Conduction Convection Research Articles

Monitor and control test room for investigating thermal performance of panels incorporating phase-change material

Abstract. This article aims to present equipment designed and developed to study the effective thermal conductivity of composite panels. The composite panel used is a rigid polyurethane foam covered with a layer of aluminum on both sides. The panel is mounted in the test chamber equipped with several sensors and actuators connected via an Arduino platform. Tests have been carried out by applying heat to impose various interior temperatures. Sensors at different locations are used to monitor and record temperatures in and around the composite panel during heating and natural cooling. A model, based on the Fourier equations of thermal conduction and natural convection heat transfer for the steady state, was developed to assess the effective thermal conductivity. The performance of the system was confirmed using temperature signals through the panels for thermal characterization of composite materials. The determined effective thermal conductivity obtained was in agreement with the experimental values reported in the technical data sheets with relative deviations of less than 10 %.

How natural convection affect cooling performance of PCM heat sink

Phase change materials (PCMs) present great potential in extending the safe working time of electronic components that work intermittently or in an adiabatic cavity. Therefore, a clear understanding of the quantified contribution of natural convection and heat conduction in the cooling performance of PCM heat sink is essential to prolong the safe working time. In this paper, the quantified contribution of natural convection (η) was experimentally investigated by changing the heating position (bottom heat and top heating). Moreover, the effects of heat flux (q) and physical parameters were discussed on the average temperature during the overall fluctuation stage (Taf), the η, safe working time, etc. The results proved that the dominant factor for the overall melting process of paraffin gradually changed from heat conduction to natural convection when the temperature fluctuation stage appeared. Specifically, the cooling performance of the PCM heat sink at q=1.24∼3.11 W·cm−2 could be improved by natural convection for 50%∼58.7%, which depended on the Taf. Moreover, correlations consisted of the maximum allowable temperature, the liquidus temperature, and the heat flux were obtained to predict the η of paraffin in the range of q=1.24∼3.73 W·cm−2. It also presented an acceptable error (17%) in predicting the η of other organic PCMs. It should be noted that some synergistic enhancement technologies for heat conduction and natural convection should be developed in future works to prolong the safe working time of electronic components with high heat flux and low allowable temperature.

Numerical Analysis of Thermal Environment in Deep Mining

To analyze heat effect in deep metal mines, it is crucial to understand the temperature field distribution around the mine tunnel. In this paper, a numerical model of the random mineral composition of the rock body is established based on finite element software to analyze the influence of the internal composition of the surrounding rock on the temperature field, and a numerical simulation model based on COMSOL finite element software is established based on the two heat exchange modes of heat conduction and heat convection in the surrounding rock. The results show that the numerical simulation results of a typical numerical simulation model using a single material are lower than the real situation; increasing the tunnel length does not increase the heat exchange efficiency between the rock wall and the air; increasing the wind velocity has a limited impact on the temperature field; the wind temperature more directly affects the mining surface; and the effect of wet air on the temperature field of the surrounding rock has a more substantial variation.

Numerical simulation of heat and mass transfer during heating and cooling parts of canned‐green‐olive pasteurization

AbstractSimultaneous modeling of heat and mass transfer was applied in a cylindrical geometry through computational fluid dynamic (CFD). Two‐dimensional equations of mass, momentum and energy conservation were solved using finite elements method. The meshes were 7,882 triangular elements where 1,056 of them were in boundaries. The simulation was solved for a metal can filled with olives (Conservolea CV) and a 6% acid‐brine. Constant thermophysical properties of fluid remained static over the processing period except for the viscosity (temperature dependent) and density (in buoyancy term). The comparison criteria, between the predicted and experimental figures, using to evaluate goodness of fit, namely the coefficient of correlation (r = .9933) and the root mean square error (RMSE = 3.6555) indicated that the model was valid. The warm‐low‐density fluid ascended through a thin boundary layer and exchanging the heat, at the top of the can, where it flowed downward through the pores between the olives. This natural convection displaced the Slowest Heating Zone (SHZ) towards the bottom of the can, and eventually stayed in a region that was about 10 ± 15% of the can height from the bottom. The inactivation time for the most‐heat‐resistant fungus (Monascus rubber) during the thermal processing of green olives at 100°C was 600 s based on SHZ. A comparison between heat transfer by conduction and conduction–convection showed that the rate of heat transfer in conduction–convection was much more than conduction, also the SHZ in conduction was displaced towards the top of the can.Practical ApplicationsComsol Multiphysic, was used in this research in order to predict temperature profile in olive pasteurized in a metal can so that the accurate location of cold point was evaluated and the process time can then be controlled to reduce overheating and nutritional reduction or under heating and safety problems. As the model was validated, all the model results would be accurate to use so that velocity pattern of the fluid was extracted and different assumptions of heat conduction also were considered. The importance of pasteurization in different industries and the significance of reducing energy consumption, reveal our research importance because the calculated‐process time was much lower than what is currently used in industry.

A physiochemical model for the combustion of aluminum nano-agglomerates in high-speed flows

A theoretical model of aluminum nanoparticle (ANP) and agglomerates has been developed to highlight the effect of flow-particle interactions and heat conduction within particles. To understand the atomic physicochemical mechanism, a series of reactive molecular dynamics (MD) simulations have been performed on single ANP and agglomerates combustion in high-speed flows. The results show that both single ANP and agglomerates experience the transition from diffusive oxidation mode to anisotropic and explosive oxidation modes as flow velocities increase. All the fundemental mechanisms in the model development are derived from fully atomic insights, including thermal and convective heat transfer between flow and particle, core-shell reaction, heat conduction, particle dispersion and drag force. The model predictions are compared with MD simulations, and the results show that our model can capture the ignition behaviors of ANP and agglomerates in a wide range of flow rates. The combustion of a serial of agglomerates (3–180 primary particles) is simulated to reveal the effects of agglomerates at different flow conditions and agglomerate sizes. At low flow rate conditions, the core-shell reactions contribute about two-thirds of the heat triggering the ignition of single ANP. At high flow rate conditions, the gas-particle convective heat transfer and heat conduction between particles become the major heat source rather than the core-shell reactions. In addition, the ignition delay of agglomerates is much shorter than that of single particle with the same equivalent radius, and the ignition becomes almost independent with the agglomerate size due to the heat accumulation inside at the flow-particle interface. Our study reveals the atomic mechanism of the ignition of ANP agglomerates and proposes a theoretic model of aluminum nanoparticles and agglomerates in high-speed flows, which is applicable to the numerical simulations of aluminum propellants and explosives.

Experimental and numerical studies on the heat transfer improvement of a latent heat storage unit using gradient tree-shaped fins

To improve the thermal performance of horizontal latent heat storage (LHS) units, this study investigates two innovative LHS units using uniform and gradient tree-shaped fins. By coupling visualization experiments and three-dimensional numerical simulations, the melting/solidification behavior and thermal properties of innovative LHS units are comprehensively analyzed and compared with traditional LHS units. The results show that tree-shaped fins facilitate heat diffusion from point to area, breaking the heat transport hysteresis in traditional LHS units, thus accelerating the melting/solidification rate. During the melting process, the gradient tree-shaped fins strengthen the heat transfer in lower parts of the LHS unit and extend the convective heat transfer duration in upper regions, promoting the synergistic strengthening of natural convection and heat conduction in the late melting stage. Compared to the uniform fin layout, the gradient tree-shaped fins effectively increase the melting rate, shortens the melting duration by 9%, and further improve the overall temperature uniformity of LHS units. However, the non-uniform transport path of gradient tree-shaped fins is not conducive to solidification heat transfer with conduction as the primary thermal regime, which increases the temperature gradient of LHS units and prolongs the solidification duration by 57.4% compared to the uniform tree-shaped fins.

Aspects of the Aligned Magnetic Field Past a Stratified Inclined Sheet with Nonlinear Convection and Variable Thermal Conductivity

An analytical study of a two-dimensional boundary layer flow of an upper-convected Maxwell fluid is examined. In addition, an aligned magnetic field over the inclined shrinking/stretching stratified sheet in a non-Darcian porous medium is considered. The heat transfer effects are employed through nonlinear convection and variable thermal conductivity. The associated higher-order nonlinear equations are transformed to ordinary first-order differential equations by using similarity transformation. The resulting ordinary first-order differential equations are then solved numerically by the shooting method. This paper aims to investigate the special effects of parameters on velocity and temperature profiles. The results are also discussed, graphically and numerically for the skin friction and Nusselt number.

Fractional model for MHD flow of Casson fluid with cadmium telluride nanoparticles using the generalized Fourier\u2019s law

The present work used fractional model of Casson fluid by utilizing a generalized Fourier’s Law to construct Caputo Fractional model. A porous medium containing nanofluid flowing in a channel is considered with free convection and electrical conduction. A novel transformation is applied for energy equation and then solved by using integral transforms, combinedly, the Fourier and Laplace transformations. The results are shown in form of Mittag-Leffler function. The influence of physical parameters have been presented in graphs and values in tables are discussed in this work. The results reveal that heat transfer increases with increasing values of the volume fraction of nanoparticles, while the velocity of the nanofluid decreases with the increasing values of volume fraction of these particles.

Fast-growing Paulownia wood fractionation by microwave-assisted hydrothermal treatment: A kinetic assessment

Microwave hydrothermal treatment (MHT), a novel advanced technology, was proposed for the fractionation of Paulownia wood (PW) at temperatures ranging 200–230 °C and residence times of 0–50 min, corresponding to severities of 2.93–4.70. This procedure allowed 80% of xylan recovery as xylooligosaccharides and an average of 95% cellulose recovery in the pretreated PW biomass, showing the selectivity of the treatment, that was also compared to conduction–convection heating autohydrolysis. Finally, a kinetic model was proposed for the prediction of PW fractionation using MHT, with the ultimate goal of being applied to a wide range of feedstocks and minimizing the number of parameters used. For that, two strategies were approached, allowing the reduction of 80 to 34 parameters, without significant influence in the kinetic fitting. To the best of our knowledge, this is the first kinetic modelization of MHT of PW, taking into account all the lignocellulosic fractions.

Expansion Velocity Model of Steam-Assisted Gravity Drainage considering Thermal Convection

Steam-assisted gravity drainage (SAGD) is an important method used in the development of heavy oil. A heat transfer model in the SAGD production process is established based on the heat transfer effect caused by the temperature difference at the front edge of the steam chamber and the heat convection effect caused by the pressure difference. The observation well temperature method is used in this model to calculate the horizontal expansion speed of the steam chamber. In this manner, an expansion speed model considering heat convection and heat conduction is established for a steam chamber with a steam-assisted gravity drainage system. By comparing this with the production data extracted from the Fengcheng Oilfield target block, it is verified that the model can be effectively applied for actual field development. Simultaneously, by using the derived model, the temperature distribution at the edge of the steam chamber and production forecast can be predicted. Sensitivity analysis of the expansion rate of the steam chamber demonstrates that the larger the thermal conductivity, the faster is the steam chamber horizontal expansion speed, and the two are positively correlated; the larger the reservoir heat capacity, the slower is the steam chamber horizontal expansion speed. A larger heat capacity of the convective liquid indicates that there are more water components in the convective liquid, the viscosity of the convective liquid is low, and the expansion speed of the steam chamber increases accordingly. This research closely integrates theory with actual field production and provides theoretical support for the development of heavy oil reservoirs.

Analysis of flow and thermal breakthrough in leaky downhole coaxial open loop geothermal system

Geothermal energy is crucial to energy transformation; however, the difficulty of reinjection and the low efficiency of heat extraction need to be solved urgently. Coaxial tube heat exchanger has no difficulty of reinjection, but the averaged heat output per unit length is very limited. A new type of leaky downhole coaxial open loop geothermal system using the technique of “no water withdrawn but heat only” is proposed, which makes full use of the convective heat transfer of the aquifer and the leakage characteristics of the aquitard. From the test, heat output is up to 930 kW, which is 3.5 times that of the traditional coaxial casing, which is a promising geothermal heat extraction technique. In this study, a coupled analytical and numerical simulation model of wellhole aquifer flow and heat transfer was established to study the heat extraction performance, as well as the flow and thermal breakthrough of the system. Through the analysis of calculation results and the introduction of critical Rayleigh number, which represents the degree of convection and heat conduction, the optimal correlation between the thickness of the aquitard, injection temperature, flow rate, and permeability ratio is established. Regarding the base case thickness of the aquitard, a value of 19.51 m was suggested, and Kratio ≥ 20 was suggested regarding the reservoir structure, which provides quantitative guidance and is significant for system optimization design.

Research on Temperature Change of Reflow Furnace Based On Mathematical Modeling

After referring to many documents, this article comprehensively considers various heat transfer methods, analyzes the heat transfer process of welded components, and establishes a temperature field distribution model based on one-dimensional transient heat transfer equation by ignoring some irrelevant conditions, and useing the finite difference method. We solve it and apply it to the optimization of furnace temperature curve. Due to the many types of reflow furnaces, this article mainly considers hot-air reflow furnaces. The heating methods are mainly heat convection and heat conduction, ignoring heat radiation. The welding area is established by the transient heat transfer equation. The temperature field distribution model is established, and the initial conditions and thermal boundary conditions are determined. Related heat transfer analysis is done for the front area, back area and gap areas. Finally, through the experimental data and the idea of least squares, the parameters of the electronic devices used in this experiment are obtained, and it also provides an idea to check whether the relevant parameters of the experimental materials are accurate. In order to make it easier for the staff to operate, this article proposes a method to find the maximum speed of conveyor belt, which has great practical significance.

A Thermal Effect Model for the Impact of Vertical Groundwater Migration on Temperature Distribution of Layered Rock Mass and Its Application

On the basis of the one-dimensional heat conduction–convection equation, a thermal effect model for vertical groundwater migration in the stratified rock mass was established, the equations for temperature distribution in layered strata were deduced, and the impacts of the vertical seepage velocity of groundwater and the thermal conductivity of surrounding rocks on the temperature field distribution in layered strata were analyzed. The proposed model was employed to identify the thermal convection and conduction regions at two temperature-measuring boreholes in coal mines, and the vertical migration velocity of groundwater was obtained through reverse calculation. The results show that the vertical temperature distribution of the layered rock mass is subject to the migration of the geothermal water; the temperature curve of the layered formation is convex when the geothermal water travels upward, but concave when the water moves downward. The temperature distribution in the stratified rock mass is also subject to the thermal conductivity of the rock mass; greater thermal conductivity of the rock mass leads to a larger temperature difference among regions of the rock mass, while weaker thermal conductivity results in a smaller temperature difference. A greater velocity of the vertical migration of geothermal water within the surrounding rock leads to a larger curvature of the temperature curve. The model was applied to a study case, which showed that the model could appropriately describe the variation pattern of the ground temperature in the stratified rock mass, and a comparison between the modeling result and the measured ground temperature distribution revealed a high goodness of fit of the model with the actual situation.

Numerical Analysis of Fluid Flow and Heat Transfer by Means of a Unified Model in a Direct Current Electric Arc Furnace

Herein, a unified 2D axially symmetric model coupling the plasma arc and molten bath in a direct current electric arc furnace is established, with the physical phenomena at the plasma arc/molten bath interface to be confronted by the “local thermodynamic equilibrium diffusion approximation” method. After ensuring model validation and grid independence test, the fluid flow and heat transfer processes are analyzed. The numerical investigation reveals that in terms of the relative importance of driving forces in the molten bath, an anticlockwise eddy is formed at the molten bath center driven by electromagnetic force, whereas a clockwise eddy is formed near the lateral part of the molten bath driven by buoyancy force. Regarding the distribution of heat flux, the convection–conduction and radiation heat govern the rate of heat transfer from the plasma arc to the molten bath. In addition, for larger arc current, higher arc power in the plasma arc region and higher heating rates in the molten bath are obtained when the arc length is held constant; for shorter arc length, lower arc power in the plasma arc region but higher heat transfer efficiency in the molten bath is attained when the arc current is held constant.

Optimization Model Design for Temperature Curve of Reflow Furnace

How to adjust the temperature zone temperature and furnace speed parameters to optimize the furnace temperature curve, so as to improve the product quality is the main problem faced by the temperature curve optimization of the reflow furnace. In this paper, the heat transfer model is established by the heat convection and heat conduction equations, and the mechanism of temperature change in the welding area is analyzed. Then, by gradually determining the objective function and comprehensively establishing the optimization model according to the known conditions, the optimal parameters are solved, so as to solve the optimization problem of furnace temperature curve. According to Newton’s cooling law, specific heat theorem and Laplace equation, the temperature function of the center of the welding zone is deduced and solved, and the analytic function model of the temperature change in the center of the welding area can be obtained by synthesizing the inherent size conditions of the reflow furnace. Taking the corresponding data of experimental temperature and time as the fitting data, the undetermined parameters of the model were solved by nonlinear least square fitting method and undetermined coefficient method. The square sum of fitting residuals is 5857.7, which proves that the model has good fitting effect. Using the new experimental data to solve the model, the temperature change of the welding center at each position and time in the reflow furnace is analyzed. The temperature in the center of the welding area at the middle point of the low temperature zone 3, 6, 7 and the end of the small temperature zone 8 is 143.81°C, 181.78°C, 201.33°C, 228.97°C, respectively.

Numerical simulation of heat transfer and fluid flow during nanosecond pulsed laser processing of Fe78Si9B13 amorphous alloys

Nanosecond pulsed laser processing is a promising method to modify the microstructure of amorphous alloy. However, the heat and mass transfer mechanisms during processing are still unclear, which prevent regulating the microstructure precisely. In this study, a 3D heat transfer and flow coupling model is established to investigate the heat transfer and fluid flow behaviors, and their effects on the surface morphology and microstructure formation during the nanosecond pulsed laser processing of Fe78Si9B13 amorphous alloy. The physical processes such as melting and solidification, melt evaporation, melt convection and heat conduction, as well as the main driving forces such as surface tension, recoil pressure and gravity are taken into account in this model. The simulation morphology is in good agreement with the experimental results, indicating the validity of this numerical model. Based on simulation data analysis, it is found that the evolution mechanism of surface morphology is mainly related to the recoil pressure caused by evaporation and the Marangoni effect induced by the surface tension spatial gradient. Combined the temperature field analysis with experimental characterization, the formation mechanism of new amorphous phase in the molten zone (cooling rate at the order of 107 K/s) and the precipitation behavior of α-Fe(Si)/Fe-B phase nanocrystals in the heat-affected zone are clarified.

A MULTIPHYSICS SIMULATION SUITE FOR SODIUM COOLED FAST REACTORS

A simulation suite has been developed to model reactor power distribution and multiphysics feedback effects in Sodium-cooled Fast Reactors (SFRs). This suite is based on the Finite Element Method (FEM) and employs a general, unstructured mesh to solve the Simplified P3 (SP3) neutron transport equations. In the FEM implementation, two-dimensional triangular elements and three-dimensional wedge elements are selected. Wedge elements are selected for their natural description of hexagonal geometry common to fast reactors. Thermal feedback effects within fast reactors are modeled within the simulation suite. A thermal hydraulic model is developed, modeling both axial heat convection and radial heat conduction within fuel assemblies. A thermal expansion model is included and is demonstrated to significantly affect reactivity. This simulation suite has been employed to model the Advanced Burner Reactor (ABR) benchmark, specifically the MET-1000. It has been demonstrated that these models sufficiently describe the multiphysics feedback phenomena and can be used to estimate multiphysics reactivity feedback coefficients.

Model of Complex Heat Transfer in the Package of Rectangular Steel Sections

During heat treatment of rectangular steel sections, a heated charge in the form of regularly arranged packages is placed in a furnace. The article presents a model of a complex heat transfer in such a package using the thermo-electric analogy. The model considers the following types of heat transfer: conduction in section walls, conduction and natural convection within gas, heat radiation between the walls of a section, as well as contact conduction between the adjacent sections. The results of our own experimental research were used for calculations of heat resistance applying to natural convection and contact conduction. We assumed that the material of sections was low-carbon steel and the gas was air. The result of the calculations of the presented model is total thermal resistance Rto. The calculations were performed for the temperature range 20–700 °C for four geometrical cases. Due to the variability of conditions for contact heat conduction, we assumed that total thermal resistance for a given charge is contained within a value range between Rto-min and Rto-max. We established that the value of Rto depends significantly on the section’s geometry. The larger the section sizes, the greater the changes of Rto. The minimal and maximal values of Rto for all packages were 0.0051 (m2·K)/W and 0.0238 (m2·K)/W, respectively. The correctness of model calculations was verified with the use of experimental data.

Numerical analysis of heat transfer characteristics of small droplets impacting on wall

The phenomenon of small droplets impacting on the wall is widely used in fields such as spray cooling. In recent years, the research on the behavior of droplets impacting on a wall has been extensively concerned by scholars. However, current research mainly focuses on the flow and heat transfer characteristics of large droplets (millimeters) impacting on a hot wall. Since the dynamic and thermodynamic characteristics of small droplets (micrometers) impacting on the hot wall are significantly different from those of large droplets, the research on the behavior of small droplets impacting on the hot wall will further facilitate the understanding of the heat transfer mechanism. In order to study the heat transfer process of small droplets impacting on the hot wall (non-boiling zone), a two-dimensional transient model of droplets impacting on the wall is established, and the phase field method is used to analyze the convective heat flux and heat conduction heat flux in the heat transfer process of small droplets. The effect of velocity, wettability and droplet size on the heat transfer characteristics of droplets impacting on the wall are explored. The simulation results show that the phase field method is feasible in studying the behavior of small droplets impacting on the wall. Furthermore, the research results show that the initial stage of droplet impacting on the wall is “cold spot”, which is conducive to the heat transfer between the small droplet and the wall. The peak heat flux during the small droplet impacting on the wall is near the three-phase contact point, and it is on the order of 10<sup>5</sup>–10<sup>6</sup> W/m<sup>2</sup>. The influence of wall wettability and droplet size on the conductive heat flux during the small droplets impacting on the wall are more significant, while velocity and droplet size have a significant influence on convective heat flux. In most cases, the conduction heat flux of small droplets impacting on the wall is about 10<sup>3</sup>–10<sup>5</sup> W/m<sup>2</sup>, and the convective heat flux is about 10<sup>4</sup>–10<sup>6</sup> W/m<sup>2</sup>. The convective heat flux is larger than the conduction heat flux, and it plays a dominant role in the whole process of heat transfer. The above conclusions are helpful in enriching the heat transfer mechanism of small droplets impacting on the hot wall, and implementing the spray cooling and other technologies.

Evaluation and optimization of melting performance in a horizontal thermal energy storage unit with non-uniform fins

The shell and tube latent heat thermal storage systems are widely used in the storage and utilization of fluctuating thermal energy resources due to high thermal storage density, constant discharge temperature, simple processing and low cost. Adding fins to phase change materials is an effective method to expand the heat transfer area and improve the heat transfer rate. However, the obvious thermal stratification phenomenon and slow melting rate problem are exited in the horizontal latent heat thermal energy storage system. In order to improve the melting rate and uniformity, different non-uniform fin arrangements were designed and investigated in this study to improve the thermal performance. A numerical model of the melting characteristics of phase change materials was established and validated by the experimental results in the literature. The effects of fin arrangement, angle and length on the thermal performance of the melting process were quantitatively evaluated by analyzing the temperature field, velocity field and liquid fraction distribution before and after melting. Results indicated that when the fin angle α=25° and the fin length L=40 mm, the melting time is decreased by 83.9% and thermal storage density is improved by 466%, which meant that the lower fin arrangement realized the synergistic enhancement of natural convection and heat conduction. On this basis, the effect of the heat transfer fluid temperature on the thermal storage performance of the optimal scheme was further studied. The non-uniform fins design proposed in this study can provide theoretical support for the design method of thermal storage system, and contribute to the efficient utilization of intermittent thermal energy resources such as solar energy and industrial waste heat.