Interfacial Heat Flux Research Articles

Novel inverse heat transfer methodology for estimation of unknown interfacial heat flux of a continuous casting mould: A complete three-dimensional thermal analysis of an industrial slab mould

Accurate quantification of interfacial heat flux between the continuous casting mould and slab/billet is essential for the design and development of the products as well as operation and quality control of the casting process. Apart from empirical correlations, inverse heat transfer methods are typically employed to predict the heat flux variation by assuming a one-dimensional variation of heat flux along the casting direction. The assumption of one-dimensional heat flux often leads to significant error especially in determining the corner heat flux which affects the shrinkage behaviour and thereby, the quality of the products of casting. Previous studies have recognized this error and assumed this error of heat flux as a constant deviation to account for the longitudinal and transverse variation of heat flux. In this work, a novel methodology has been presented to predict the variable interfacial heat flux of a three-dimensional mould domain by estimating the parameters of a characteristic heat flux profile using an inverse heat transfer technique based on Salp Swarm Algorithm (SSA). This methodology uses limited experimental data or on-site plant recorded data. Representative cases of billet and slab moulds have been considered based on the available plant data. Results indicate that the mould corner heat flux is considerably different from that of the typically assumed value of 67% of the centre heat flux as reported in the literature with deviation reaching as high as 56% near the meniscus for a slab casting mould. The proposed methodology is simple to implement and is recommended for studies aimed towards realistic estimation of unknown boundary heat flux in a continuous casting process.

Scale Effects in Nanoscale Heat Transfer for Fourier's Law in a Dissimilar Molecular Interface.

The dependence of the heat transfer of a nanoscopic liquid channel residing at the solid–liquid interface is traditionally ascribed to the temperature jump, interfacial thermal resistance, wettability, and heat flux. Other contributions stemming from the channel width dependence such as the boundary position are typically ignored. Here, we conducted nonequilibrium molecular dynamics simulations to better understand the relation between channel width and boundary positions located at the solid–liquid interface. The system under investigation is a simple liquid confined between the solid from nanochannels of different sizes (3.27–7.35 nm). In this investigation, the existence of the correlation between the boundary position and the channel width is observed, which follows an exponential function. The thermal conductivity of the boundary positions is compared with the experimental value and Green–Kubo prediction to verify the actual boundary position. Atomistic simulation reveals that the solid–liquid boundary position, which matches the experimental value of thermal conductivity, varies with the channel width because of the intermolecular force and the phonon mismatch of the solid and the liquid.

Numerical and experimental analysis of rapid solidification considering undercooling effect during water droplet impact on a substrate

Freezing of water droplets on a cold surface can involve rapid solidification and undercooling. In this numerical and experimental study, the role of rapid solidification considering the undercooling effect during the impact and spreading of a water droplet onto a cold substrate is investigated. Various attendant physical phenomena, such as free surface evolution, fluid flow, heat transfer, rapid solidification and undercooling at the moving solid-liquid front are accounted in the computational model. In the coupled thermo-fluidic-rapid solidification model, the free surface of the liquid droplet is tracked with the help of volume of fluid method, while the solid-liquid front is tracked with the help of rapid solidification kinetics. The rapid solidification model lets freezing to occur at nucleation temperature which is lower than the freezing point. Results of the rapid solidification model are compared with the conventional solidification model where freezing occurs as soon as the temperature reaches the equilibrium freezing point. A realtime imaging setup is used to experimentally measure droplet spreading and freezing behaviour. The numerical predictions are validated with the experimental results. The model successfully captures undercooling and recalescence. Interfacial heat transfer is analyzed with the help of droplet-substrate heat flux. Undercooling and rapid solidification significantly influence the heat flux evolution. In the end, the effect of substrate temperature and droplet impact velocity is described. The understanding developed in this study regarding the role rapid solidification on interfacial heat flux evolution can be useful for research on ice accretion in aircraft.

Influences of Polydisperse Sea Spray Size Distributions on Model Predictions of Air‐Sea Heat Fluxes

AbstractQuantifying the influence of sea spray on air‐sea fluxes under high‐wind conditions is challenging due to a variety of factors. Among existing models, the so‐called bulk air‐sea flux model is commonly used in meteorological applications due to its simplicity, which often involves strong but untested assumptions on spray‐mediated heat fluxes and feedback effects. For example, a common assumption is to treat each droplet size as an independent contribution; that is, it does not interact with other sizes. Thus, the interactions between different size classes of spray are often neglected. In this study, we focus on the polydispersity of the spray size distribution and investigate the appropriateness of assuming an independent contribution from different spray size classes. We implement direct numerical simulations (DNS) with Lagrangian tracking of spray droplets. Based on DNS results, the bulk spray model fails to capture the interactions between different sizes that are observed directly from the droplet and feedback statistics in DNS. Thus, assuming independent contributions from spray droplets results in significant overestimates on the total heat fluxes. We further test different representative sizes of a spray size distribution. We find that the volume‐weighted representative size is capable of predicting the droplet‐modified temperature and humidity fields and generally captures the vertical profiles of spray‐mediated and interfacial heat fluxes. The results indicate that the computation of spray‐mediated fluxes can be simplified in large‐scale parameterizations.

Constructing efficient heat transfer channels at the interface of Diamond/Cu composites

ABSTRACT Understanding the mechanism of interfacial heat flux transfer is the basis of improving the thermal conductivity of diamond reinforced metal matrix composites. In this paper, the diamond/Cu(Ti) (38 vol.% diamond) composites with roughened surfaces are prepared by vacuum hot pressing sintering, and the effect of interfacial contact area on the thermal conductivity of composites is investigated by experiments and finite element simulations. A 48% (from 347 to 512 W·m−1·K−1, which is close to 90% of the theoretical value) enhancement in thermal conductivity is obtained. The roughened interfaces increase the contact areas, which provide more heat transfer channels and concentrated thermal flux routes and then optimize the efficiency of thermal flux transfer and then improve the thermal conductivity of the composites. These results provide the experimental and theoretical basis for improving the thermal conductivity of composites by the design of interface structure.

Estimation of Casting Mold Interfacial Heat Transfer Coefficient in Pressure Die Casting Process by Artificial Intelligence Methods

Pressure casting process, which is based on the principle of filling and solidifying the liquid metal into the mold cavity with the effect of speed and pressure, enables to obtain a serial product. The pressure casting process usually involves a thermal process. Starting with the casting process, the thermal resistances, especially formed at the casting mold interface, and the resultant interfacial heat transfer coefficient (IHTC) are among the most important factors determining the mechanical and physical properties of the produced part. The IHTC depends on the mold temperature, casting temperature, injection pressure, injection rate, vacuum application and many other incalculable parameters. In this study, it was aimed to determine the heat transfer coefficient and heat flux of the casting mold interface which has a significant effect on the quality of parts in the pressure casting of cylindrical mold geometry of AlSi8Cu3Fe aluminum alloy. The study was carried out depending on different casting temperatures, injection pressure, injection speed and vacuum application to the mold cavity. Temperatures were measured with thermocouples placed in the mold and casting material, IHTC and heat flux were calculated with finite difference method by using experimentally measured temperatures. In the application of artificial intelligence methods, casting temperature, injection speed, injection pressure and vacuum conditions are given as input parameters and interfacial flow coefficient and heat flux are accepted as output parameters. With the help of these parameters, DTR, MLR and ANNR deep learning algorithms were used to estimate the interfacial heat transfer coefficient. Among these algorithms, ANNR algorithm was found to be the most accurate estimating model at the rate of 99.9%. For the obtained model, a computer program was prepared for the users to be able to see and follow the experimental results and the results obtained from the model at the same time.

Accuracy of interface schemes for conjugate heat and mass transfer in the lattice Boltzmann method

The lattice Boltzmann method (LBM) is attractive for conjugate heat and mass transfer modeling due to its capability to satisfy the interfacial conjugate conditions without nested iterations. This paper presents a comparison of the popular interface schemes proposed in the literature with the focus on their numerical accuracy and convergence orders. The various interface schemes examined include the geometry-considered interpolation-based treatment that constructs second-order accurate corrections to the distribution functions across the interface by treating the interface as a shared boundary for the adjacent domains, as well as representative modified schemes that bypass the local geometry and topology consideration by either reformulating the macroscopic governing energy equation with additional source terms, or proposing modified microscopic equilibrium distribution functions in the lattice Boltzmann model. It is recognized that for the interface schemes based on governing equation reformulation, approximation of the discontinuous heat capacitance gradient at the interface is required to account for the interfacial heat flux continuity. Through analysis and numerical tests including both straight and curved interfaces, it is shown that in order to preserve the second-order accuracy in the LBM, the local interface geometry must be considered; and the modified geometry-ignored interface schemes result in degraded convergence orders – at most first order for general cases and only zeroth order is achieved for the schemes requiring discontinuous heat capacitance gradient approximation. In addition, much higher error magnitude is observed for the numerical solutions obtained from using these modified schemes without considering the interface geometry.

Further study on wall film effects and flame quenching under engine thermodynamic conditions

In direct-injection engines, the formation of fuel wall film on piston surface and liner wall is a primary cause for emissions of unburnt hydrocarbons and particulate matter. It is therefore important to investigate the behavior and effect of a wall fuel film under typical engine conditions. Following our previous study of wall film effects on flame propagation and quenching under constant thermodynamic conditions (Tao et al. IJER, 2018), more complexities rooted in real engine conditions have been considered in the current work, including two real engine in-cylinder thermodynamic trajectories occurring at catalyst warming (CW) and low-speed high-load (LSHL) conditions, varying fuel wall film thickness accounting for both vaporization and condensation, and the stagnation boundary layer flow over the wall film. To shed light on the role of wall heat transfer, parameter sweeping of wall temperature is conducted from 303 K to 363 K. Two representative wall film models using empirical vaporization rate and gas-liquid interface heat flux are compared with our numerical simulation. A good correlation between vapor boundary thickness and quenching distance has been found. Competition between enhanced vaporization due to tangential convection and aggravate condensation from elevated pressure is also demonstrated. The results lead to useful insights into the behavior of a wall film in real engine in-cylinder thermodynamic conditions and could be used to construct low dimensional empirical wall film models in three-dimensional engine combustion modeling.

Formation of Naturally Deposited Film and Its Effect on Interfacial Heat Transfer during Strip Casting of Martensitic Steel

A strip-casting simulator has been successfully developed to simulate the initial contacting conditions between the twin roller and melt during the strip-casting process, in which the peak/average heat flux, secondary dendrite arm space and cooling rate of the martensitic strip cast are similar to those observed in the actual strip caster. During the casting experiments, a layer of dark deposited film can be found on the substrate, whose composition is 69.66Mn-15.36O-11.03Fe-3.95Si (wt.%). The deposited film starts to melt during the 5th immersion experiment and the melting area of the film increases with the repeat of the immersion test. The presence of solid deposited film first impairs the interfacial heat transfer; however, with the accumulation of the deposited film, melting of the film occurs that enhances the interfacial heat fluxes due to the improved melt/substrate interfacial contact, as the cavities or air pockets between the melt and the substrate are gradually filled with the increasing of the melting area of the deposited film. Compared with substrate roughness, the effect of the deposited film on heat transfer is more significant.

An experimental approach based on inverse heat conduction analysis for thermal characterization of phase change materials

A new method based on solution to inverse heat conduction problem for the assessment of solidification parameters of PCM salts has been proposed. The method estimates the mold -salt interfacial heat flux and it is used to calculate the latent heat of salt PCMs using calorimetry based energy balance equations. This method is more accurate compared to Computer Aided Cooling Curve Analysis (CACCA) techniques as it eliminates the drawbacks involved with base line fitting calculations and errors introduced due to the improper selection of solidification points. Pure salt PCMs such as KNO3 and solar salt were used for the validation of this technique. Both air and furnace cooling were adopted to demonstrate the effect of cooling rate on solidification characteristics. The wettability of salt samples on mild steel surface was analyzed to account for the difference in the thermal behavior of salts.

An Efficient Electrochemical-Thermal Tanks-in-Series Model for Lithium-Ion Batteries

This article extends the Tanks-in-Series methodology (J. Electrochem. Soc., 167, 013534 (2020)) to generate an electrochemical-thermal model for Li-ion batteries. Energy balances based on porous electrode theory, including flux and generation terms, are volume-averaged for each region in a cathode-separator-anode representation, including current collectors. The original Tank model is thus augmented by a volume-averaged energy balance in each region, containing source terms and interfacial heat fluxes that are approximated accordingly. Cell-level quantities and temperature predictions are evaluated against a pseudo 2-dimensional (p2D) model. Acceptable voltage errors are achieved for relatively aggressive conditions of discharge and external heat transfer. Predictions of electrochemical variables are examined, and implications of the approximations discussed. The simplified methodology is also demonstrated for examples of large-scale models used in studying practical cell configurations. The Tanks-in-Series approach leads to a substantial reduction in equation system size, with attendant savings in computation time. This suggests potential in applications such as optimal charging, cell-balancing and estimation, and aids efforts to incorporate electrochemical models in advanced Battery Management Systems.

Numerical Study of High Performance Ablative Thermal Protect System by Adding Phase Change Material

Under extreme thermal environment, ablation process of thermal protection system is a key issue in atmospheric re-entry and hypersonic flight vehicles; it displays a strong coupling between ablation mass, velocity and heat transfer. This article presents a method for combining the ablating and melting process, building a right triangle carbon-carbon model for ablation mixed with octadecane phase change material to absorb the heat of combustion delaying the movement of burning interface. For the moving of boundary, it is treated by the modified Stefan model coupled with chemical reaction and thermal radiation at the front leading boundary. The governing equation of heat transfer considering the melting process of phase change material is given by referring the enthalpy method. The effect of volume ratio and aerodynamic heating on the ablation interface and net heat flux on the interface are investigated. Result shows that high volume ratio of the phase change material delays the movement of the interface, and decreases the net heat flux of the interface; on the other hand, high aerodynamic heat accelerates the movement of the interface and increases the interface net heat flux at a given time point. This study can give a rule on how the volume ratio of phase change material influence the ablative process quantitatively.

Study on heat transfer behaviors between Al-Mg-Si alloy and die material at different contact conditions based on inverse heat conduction algorithm

The heat transfer between Al-Mg-Si alloy and die steel during warm or hot forming process is of great influence on the temperature and stress fields of product. The interfacial heat transfer coefficient (IHTC) is also an indispensable boundary condition in the numerical simulation of warm or hot forming process, which is affected by many factors and hard to be quantified. In this study, an inverse heat conduction algorithm and new experimental apparatus were developed to determine the transient IHTC between Al-Mg-Si alloy and die steel under low contact pressure and large surface roughness. The effectiveness and feasibility of the algorithm and apparatus were verified by comparison of the calculated and measured temperatures. The influences of initial temperature of aluminum alloy, surface roughness of die steel, interfacial contact pressure and heat flux direction on the IHTC were evaluated. The results show that the calculated temperatures are in good agreement with those obtained from different measuring locations, which indicates that the inverse heat conduction method and experimental apparatus are feasible and reliable. After the samples contact with each other, the IHTC rises sharply in a short time, then slowly increases to a peak value and finally tends to decrease slightly. With the increase of the initial temperature of aluminum sample, interfacial contact pressure and the decrease of surface roughness of die steel, the IHTC increases significantly. The IHTC for the heat flux transfer from aluminum alloy to die material is obviously larger than that from die material to aluminum alloy.

Evaporation of Sessile Water Droplets on Horizontal and Vertical Biphobic Patterned Surfaces.

This paper presents an experimental study on thermal transport to single water droplets evaporating on heated biphobic surfaces consisting of a superhydrophobic matrix with a circular hydrophobic pattern with strong contact line pinning. A single water droplet of 8 μL volume is placed on a preheated surface and allowed to evaporate in an open laboratory environment. We investigate the influence of substrate orientation (horizontal and vertical) on evaporation dynamics. Using optical and infrared imaging, we report droplet fluid dynamics and heat transfer characteristics of the evaporating droplet. Overall, evaporation is more efficient on the vertical surface, exhibiting higher total heat transfer rates and up to 10% shorter evaporation times. Counterintuitively, on the vertical surface, the substrate-droplet interfacial heat flux was higher near the lower contact line than in the upper region, despite a high contact angle and an expected wedge effect at the bottom. At the same time, the temperature is colder in the lower part of the droplet. We attribute this apparent anomaly to the competition between sensible heating and evaporation, and a modified convective flow signature (both within the droplet and the gas phase) compared to a horizontal surface. We also show that the thermal signature becomes uniform once the contact angles at the upper and lower contact lines become equal toward the end of the evaporation process. Insights from this work can guide the design of spray cooling devices or be used to alter particle deposition patterns during evaporation-based fabrication techniques and ink-jet printing.

Pore scale numerical simulation of heat transfer in propagating thermal wave during filtration combustion of rich and lean methane-air mixtures

The porous media combustion phenomenon was numerically studied with focus on the heat transfer effect in propagating combustion wave for lean and ultra-rich mixture compositions using the approach when the three-dimensional porous structure and interstitial flow are simulated directly at pore scale with explicit consideration of the thermal interaction between fluid and solid phases including the detailed chemical kinetics model and solid-to-solid radiation. The results demonstrate that irregularity of the porous structure leads to a large spatial variation of the process parameters and the flow inhomogeneity. The most intensive heat sources placed within the cavities where the flow is developed. During the process, the interface heat transfer and radiation contribute to heat recuperation mechanism that leads to thermal non-equilibrium in the combustion wave. The heat is transferred through the bed via radiation layer-by-layer due to restricted visibility of the particles. The numerical data about a local variation of the process parameters were presented. The data of this type can be used for modification of the volume-averaged models within the context of spatial variation consideration. It was shown that there is a correlation between the heat release rate, the interface heat flux, the radiative heat flux, and its root mean square values.

Heat transfer behaviour of funnel mould copper plates during thin slab continuous casting and channel structure optimization

ABSTRACT The heat transfer in funnel mold during thin slab continuous casting is rather complex and sensitive that the flow and temperature of cooling water as well as the roughness of channel walls may have significant influences on it. Herein, a 3-D heat transfer model of funnel copper plates coupling with the flow of cooling water in the channels was developed with the consideration of the fluid-solid interaction. The results show that the interfacial heat flux between the copper plate and cooling water decreases significantly with the increase of distance from channel root, and the temperature distribution of mold lower part is more uneven than that of the upper part. According to the magnitude and distribution of mold temperature, structure of mold copper plates like fillet radius and depth of concave channel, length of circular channels in wide face and roughness of channel wall were optimized.

A moment-of-fluid method for diffusion equations on irregular domains in multi-material systems

A new numerical method is developed for the solution of the diffusion problem in a system of several materials. In such a system, the diffusion coefficients are piecewise continuous and jumps in their values can occur across the complex-shaped interfaces between contiguous materials.The boundary conditions along the complex-shaped interfaces can either be a jump condition boundary condition, a Neumann boundary condition, or a Dirichlet boundary condition.The moment-of-fluid (MOF) procedure is employed to reconstruct the interfaces. This procedure enables accurate reconstruction of any number of material interfaces in a computational cell. Furthermore, MOF is a volume preserving reconstruction, as well as capable of capturing thin filamentary regions without the necessity of adaptive mesh refinement. The proposed method is tested on multi-material diffusion problems which demonstrates its potential to enable numerical simulation of complex flows of technological importance relevant to predicting the heat transfer rate in materials and manufacturing processes. Results using the new method are reported on problems in complex (filamentary) domains, and it is found that the method is very efficient at approximating the temperature, the temperature gradient, and the interfacial heat flux, as compared to traditional approaches.

The impact of the casting thickness on the interfacial heat transfer and solidification of the casting during permanent mold casting of an A356 alloy

Many important quality indicators for components manufactured using permanent mould casting, such as the presence of shrinkage porosity, microstructure features, dimensional stability, cycle time and filling mechanisms are controlled directly or indirectly by the heat transfer mechanisms linking the casting to the mould. While interfacial heat transfer in permanent mould casting has been significantly investigated and widely reported in the literature, the geometrical dependence of heat transfer parameters has not been studied or reported in detail. Understanding this dependency is very important as the same cast component most often is constituted by different sections and geometrical variations. In this paper, experimental methods and analytical correlations have been developed and presented that enable an accurate determination of the time dependent interfacial heat flux density and heat transfer coefficient at the casting-mould interface. The variation of these parameters is investigated and analysed for three different casting sections and two types of thermal barrier coatings.

A simple statistical-mechanical interpretation of Onsager reciprocal relations and Derjaguin theory of thermo-osmosis.

The application of a temperature gradient along a fluid-solid interface generates stresses in the fluid causing "thermo-osmotic" flow. Much of the understanding of this phenomenon is based on Derjaguin's work relating thermo-osmotic flows to the mechano-caloric effect, namely, the interfacial heat flow induced by a pressure gradient. This is done by using Onsager's reciprocity relationship for the equivalence of the thermo-osmotic and mechano-caloric cross-term transport coefficients. Both Derjaguin theory and Onsager framework for out-of-equilibrium systems are formulated in macroscopic thermodynamics terms and lack a clear interpretation at the molecular level. Here, we use statistical-mechanical tools to derive expressions for the transport cross-coefficients and, thereby, to directly demonstrate their equality. This is done for two basic models: i) an incopressible continuum solvent containing non-interacting solute particles, and ii) a single-component fluid without thermal expansivity. The derivation of the mechano-caloric coefficient appears to be remarkably simple, and provides a simple interpretation for the connection between interfacial heat and particle fluxes. We use this interpretation to consider yet another example, which is an electrolyte interacting with a uniformly charged surface in the strong screening (Debye-Hückel) regime.

Numerical Simulation of Conjugate Heat Transfer in Forced Convective Boundary Bilayered Cylindrical Pipe with Different Peclet Numbers

The heat transfer performance of bilayered composite systems through which thermally developing laminar fluids flow for cases in which axial conduction is either significant or negligible has been investigated. The heat transfer problems considered as two dimensional conjugate problems with appropriate boundary conditions were solved via computational fluid dynamics (CFD) approach in ANSYS 16.0. A parametric study was conducted to investigate the effects of Péclet number (Pe), ratio of the thermal conductivity of the laminate composite (k21) and the laminate composite dimensionless-thickness ratio on the wall-fluid interfacial temperature and interfacial heat flux for Pe of 5, 100 and 1000, varying between 0.4 and 1.6, Bi of 5, kwf of 20, k21 between 0.025 and 1, and of 0.71. The effect of Pe was found to be more pronounced on the interfacial heat flux. Also, the changes in k21 and were shown to reduce with reduction in Pe. Keywords— Composite cylinder, convective heat transfer, Numerical simulation; thick-walled pipes.