Inhomogeneous Heat Flux Research Articles

Thermal management for microelectronic chips under non-uniform heat flux with supercritical CO2

With the rapid growth of information technology and the evolution in the use of microelectronic chips, these components are facing major challenges of high heat dissipation and inhomogeneous heat flux. To address the hotspot issues, a combination of microchannel heat sinks (MCHS) with cavity-rib designs and supercritical fluids is a potential solution. This study compares the thermo-hydraulic properties of water and supercritical carbon dioxide (sCO2) under various boundary conditions and hotspot locations during non-uniform heating. The results showed that sCO2 can effectively improve temperature uniformity along the heat sink in the presence of hotspots as compared to water. Considering a mass flow rate of 600 kg/(m2·s), the inhomogeneity index of the basal temperature of sCO2 is found to be 0.24, significantly lower than 4.22 for water. This indicates that sCO2 eliminates hot spots by rapidly increasing specific heat capacity near the pseudo-critical temperature. Furthermore, it is noted that maintaining the operating temperature of sCO2 near the pseudo-critical temperature can increase the specific heat capacity of the fluid in a short time, in addition to reducing the corresponding density and viscosity. Consequently, the entropy generation rate of sCO2 under ideal conditions is 46.6 % of that of water. Therefore, the proposed combination of a microchannel of complex structure and sCO2 in this study is demonstrated to effectively reduce the influence of hot spots and improve the overall thermal performance of heat sinks.

Conjugate heat transfer of a turbulent tube flow of water and GaInSn with azimuthally inhomogeneous heat flux

An experimental study of the conjugate heat transfer in a turbulent tube flow with azimuthally homogeneous and inhomogeneous heat flux distribution, where the tube is heated with a constant heat flux only over the half circumference, is presented. Using two fluids with clearly different Prandtl numbers (water and a liquid metal alloy), thermohydraulic effects that occur when fluids with very low Prandtl number are used in contrast to ordinary fluids (e.g. water with Pr≈1) are discussed. The test section is validated with water (Pr=5−7.4) for a Reynolds number in the range of 5·103<Re<4.2·104. The experimental data agree excellently with literature data. The maximum nondimensional temperature at the inner surface of the tube is expressed using a simple relationship based on the efficiency of a fin with an adiabatic tip. A near eutectic alloy of gallium, indium and tin (GaInSn, Pr=0.03) is used for the liquid metal experiments. The Péclet number is varied within the range of 240<Pe<3·103. Based on the experimental data of this work, an adapted correlation for the Nusselt number in a turbulent liquid metal tube flow with azimuthally homogeneous heat flux is provided:Nu=4.364+0.0276·Pe0.803The experimental data underlines, that the azimuthally averaged Nusselt number for an azimuthally inhomogeneous heat flux distribution can also be calculated with this correlation with an acceptable level of accuracy. Remarkably, the ratio of the local convective heat transfer coefficient to the azimuthally averaged value for GaInSn reaches a value up to 0.6 at the location of the maximum wall temperature. This is in strong contrast to water, where this ratio is close to unity.

Hybrid thermal and optical modeling of a solar air heater with a non-flat plate absorber

In this study, we developed a model based on a SAH. We can enhance air turbulence by creating a non-flat plate on a SAH absorber using a ratio of (e/H = 6), thereby increasing the solar collector’s convective heat transfer coefficient, Nusselt number, and thermal performance. A validation experiment was conducted to determine the accuracy of the developed model. Ray tracing and FEM simulation techniques were used to analyze the optical and thermal properties of the system simultaneously. Various operational and structural conditions were applied to analyze the system’s thermal performance under inhomogeneous heat flux on the absorber’s surface. The data demonstrate that non-flat plate surfaces contribute to wall-induced turbulence, which affects air temperatures. Outcomes demonstrate that mass flow rate excessively affects thermal efficiency, useful energy, and outlet temperatures. Thus, when the inlet air flow rate increases from 0.02 to 0.06 kg/s, the average hot air temperature at the SAC outlet during the daytime reduces from 55.6 to 47.82 °C, applicable heat energy increase from 646.5 to 970 W, and the average thermal efficiency increased from 28.8 to 54.7 %. Instantaneous non-flat absorber plates increased average thermal efficiency and heat transfer coefficient (h) to 9.10 and 27.24 % compared with flat plate absorbers (e/H = 1) at the same mass flow rate (0.05 kg/s). The highest Nusselt number increase observed during the day is 141.5% for non-flat plate compared to flat plates.

Topology Optimization Method of a Cavity Receiver and Built-In Net-Based Flow Channels for a Solar Parabolic Dish Collector.

The design of a thermal cavity receiver and the arrangement of the fluid flow layout within it are critical in the construction of solar parabolic dish collectors, involving the prediction of the thermal-fluid physical field of the receiver and optimization design. However, the thermal-fluid analysis coupled with a heat loss model of the receiver is a non-linear and computationally intensive solving process that incurs high computational costs in the optimization procedure. To address this, we implement a net-based thermal-fluid model that incorporates heat loss analysis to describe the receiver's flow and heat transfer processes, reducing computational costs. The physical field results of the net-based thermal-fluid model are compared with those of the numerical simulation, enabling us to verify the accuracy of the established thermal-fluid model. Additionally, based on the developed thermal-fluid model, a topology optimization method that employs a genetic algorithm (GA) is developed to design the cavity receiver and its built-in net-based flow channels. Using the established optimization method, single-objective and multi-objective optimization experiments are conducted under inhomogeneous heat flux conditions, with objectives including maximizing temperature uniformity and thermal efficiency, as well as minimizing the pressure drop. The results reveal varying topological characteristics for different optimization objectives. In comparison with the reference design (spiral channel) under the same conditions, the multi-objective optimization results exhibit superior comprehensive performance.

Turbulent heat transfer in a liquid metal tube flow with azimuthally inhomogeneous heat flux

An experimental study of the convective heat transfer in a turbulent liquid metal tube flow with azimuthally inhomogeneous heat flux is presented. Prior to the liquid metal experiments, the validation of the test section was realized using water. These results showed a very good agreement with literature data. For the liquid metal experiments, an eutectic alloy of gallium, indium and tin (GaInSn) was used. The Péclet number was varied between 1400 and 3600, thus in a regime of forced convection. Experiments with homogeneous heating over the full circumference of the tube and inhomogeneous heating over half of the circumference with the other half being insulated, were performed. The azimuthally averaged Nusselt number and the temperature distribution in the tube wall were investigated. The results suggest that the azimuthally averaged Nusselt number for water and liquid metal tube flows with inhomogeneous heating over the circumference can be calculated sufficiently well with literature correlations for uniform heat flux. For an inhomogeneous heat flux the azimuthal temperature gradient in the tube wall increases for higher Reynolds number and is more pronounced for GaInSn than for water. Furthermore, impurities like oxide particles significantly decrease the liquid metal convective heat transfer coefficient.

CFD/FEA Co-Simulation Framework for Analysis of the Thermal Barrier Coating Design and Its Impact on the HD Diesel Engine Performance

Thermal barrier coatings (TBCs) have been investigated both experimentally and through simulation for mixing controlled combustion (MCC) concepts as a method for reducing heat transfer losses and increasing cycle efficiency, but it is still a very active research area. Early studies were inconclusive, with different groups discovering obstacles to realizing the theoretical potential. Nuanced papers have shown that coating material properties, thickness, microstructure, and surface morphology/roughness all can impact the efficacy of the thermal barrier coating and must be accounted for. Adding to the complexities, a strong spatial and temporal heat flux inhomogeneity exists for mixing controlled combustion (diesel) imposed onto the surfaces from the impinging flame jets. In support of the United States Department of Energy SuperTruck II program goal to achieve 55% brake thermal efficiency on a heavy-duty diesel engines, this study sought to develop a deeper insight into the inhomogeneous heat flux from mixing controlled combustion on thermal barrier coatings and to infer concrete guidance for designing coatings. To that end, a co-simulation approach was developed that couples high-fidelity computational fluid dynamics (CFD) modeling of in-cylinder processes and combustion, and finite element analysis (FEA) modeling of the thermal barrier-coated and metal engine components to resolve spatial and temporal thermal boundary conditions. The models interface at the surface of the combustion chamber; FEA modeling predicts the spatially resolved surface temperature profile, while CFD develops insights into the effect of the thermal barrier coating on the combustion process and the boundary conditions on the gas side. The paper demonstrates the capability of the framework to estimate cycle impacts of the temperature swing at the surface, as well as identify critical locations on the piston/thermal barrier coating that exhibit the highest charge temperature and highest heat fluxes. In addition, the FEA results include predictions of thermal stresses, thus enabling insight into factors affecting coating durability. An example of the capability of the framework is provided to illustrate its use for investigating novel coatings and provide deeper insights to guide future coating design.

Topology optimization of the fluid flow layout in a thermal cavity receiver under inhomogeneous heat flux

Topology optimization of the fluid flow layout in a thermal cavity receiver under inhomogeneous heat flux

Rayleigh–Bénard convection with a melting boundary

We study the evolution of a melting front between the solid and liquid phases of a pure incompressible material where fluid motions are driven by unstable temperature gradients. In a plane-layer geometry, this can be seen as classical Rayleigh–Bénard convection where the upper solid boundary is allowed to melt due to the heat flux brought by the fluid underneath. This free-boundary problem is studied numerically in two dimensions using a phase-field approach, classically used to study the melting and solidification of alloys, which we dynamically couple with the Navier–Stokes equations in the Boussinesq approximation. The advantage of this approach is that it requires only moderate modifications of classical numerical methods. We focus on the case where the solid is initially nearly isothermal, so that the evolution of the topography is related to the inhomogeneous heat flux from thermal convection, and does not depend on the conduction problem in the solid. From a very thin stable layer of fluid, convection cells appear as the depth – and therefore the effective Rayleigh number – of the layer increases. The continuous melting of the solid leads to dynamical transitions between different convection cell sizes and topography amplitudes. The Nusselt number can be larger than its value for a planar upper boundary, due to the feedback of the topography on the flow, which can stabilize large-scale laminar convection cells.

A comparison between transient CFD and FEM simulations of solar central receiver tubes using molten salt and liquid metals

Abstract The design of central receivers in solar thermal power plants is crucial for efficiency and operating behavior of the plant. The local heat flux distribution on the absorber tubes varies, depending on time, weather conditions and aim point strategy. A proper receiver design needs accurate thermodynamic models to detect local temperature distribution, especially hot spots on the absorber tubes. Moreover, due to highly transient boundary conditions, the dynamic behavior of the model is important. Starting with a detailed CFD model of a single receiver tube several simplified FEM models were investigated. The influence of an inhomogeneous heat flux distribution on the absorber and the dynamic behavior after a sudden change of heat flux (e.g. due to passage of clouds) were analyzed. In order to consider radiation exchange between surfaces, simulations with a whole receiver panel were also conducted. The FEM model with one-dimensional fluid elements and constant heat transfer coefficients shows a very good agreement with the detailed CFD model. Further simplifications like the presented model, where the tubes are discretized as projected surfaces are computationally very efficient and can be used for relative comparison between receiver configurations. However, this simplification has deviations in the prediction of tube temperatures and radiation losses. Finally, the receiver simulation of the Solar Two power plant validates the FEM model with the measured data for solar salt. The investigation of liquid metals considers a single tube with an inhomogeneous heat flux on its surface. The detailed analysis shows, that the Nusselt number correlation plays an important role for the tube wall temperature. If the Nusselt number is overestimated in the region of the peak heat flux, the simplified model results in a lower tube wall temperature.

Convection in rotating spherical fluid shells with inhomogeneous heat flux at the outer boundary

The Earth's core is subject to a laterally varying heat flux at the outer boundary, which may account for correlations between the geomagnetic field and lower mantle structure. Studies of nonmagnetic, rotating convection in a spherical shell with fixed temperature boundary conditions have revealed flows resonating with, or locked to, the boundary anomalies when the length scales of the convection are close to those of the boundary condition. Here we study a similar system but for fixed heat flux upper boundary conditions, as in the Earth's core. We first map out the onset of thermal instability in a rotating shell of aspect ratio 0.4 for uniform outer boundary cooling with both rigid and stress-free boundaries. A preference for large scale (azimuthal wavenumber m = 1) flows, not observed for the uniform temperature case, persists to Ekman numbers down to almost 10− 4. The preference for large scales is greatest for rigid boundaries and high (≥ 1) Prandtl numbers. Hemispheric asymmetry appears in the weakly nonlinear regime, with small scale columnar convection coexisting with larger scale flows. We next study the effect of heterogeneous cooling of strength ε proportional to the Y 2² spherical harmonic, which resembles the assumed heat flow at the core-mantle boundary. We illustrate the results with two sets of parameters, (1) when the most unstable mode in the uniform case is m = 2, the same as the heterogeneous boundary condition, and (2) when it is m = 1. We follow the numerical solutions from steady flows dominated by boundary heating, through periodic flows drifting at non-uniform rates, to chaotic flows. In case (1) both thermal convection and boundary-driven flow are dominated by the same azimuthal wavenumber m = 2 as the boundary condition; they give way to periodic flows of the same symmetry (even m) at low boundary heterogeneity. At higher ε the symmetry is broken as modes with odd m are excited. In case (2) at low ε the m = 1 and m = 2 modes compete, while higher ε imposes an m = 2 symmetry. Boundary effects depend strongly on the most unstable wavenumber at onset of convection with uniform boundary cooling: these simple linear results are a good guide to the probable behaviour of more complex, nonlinear regimes and have already been used to find suitable parameter ranges in a geodynamo calculation.

Longwave Marangoni convection in an inhomogeneously heated liquid

The supercritical Marangoni convection has been studied in a plane-parallel liquid layer, bounded by a free deformable gas-liquid interface from above and by a low-heat-conductivity wall from below, occurring under conditions of inhomogeneous heating in the horizontal plane. In a longwave approximation with a small inhomogeneity of heat flux, the process is described by a system of two-dimensional nonlinear equations for the temperature perturbations, vorticity, and free surface deformation. The concept of quasiequilibrium, implying stability of long-range flows, is introduced, which allows the inhomogeneous heat flux to be modeled by a step function. The linear stability is analyzed in the cases of planar and axisymmetric heat fluxes. The boundaries of stability of the convection regimes are determined on the plane of parameters characterizing the degree of supercriticity inside a heated spot and the depth of damping outside the spot. For an axisymmetric spot, the domains of stability with respect to perturbations for various azimuthal numbers are established.

LES STUDY ON THE ENERGY IMBALANCE PROBLEM FOR HETEROGENEOUS SURFACE

The so-called energy imbalance problem is investigated through numerical experiments using Large Eddy Simulation (LES). LES experiments are done for daytime atmospheric boundary layers over a flat surface with inhomogeneous heat flux. The heat flux is represented by a one-dimensional sinusoidal curve with a variable wavelengtha nd amplitude.The following are the main results. 1) When the amplitude is enough, the bias and variance of imbalance is increase. A weak inhomogenity of surface heating, however, may relax the negative bias of imbalance. This is attributed to the heat transport efficiency of vertical mean wind. 2) Although longer wavelengths generally give a smallerb ias of imbalance, the 2km wavelength singularly increases the bias of imbalance. 3) The bias and variance of imbalance decrease in accordance with horizontal wind. Longer averaging time gives a smaller bias but a larger variance of imbalance. The tendency of these two results is almost the same as in the homogeneoush eatingc ase.

RECENT GEODYNAMO SIMULATIONS AND OBSERVATIONS OF THE GEOMAGNETIC FIELD

In 1995, two groups [Kageyama et al., 1995; Glatzmaier and Roberts, 1995a, 1995b] reported results of numerical integrations of fully three‐dimensional, fully nonlinear dynamos. Their papers were precursors of a stream of such models that have focused particularly on the geodynamo. They provide us, in unprecedented detail, with spectacular realizations of interesting geomagnetic field behaviors, such as secular variation and even polarity reversals. The proliferation of models has, however, created some confusion and apparently conflicting results. This can be partly attributed to the different ways in which different groups have modeled the core, normalized their equations, defined their dimensionless parameters, chosen their boundary conditions, and selected their energy sources. This has made it difficult to compare the results of different simulations directly. In this paper, we first try, as far as possible, to overcome this difficulty, so that all reported results can be compared on common ground. We then review the results, emphasizing three major topics: (1) onset and evolution of convection, (2) character of the magnetic field generated, and (3) comparison with the observed geomagnetic field. Although there are large differences in the way that the simulations are defined, the magnetic fields that they generate have some surprising similarities. The fields are dominated by the axial dipole. In some models they are most strongly generated in shear layers near the upper and lower boundaries and near the tangent cylinder, an imaginary surface touching the inner core on its equator. Convection rolls occur within which a type of the α effect distorts the toroidal field lines to create poloidal magnetic field. Some features of the models are found to strongly affect the fields that they produce. In particular, the boundary conditions defining the energy flow (e.g., an inhomogeneous heat flux or distribution of buoyancy sources) are very influential and have been extensively studied. They change the frequency and the mode of magnetic polarity reversals as well as the ratio in strengths of the dipole and nondipole moments. As the ultimate goal of geodynamo simulations is to explain the features of the real geomagnetic field, it is essential that proper comparisons be made between simulation results and observations. It is remarkable that polarity reversals reminiscent of the paleomagnetically observed field reversals have already been simulated by some of the models. Other features such as drift of the field, its secular variation, and statistical properties of Gauss coefficients are discussed in this paper and are compared with observations. These comparisons are rather primitive, not only because self‐consistent dynamo models are still too new and too few but also because many of the observations (and especially the paleomagnetic data) are themselves not yet reliable or decisive enough. The aim of the third part of this paper is therefore more to demonstrate the potential use of simulations than to elucidate the nature of geomagnetic field generation.

Evidence for Maxwell's thermal pressure via light-induced velocity-selective heating or cooling.

The recently observed kinetic effect [R. W. M. Hoogeveen and L. J. F. Hermans, Phys. Rev. Lett. 65, 1563 (1990)] due to a light-induced velocity-selective heating or cooling is incorporated into the standard kinetic theory based on a generalized Boltzmann equation. The measured pressure difference results from a spatially inhomogeneous heat flux analogous to the thermal pressure which Maxwell had anticipated for rather different experimental conditions.