered way and was synthesized recently (Science 360 (2018), 199). The dependence of thermal conductivity on sample size, edge chirality, and porosity concentration are investigated. Our results indicate that the thermal conductivity of NPG is about two orders smaller compared with the pristine graphene. Therefore this sheet can be used as a thermoelectric material. Also, the porosity concentration helps us to tune the thermal conductivity. Moreover, the results show that the thermal conductivity increases with growing the sample length due to ballistic transport. On the other hand, along the armchair direction, the thermal conductivity is larger than the zigzag direction. We also examined the thermal properties of the interface of NPG and graphene. The temperature drops significantly through the interface leading to an interface thermal resistance. The interface thermal resistance changes with imposed heat flux direction, and this difference cause significantly large thermal rectification factor, and heat current prefers one direction to another. Besides, to investigate those quantities fundamentally, we study the phonon density of states and scattering of them.

Validation of Heat Transfer between Theoretical and Experimental from the Internal Surface of Vertical Tubes with Internal Rings Heated by Electrical Heating Coils

The comparison between experimental and theoretical heat transfer inside heated vertical channels that dissipate heat from the internal surface with and without internal rings is studied. The experimental setup consists of a circular pipe which is heated electrically by providing constant heat flux on the wall. The theoretical and experimental analysis is conducted in several pipes of same diameter but different lengths. The length of the pipe varies from 450 mm to 850 mm. The length to diameter ratios are taken as L/D = 10, 12.22, 15.56, and 18.89. The value of imposed heat flux varies from 250 to 3340 W/m2. The internal ring thickness varies from 4 mm to 8 mm. separation distance between the internal rings varies from 75mm to 300 mm. The theoretical results are compared with experimental data to ascertain numerical accuracy of the method. The effects of L/D ratio, thickness of internal rings and separation distance on the heat transfer performance are studied. The experimental result is compared with theoretical, theoretical results are found by using ANSYS. In this study theoretical result for wall temperature along the height of tube, fluid temperature at exit of tube are compared with experimental data.

Experimental thermal and hydraulic characterization of R448A and comparison with R404A during flow boiling

Refrigerant R404A is going to be banned in Europe for different applications due to its very high GWP of 3943. R448A is a suitable alternative (GWP of 1390) among other new mixtures, and is thus receiving considerable attention in literature. However, despite several overall system studies, there is a lack of flow boiling data for this new blend. This paper therefore presents an experimental investigation on two-phase heat transfer and pressure drop of R448A in a single horizontal stainless steel (AISI 316) tube with an internal diameter of 6.0 mm. The effect of the operating parameters is firstly analyzed for the whole range of vapor qualities, by changing the mass flux from 146 to 601 kg/m2 s and the bubble saturation temperature from 23.3 to 56 °C (reduced pressures from 0.266 to 0.554). For the heat transfer coefficient measurements, the imposed heat flux is also varied from 2.5 to 40 kW/m2, leading to a total amount of 460 data points. Several pressure drop and heat transfer coefficient data are then compared to those of conventional refrigerant mixture R404A at the same operating conditions, showing different relative importance of nucleate and convective boiling contributions. Finally, the agreement between the R448A experimental database and some two-phase boiling heat transfer coefficient and frictional pressure drop prediction methods is evaluated with a statistical analysis. The best results are respectively obtained with the correlations of Gungor and Winterton and of Friedel.