Heat Flux Parameters Research Articles

Analysis of the simulated global temperature using a simple energy balance stochastic model

This work presents a study of the response of the simulated global temperature variability to additive and multiplicative stochastic parameterizations of heat fluxes, along with a description of the long-term variability in terms of simple autoregressive processes. The Earth's global temperature was simulated using a globally averaged energy balance climate model coupled to a thermodynamic ocean model. It was found that simple autoregressive processes explain the temperature variability in the case of additive parameterizations; whereas in the case of multiplicative parameterizations, the description of the temperature variability would involve higher order autoregressive processes, suggesting the presence of complex feedback mechanisms originated by the multiplicative forcing. Also, it was found that multiplicative parameterizations produced a rich structure that emulates closely observed climate processes. Finally, a new approach to describe the stability in the steady state of a general one-dimensional stochastic system, through its potential function, was proposed. From an analytical expression of the potential function, further insight into the description of a stochastic system was provided.

Damage Morphologies in Targets Exposed to a New Plasma Deflagration Accelerator for ELM Simulation

Transient events in fusion power plants such as DEMO and ITER are known to pose a severe threat to plasma facing components (PFCs) due to melting and erosion after repeated edge localized mode (ELM) loads. In situ experimental testing of potential PFC materials at fusion relevant conditions is difficult and expensive, and as a result plasma devices capable of replicating the desired transient conditions are of increasing interest. At Stanford University, an experimental facility designed to mimic the heat flux, particle fluence, and other key characteristics of ELMs and disruption events in a controlled setting has been developed. A pulsed plasma accelerator operating in the deflagration mode is used to generate high-velocity (40–100 km/s) directed plasma jets that are stagnated on target material samples. In this paper, we present probe data characterizing the plasma parameters of the accelerated plume using hydrogen as the working gas, as well as preliminary target studies of silicon and copper witness plates exposed to pulses at various total and peak shot energies. Results from the probe analysis indicate achieved energy fluxes and heat flux parameters that are ELM-like, and the observed linearly correlated damage morphologies on the witness plates indicate that initial surface roughness plays a significant role in the growth characteristics of surface damage patterns. These results lay the groundwork for future studies of ELM-like loading on reactor-relevant materials using the Stanford plasma accelerator facility.

The Correlative Approach of 3D Imaging Techniques, Simulation and Diffusion Experiments to Explore Transport Properties in Porous Otm Support Material

Solid state electrochemical energy devices such as batteries, fuel cells and oxygen transport membranes (OTMs) have the potential to revolutionize distributed low-carbon power supply. However, in order to accelerate their commercialization across a range of applications, a much improved understanding of the underlying material microstructure is required. In particular, the rate limiting step of an OTM membrane applied for syngas production is found in concentration losses caused by mass transport limitations. In this field, microstructural parameters, such as tortuosity, porosity and average pore diameter, play a vital role in characterising, comparing and evaluating porous materials. However, unlike the latter two parameters, tortuosity cannot be measured directly which is why different methods have been developed for this purpose. These differ considerably from each other in terms of calculation approach and data preparation techniques. Here, we utilise X-ray nano computed tomography (CT) techniques to reveal the complex microstructure and resolve geometric features affecting mass transport of tubular porous support layers of OTMs to examine the relationship between the pore structure and mass transport (Figure 1). This is achieved via image based tortuosity calculation methods: a fast marching computational technique and a Laplace solver using MATLAB is employed to examine the geometrical tortuosity, and StarCCM+ and COMSOL software packages are used to model the heat flux and effective transport parameters of the porous phase, respectively. In turn, the results are validated using diffusion cell experiments to evaluate the bulk transport properties of the same samples for different binary gas mixtures at different temperatures. Tortuosity is then extracted by applying equimolar and equimass diffusion models [1]. We conclude, that image based calculation methodologies arrive at lower tortuosity values in comparison to diffusion cell experiments (Figure 2). Even the widely used Bruggeman [2] and Maxwell relations prove to be unfit to estimate tortuosity values in the analysed microstructure. The observed difference may stem from Knudsen diffusion effects which are not accounted for in the entirety of tomography based modelling techniques. Secondly, tortuosity values extracted via diffusion cell experiments are a function of gas mixture, temperature and microstructural characteristics rather than a constant value. Consequently, care must be taken in applying purely continuum interpretations of diffusion processes in these complex porous media.

Effects of surface orientation on nucleate boiling heat transfer in a pool of water under atmospheric pressure

The basic wall boiling model widely used in computation fluid dynamics codes gives no regard to influences of surface orientation upon boiling mechanism. This study aims at examining the effects of surface orientation on wall heat flux and bubble parameters in pool nucleate boiling and incorporating those into the wall boiling model. Boiling experiments on a flat plate heater submerged in a pool of saturated water were conducted under atmospheric pressure. Relevant bubble parameters as well as boiling heat transfer characteristics were simultaneously measured using a unique optical setup integrating shadowgraph, total reflection and infrared thermometry techniques. It was observed that as an upward-facing heater surface with a constant wall superheat of 7.5°C inclines from horizontal towards vertical, the heat flux significantly increased; nucleation site density increased intensively at the upper part of the heater surface where thermal boundary layer might become thickened; isolated boiling bubbles tend to slide up due to buoyancy and coalesce with each other, thus forming one single large bubble. Such observations on the wall heat flux and bubble parameters according to surface orientation could not be predicted by the present basic wall boiling model only centered with isolated bubbles. A modified wall boiling model incorporating the effects of merging of isolated bubbles on an inclined surface was proposed. The model reasonably predicted the experimental data on various orientation angles.

Mathematical Model of Heat Transfer in Morphological Part of Vegetation at Influence by Thermal Radiation from Surface Forest Fire Front

Numerical research results of heat transfer in layered tree trunk influenced by heat flux from forest fire are presented. The problem is solved in two-dimensional statement in Cartesian system of co-ordinates. The typical range of influence parameters of heat flux from forest fire is considered. Temperature distributions in different moments of time are obtained. Condition of tree damage by forest fire influence is under consideration in this research.

Mathematical Modeling of Thermal Influence from Forest Fire Front on a Coniferous Tree Trunk

Numerical research results of heat transfer in layered tree trunk influenced by heat flux from forest fire presented. The problem solved in two-dimensional statement in Cartesian system of co-ordinates. The typical range of influence parameters of heat flux from forest fire considered. Temperature distributions in different moments of time obtained. Condition of tree damage by forest fire influence is under consideration in this research.

Forced convection heat and mass transfer of MHD nanofluid flow inside a porous microchannel with chemical reaction on the walls

Purpose – The purpose of this paper is to focus on convective heat and mass transfer characteristics of Cu-water nanofluid inside a porous microchannel in the presence of a uniform magnetic field. The walls of the microchannel are subjected to constant asymmetric heat fluxes and also the first order catalytic reaction. To represent the non-equilibrium region near the surfaces, the Navier’s slip condition is considered at the surfaces because of the non-adherence of the fluid-solid interface and the microscopic roughness in microchannels. Design/methodology/approach – Employing the Brinkman model for the flow in the porous medium and the “clear fluid compatible” model as a viscous dissipation model, the conservative partial differential equations have been transformed into a system of ordinary ones via the similarity variables. Closed form exact solutions are obtained analytically based on dimensionless parameters of velocity, temperature and species concentration. Findings – Results show that the addition of Cu-nanoparticles to the fluid has a significant influence on decreasing concentration, temperature distribution at the both walls and velocity profile along the microchannel. In addition, total heat transfer in microchannel increases as nanoparticles add to the fluid. Slip parameter and Hartmann number have the decreasing effects on concentration and temperature distributions. Slip parameter leads to increase velocity profiles, while Hartmann number has an opposite trend in velocity profiles. These two parameters increase the total heat transfer rate significantly. Originality/value – In the present study, a comprehensive analytical solution has been obtained for convective heat and mass transfer characteristics of Cu-water nanofluid inside a porous microchannel in the presence of a uniform magnetic field. Finally, the effects of several parameters such as Darcy number, nanoparticle volume fraction, slip parameter, Hartmann number, Brinkman number, asymmetric heat flux parameter, Soret and Damkohler numbers on total heat transfer rate and fluid flow profiles are studied in more detail. To the best of author’s knowledge, no study has been conducted to this subject and the results are original.

Seasonal surface urban energy balance and wintertime stability simulated using three land‐surface models in the high‐latitude city Helsinki

The performance of three urban land‐surface models, run in off‐line mode, with their default external parameters, is evaluated for two distinctly different sites in Helsinki: Torni and Kumpula. The former is a dense city‐centre site with 22% vegetation, while the latter is a suburban site with over 50% vegetation. At both locations the models are compared against sensible and latent heat fluxes measured using the eddy covariance technique, along with snow depth observations. The cold climate experienced by the city causes strong seasonal variations that include snow cover and stable atmospheric conditions.Most of the time the three models are able to account for the differences between the study areas as well as the seasonal and diurnal variability of the energy balance components. However, the performances are not systematic across the modelled components, seasons and surface types. The net all‐wave radiation is well simulated, with the greatest uncertainties related to snow‐melt timing, when the fraction of snow cover has a key role, particularly in determining the surface albedo. For the turbulent fluxes, more variation between the models is seen which can partly be explained by the different methods in their calculation and partly by surface parameter values. For the sensible heat flux, simulation of wintertime values was the main problem, which also leads to issues in predicting near‐surface stabilities particularly at the dense city‐centre site. All models have the most difficulties in simulating latent heat flux. This study particularly emphasizes that improvements are needed in the parametrization of anthropogenic heat flux and thermal parameters in winter, snow cover in spring, and evapotranspiration, in order to improve the surface energy balance modelling in cold‐climate cities.

A RBF model for predicting the pool boiling behavior of nanofluids over a horizontal rod heater

Pool boiling is an effective means of heat transfer which can handle high fluxes in boiling while maintaining minimum temperature differences over the heated surface. Addition of nanoparticles and surfactants to the base fluid are potential methods for enhancing the pool boiling heat transfer coefficient which can be useful in thermal management of complex and high performance electronic systems. This communication provides a Radial Basis Function (RBF) model to predict the behavior of a surfactant and three different types of nanoparticles on pool boiling heat transfer of water over a horizontal rod heater. In this model, the inputs include experimental condition parameters of heat flux, type of water (distilled or treated water), and concentration of SDS (Sodium Dodecyl Sulfate), nano-alumina, nano-silica with two different particle sizes, and nano-Zinc Oxide. Genetic algorithm is used for determination of the optimum values. Statistical error analysis with different parameters is also implemented for validation of the predictive model. The model is based on three sets of experiments. The effects of two different types of water, SDS and/or nano-alumina (a), the effects of two particle sizes of nano-silica (b), and the effect of combination of nano-Zinc oxide and SDS (c) on pool boiling heat transfer of water as based fluid. In all above sets of tests, the effects of the nanoparticles and SDS coated on the surface of the heater were investigated by repeating the experiments after cleaning all parts of the device except its heater surface. Furthermore, Surface Tension and Dynamic Viscosity, the two crucial thermo-physical characteristics of fluids, were determined for justifying the behavior of the materials used in the experiments. The results showed that the treated water has a better boiling performance in comparison to distilled water; the presence of SDS, Alumina, and the combination of Zinc oxide and SDS enhance the boiling performance of the base fluid; both kinds of nano-silica deteriorates the pool boiling heat coefficient of water and the smaller one has more reduction effect; the combination of the Zinc Oxide and SDS is the best coolant among the aforementioned ones. Finally, the experimental results are modeled using radial basis function neural networks and the outputs of the model are in great agreement with the experimental data.

Thermal behavior of a microdevice under transient heat loads

An experimental study was carried out to investigate the transient response of a thermal microsystem to both a step change and a square wave pulse change in heat flux. The microsystem consisted of a single microchannel etched on a silicon microdevice that was bonded to a Pyrex wafer. A thin-film titanium heater was deposited on the Pyrex substrate. The heater acted as the power source as well as the resistance temperature device. The influence of flow convection on the transient response was studied for two fluids: air and HFE-7000. The effects of heat flux, Reynolds number, fluid properties, and pulse parameters (amplitude, width, duty cycle) on the transient temperature response were identified. The temperature response consisted of an initial rapid temperature rise followed by slower convection dynamics. For longer pulse widths, the temperature of the microdevice reached steady state. Higher order dynamics were identified at the beginning of the temperature response. Convection dynamics were approximated as a first-order response, and the effects of Reynolds number and fluid properties on the time constant of the first order response were identified.

Water Mass Transformations Driven by Ekman Upwelling and Surface Warming in Subpolar Gyres

AbstractThe Sverdrup relationship when applied to the Southern Ocean suggests that some isopycnals that are deep in the eastern Pacific will shoal in the Atlantic. Cold waters surfacing in the South Atlantic at midlatitudes would be warmed by the atmosphere. The potential for water mass transformations in this region is studied by applying a three-layer planetary geostrophic model to a wide ocean basin driven by the Ekman upwelling typical of the Southern Ocean surface winds. The model uses a simple physically based parameterization of the entrainment of mass into the surface layer with zonally symmetric atmospheric surface fields to find steady-state subpolar gyre solutions. The solutions are found numerically by specifying suitable boundary conditions and integrating along characteristics. With reasonable parameter settings, transformations of more than 10 Sverdrups (Sv; 1 Sv ≡ 106 m3 s−1) of water between layers are obtained. The water mass transformations are sensitive to the strength of the wind stress curl and the width of the basin and relatively insensitive to the parameterization of the surface heat fluxes. On the western side of the basin where the cold waters are near the surface, there is a large region where there is a local balance between the Ekman pumping and the exchange of mass between layers. Simple formulas are derived for the water mass transformation rates in terms of the difference between the maximum and minimum northward Ekman transports integrated across the basin and the depths of the isopycnal layers on the eastern boundary. The relevance of the model to the Southern Ocean and the Atlantic meridional overturning circulation is briefly discussed.

Correlation analysis of heat flux and cone calorimeter test data of commercial flame-retardant ethylene-propylene-diene monomer (EPDM) rubber

The effects of the heat flux on the thermal decomposition of the commercial flame-retardant ethylene-propylene-diene monomer rubber in a cone calorimeter with a piloted ignition were quantitatively investigated. Correlation analysis of the heat flux and various characteristic parameters, including the ignition time, the thermal thickness, the mass loss rate (MLR), the heat release rate (HRR) and the effective heat of combustion, was conducted. It was found that the transformed ignition time (1/t ig)0.55 and 1/t ig, the peak and average MLR, the first and second peak HRR, the HRR in the quasi-steady stage and the average HRR all increased linearly with the heat flux. The thermal thickness (δ P) decreased with the heat flux and was proportional to $$ \rho/\dot{q}^{\prime\prime} $$ . The specimens under the heat fluxes ≤35 kW m−2 behaved as thermally thin solids, while the thermal decomposition behavior of the specimens under the heat fluxes >35 kW m−2 may be characterized employing the thermally thick heating model. The flammability properties including the critical heat flux, the minimum heat flux, the ignition temperature, the heat of gasification and the heat of combustion, which were calculated theoretically based upon the correlations of the ignition time data, the MLR data and the HRR data with the heat flux, were in accordance with the experimental measured values.

Design of radiant floor heating panel in view of floor surface temperatures

The radiant floor heating panel should be designed to maintain the indoor condition within the comfort range, to prevent discomfort when contacting floor surfaces of uneven temperature distribution, and to prevent skin burn and unwanted deformation of materials. For these reasons, heat flux and floor surface temperature distribution should be examined at the design stage. However, the current design convention focuses mainly on securing enough heat flux and not much of attention is given to floor surface temperature distribution.In this study, design charts were developed that help designers to consider heat flux, difference between maximum and minimum floor surface temperature (DFST), and maximum floor surface temperature (MFST) at the design stage through investigating the relationships between heat flux and design parameters and conducting numerical simulations to analyze floor surface temperature distributions. These charts were validated through experiments. Then some applications and limitations were suggested for utilizing the design charts.The design charts can be applied to panels with no floor covering, linoleum and oak wood as floor coverings. Design alternatives for other floor coverings can also be developed by interpolating the values from the design charts, because there are linear relationships between the required average water temperature and heat flux.The results of this study can be used to examine the designed panel to verify whether it can provide enough heat flux and that DFST and MFST are appropriate. Additionally, the developed design charts help the designer to compare design alternatives, thus enhancing the flexibility of the panel design.

Advancement toward coupling of the VAMPER permafrost model within the Earth system model <I>i</I>LOVECLIM (version 1.0): description and validation

Abstract. The VU Amsterdam Permafrost (VAMPER) permafrost model has been enhanced with snow thickness and active layer calculations in preparation for coupling within the iLOVECLIM Earth system model of intermediate complexity (EMIC). In addition, maps of basal heat flux and lithology were developed within ECBilt, the atmosphere component of iLOVECLIM, so that VAMPER may use spatially varying parameters of geothermal heat flux and porosity values. The enhanced VAMPER model is validated by comparing the simulated modern-day extent of permafrost thickness with observations. To perform the simulations, the VAMPER model is forced by iLOVECLIM land surface temperatures. Results show that the simulation which did not include the snow cover option overestimated the present permafrost extent. However, when the snow component is included, the simulated permafrost extent is reduced too much. In analyzing simulated permafrost depths, it was found that most of the modeled thickness values and subsurface temperatures fall within a reasonable range of the corresponding observed values. Discrepancies between simulated and observed permafrost depth distribution are due to lack of captured effects from features such as topography and organic soil layers. In addition, some discrepancy is also due to disequilibrium with the current climate, meaning that some observed permafrost is a result of colder states and therefore cannot be reproduced accurately with constant iLOVECLIM preindustrial forcings.

Closed-form solution of a thermocapillary free-film problem due to Pukhnachev

We consider the steady two-dimensional thin-film version of a problem concerning a weightless non-isothermal free fluid film subject to thermocapillarity, proposed and analysed by Pukhnachev and co-workers. Specifically, we extend and correct the paper by Karabut and Pukhnachev (J. Appl. Mech. Tech. Phys. 49, 568–579, 2008), in which the problem is solved numerically, and in which it is claimed that there exists a unique solution for any value of a prescribed heat-flux parameter in the model. We present a closed-form (parametric) solution of the problem, and from this show that, on the contrary, solutions exist only when the heat-flux parameter is less than a critical value found numerically by Karabut and Pukhnachev, and that when this condition is satisfied there are in fact two solutions, one of which recovers that obtained numerically by Karabut and Pukhnachev, the other being new.

Experimental study of heat transfer and flow resistance of supercritical pressure water in a SCWR sub-channel

Heat transfer experiments of supercritical pressure water in a sub-channel of SCWR fuel bundle have been performed at Xi’an Jiaotong University. Experimental parameters covered the pressures of 23–28MPa, mass fluxes of 700–1300kg/(m2s) and heat fluxes on the inner wall surface of 200–1000kW/m2. Experimental results showed that the system parameters of heat flux, pressure and mass flux have great effects on heat transfer, most of these effects are associated with the strong variations of thermophysical properties of supercritical water. Five heat transfer correlations have been assessed with the current set of database, it was found that the correlations of Mokry gives the best predictions of Nusselt number for the flow channel. Based on the form of Mokry correlation, a new empirical heat transfer correlation was developed to improve the predicted accuracy. In the present paper, the wall temperature and heat transfer coefficient of the test section were compared with those of a 2×2 central sub-channel. It was found that the heat transfer performance of the present flow channel is worse than that of the real central sub-channel. The flow resistance of supercritical water is reflected in the form of pressure drop, which was discussed with the bulk-flow enthalpy and mass flux.

Cylindrical Thermal Cloak Based on the Path Design of Heat Flux

When heat flux flows in a given medium, its path will solely be determined. This implies that material parameters determined by the predesigned path of heat flux will guide heat to flow along the designed path. Based on this idea, we develop a new method for the design of the cylindrical thermal cloak which can make heat flux detour the cloaked object. For the inhomogeneous anisotropic medium, we derive the relation between the path trajectory of heat flux and material parameters and obtain two differential equations and one boundary condition which are used to determine material parameters in the cylindrical cloak. The transient behavior on the flow of heat flux is simulated by Comsol Multiphysics and the transient thermal protection of the cylindrical cloak for the cloaked object is examined. The effect of the product of density and specific heat on the dynamic diffusion process of heat flux is analyzed. Since one can flexibly design the path of heat flux in the cloak, it has the large degree of freedom to construct thermal cloaks with the specific distributions of material parameters. The present method provides a new blue print for the transient thermal protection of a specific target.

Modelling snow ice and superimposed ice on landfast sea ice in Kongsfjorden, Svalbard

Snow ice and superimposed ice formation on landfast sea ice in a Svalbard fjord, Kongsfjorden, was investigated with a high-resolution thermodynamic snow and sea-ice model, applying meteorological weather station data as external forcing. The model shows that sea-ice formation occurs both at the ice bottom and at the snow/ice interface. Modelling results indicated that the total snow ice and superimposed ice, which formed at the snow/ice interface, was about 14 cm during the simulation period, accounting for about 15% of the total ice mass and 35% of the total ice growth. Introducing a time-dependent snow density improved the modelled results, and a time-dependent oceanic heat flux parameterization yielded reasonable ice growth at the ice bottom. Model results suggest that weather conditions, in particular air temperature and precipitation, as well as snow thermal properties and surface albedo are the most critical factors for the development of snow ice and superimposed ice in Kongsfjorden. While both warming air and higher precipitation led to increased snow ice and superimposed ice forming in Kongsfjorden in the model runs, the processes were more sensitive to precipitation than to air temperature.Keywords: Snow ice; superimposed ice; thermodynamic modelling; landfast sea ice; Kongsfjorden.(Published: 24 August 2015)Citation: Polar Research 2015, 34, 20828, http://dx.doi.org/10.3402/polar.v34.20828

Estimation of Ice Shelf Melt Rate in the Presence of a Thermohaline Staircase

AbstractDiffusive convection–favorable thermohaline staircases are observed directly beneath George VI Ice Shelf, Antarctica. A thermohaline staircase is one of the most pronounced manifestations of double-diffusive convection. Cooling and freshening of the ocean by melting ice produces cool, freshwater above the warmer, saltier water, the water mass distribution favorable to a type of double-diffusive convection known as diffusive convection. While the vertical distribution of water masses can be susceptible to diffusive convection, none of the observations beneath ice shelves so far have shown signals of this process and its effect on melting ice shelves is uncertain. The melt rate of ice shelves is commonly estimated using a parameterization based on a three-equation model, which assumes a fully developed, unstratified turbulent flow over hydraulically smooth surfaces. These prerequisites are clearly not met in the presence of a thermohaline staircase. The basal melt rate is estimated by applying an existing heat flux parameterization for diffusive convection in conjunction with the measurements of oceanic conditions at one site beneath George VI Ice Shelf. These estimates yield a possible range of melt rates between 0.1 and 1.3 m yr−1, where the observed melt rate of this site is ~1.4 m yr−1. Limitations of the formulation and implications of diffusive convection beneath ice shelves are discussed.

The effect of high-flux H plasma exposure with simultaneous transient heat loads on tungsten surface damage and power handling

The performance of the full-W ITER divertor may be significantly affected by the interplay between steady-state plasma exposure and transient events. To address this issue, the effect of a high-flux H plasma on the thermal shock response of W to ELM-like transients has been investigated. Transient heating of W targets is performed by means of a high-power Nd:YAG laser with simultaneous exposure to H plasma in the linear device Magnum-PSI. The effects of simultaneous exposure to laser and plasma have been compared to those sequentially and to laser only. Transient melting is found to be aggravated during plasma exposure and to occur at lower heat flux parameters. Roughness and grain growth are observed to be driven by peak temperature, rather than by the loading conditions. The temperature evolution of the W surface under a series of transients is recorded by fast infrared thermography. By accounting for changes in the reflectivity at the damaged surface as measured by ellipsometry, a reduction in power handling capabilities of the laser/plasma affected W is concluded. The evidence of reduced power handling of the W surface under conditions as described here is of great concern with respect to the durability of W PFCs for application in fusion devices.