Boundary Heat Transfer Coefficient Research Articles

Whole field measurements to quantify the thermal impact of single vapor bubble under nucleate flow boiling regime

The work reports on simultaneous measurement of bubble dynamics and thermal field to understand the local effects of bubble motion on thermal boundary layer behavior and heat transfer characteristics under subcooled flow boiling conditions. Single vapor bubble was generated using a specially designed ITO glass heater to avoid the phenomenological complexities and to obtain reproducible data. Flow boiling experiments were carried out in a vertically oriented rectangular channel with water for varying Reynolds numbers (Re = 600–4800), keeping constant subcooling level and power input. The thermal field around the vapor bubble along with the dynamics has been visualized using a non-intrusive optical technique; rainbow schlieren deflectometry, which was configured with a high-speed color camera to acquire high spatial and temporal resolution. The recorded experimental data have been analyzed qualitatively as well as quantitatively and the obtained results have been presented in the form of whole field temperature distribution, the dynamics of thermal boundary layer, local heat transfer coefficients etc. It was observed that the effect of bubble formation on the wall temperature variation, thermal boundary layer and heat transfer coefficient was relatively higher during the growth period (until the bubble lift-off) compared to the waiting period after the lift-off of the bubble. The experimental results showed that the bubble-induced heat transfer significantly enhance the overall heat transfer rate from the heated surface while the degree of enhancement was observed to be reducing with increasing Reynolds number.

A Coupled 1D–3D Numerical Method for Buoyancy-Driven Heat Transfer in a Generic Engine Bay

Energy efficient vehicles are essential for a sustainable society and all car manufacturers are working on improved energy efficiency in their fleets. In this process, an optimization of aerodynamics and thermal management is most essential. The objective of this work is to improve the energy efficiency using encapsulated heat generating units by focusing on predicting temperature distribution inside an engine bay. The overall objective is to make an estimate of the generated heat inside an encapsulation and consecutively use this heat for climatization purposes. The study presents a detailed numerical procedure for predicting buoyancy-driven flow and resulting natural convection inside a simplified vehicle underhood during thermal soak and cool-down events. The procedure employs a direct coupling of one-dimensional and three-dimensional methods to carry out transient one-dimensional thermal analysis in the engine solids synchronized with sequences of steady-state three-dimensional simulations of the fluid flow. The boundary heat transfer coefficients and averaged fluid temperatures in the boundary cells, computed in the three-dimensional fluid flow model, are provided as input data to the one-dimensional analysis to compute the resulting surface temperatures which are then fed back as updated boundary conditions in the flow simulation. The computed temperatures of the simplified engine and the exhaust manifolds during the thermal soak and cool-down period are in favorable agreement with experimental measurements. The present study illustrates the capabilities of the coupled thermal-flow methodology to conduct accurate and fast computations of buoyancy-driven heat transfer. The methodology can be potentially applied to design and analysis of multiple demand vehicle thermal management systems in hybrid and electrical vehicles.

Evaluation of multi-objective inverse heat conduction problem based on particle swarm optimization algorithm, normal distribution and finite element method

The boundary heat transfer coefficient (BHTC) and thermal conductivity are the most essential thermal physical parameters, which have a significant effect on the calculation accuracy of physical fields in the numerical simulation. To simultaneously estimate the temperature-dependent BHTC and thermal conductivity by solving the inverse heat conduction problem (IHCP), a hybrid method (ZPSO) based on particle swarm optimization algorithm (PSO), normal distribution method and finite element method (FEM) is presented, where normal distribution method representing the transient solution space is used to improve the convergence speed. A two-dimensional direct heat conduction problem (DHCP) with the temperature-dependent thermal-physical parameters is simulated based on FEM. Some temperature curves at certain position of FEM model are attained in the simulation. The temperature-dependent BHTC and thermal conductivity are simultaneously evaluated by PSO–FEM and ZPSO–FEM according to the temperature curves attained in DHCP. Comparing the temperature-dependent thermal-physical parameters attained in the IHCP to that used in the DHCP, the results show that the BHTC and thermal conductivity evaluated by the ZPSO are well consistent with those used in the DHCP. The evaluation results show that the convergence of the hybrid method is well, and the convergence speed is accelerated by the ZPSO.

Thermal Tomography with Unknown Boundary

Thermal tomography is an imaging technique for deducing information about the internal structure of a physical body from temperature measurements on its boundary. This work considers time-dependent thermal tomography modeled by a parabolic initial/boundary value problem without accurate information on the exterior shape of the examined object. The adaptive sparse pseudospectral approximation method is used to form a polynomial surrogate for the dependence of the temperature measurements on the thermal conductivity, the heat capacity, the boundary heat transfer coefficient, and the body shape. These quantities can then be efficiently reconstructed via nonlinear, regularized least squares minimization employing the surrogate and its derivatives. The functionality of the resulting reconstruction algorithm is demonstrated by numerical experiments based on simulated data in two spatial dimensions.

On the simultaneous recovery of boundary heat transfer coefficient and initial heat status

Abstract Consider the heat conduction process with heat flux exchanges on the boundary of a 2-dimensional domain. The aim is to identify both the boundary heat exchange coefficient and the initial heat distribution simultaneously from the final measurement data of the heat field. We prove the uniqueness for this nonlinear inverse problem for the strictly positive exchange coefficient and initial heat distribution in terms of the maximal principle and the eigenfunction expansions. Then a regularizing scheme combining the data mollification and quasi-reversibility method along time direction together is established to recover two unknowns, with the choice strategies for the regularizing parameters and the error estimates on the regularizing solutions. The reconstruction implementations are carried out in terms of the potential representation of the heat field, with numerical examples showing the validity of the proposed scheme.

Numerical Simulation of Multi-Crystalline Silicon Crystal Growth Using a Macro–Micro Coupled Method during the Directional Solidification Process

In this work, the crystal growth of multi-crystalline silicon (mc-Si) during the directional solidification process was studied using the cellular automaton method. The boundary heat transfer coefficient was adjusted to get a suitable temperature field and a high-quality mc-Si ingot. Under the conditions of top adiabatic and bottom constant heat flux, the shape of the crystal-melt interface changes from concave to convex with the decrease of the heat transfer coefficient on the side boundaries. In addition, the nuclei form at the bottom boundary while columnar crystals develop into silicon melt with amzigzag-faceted interface. The higher-energy silicon grains were merged into lower energy ones. In the end, the number of silicon grains decreases with the increase of crystal length.

Identification of the boundary heat transfer coefficient from interior measurement of temperature field

Consider the heat conduction process for a homogeneous solid rod with one endpoint contacted with some liquid media. The aim is to identify the boundary heat transfer coefficient from the measured temperature field, which is essentially nonlinear and ill-posed. Based on the 1-dimensional heat equation model with Robin boundary condition, we prove the recognizability of the time-dependent Robin coefficient from the temperature field specified at only one interior point. To give a stable reconstruction for noisy inversion input data, we propose a regularizing scheme by minimizing a cost functional including penalty term with rigorous mathematical analysis. A steepest iterative scheme is established to solve this non-quadratic optimizing problem.

A Heat Conduction and Convection Analytical Benchmark for Adjoint Solution Verification of Computational Fluid Dynamics Codes Used in Reactor Design

This work presents a heat transport benchmark problem when modeling the steady-state radial conduction in a fuel rod coupled to the axial heat convection in a coolant surrounding the rod and flowing along it. This benchmark problem admits exact analytical solutions for the spatially dependent temperature distributions within the rod and the surrounding coolant. The adjoint sensitivity analysis methodology (ASAM) is applied to compute the analytical expressions of the adjoint state functions for this benchmark problem. In turn, these adjoint state functions are used to compute exactly the first-order sensitivities of the various temperature distributions to the benchmark’s thermal-hydraulics parameters. Locations of particular importance are those where the rod, the rod surface, and the coolant temperatures attain their maxima. The analytical expressions of the benchmark sensitivities thus obtained are subsequently used to compute numerical values of the sensitivities of the various temperature distributions that would arise in the preliminary design of the G4M Reactor to thermal-hydraulics parameters characteristic of this reactor.The exact benchmark sensitivities are used for verifying the numerical results produced by the FLUENT Adjoint Solver, a code that has been used for computing thermal-hydraulics processes within the G4M Reactor. This solution verification process indicates that the current FLUENT Adjoint Solver cannot compute any sensitivities for the temperature distribution within the solid rod. However, the FLUENT Adjoint Solver is capable of computing the sensitivities of fluid temperatures to boundary parameters (e.g., boundary temperature, boundary velocity, and boundary pressure), but yields accurate results only for the sensitivities of the fluid outlet temperature and the maximum rod surface temperature to the inlet temperature and inlet velocity, respectively. Even for these sensitivities, the FLUENT Adjoint Solver typically needed over 20 000 iterations to converge to the correct solution. In fact, if the exact sensitivity results had not been known a priori, employment of a user-defined iteration-stopping criterion would have likely produced an erroneous result, which would have been noticed by the user only if the user had had the foresight of computing the respective sensitivities independently, via finite-differences using FLUENT recomputations. Several other important sensitivities, including sensitivities to the boundary heat transfer coefficient and sensitivities to material properties (thermal conductivity and specific heat), cannot be obtained from the current FLUENT postprocessing output.Ideally, the solution verification of the adjoint functions produced by the FLUENT Adjoint Solver would be performed by directly comparing these to the exact expressions of the adjoint functions for the benchmark problem. Such a direct comparison and, hence, a direct solution verification of the FLUENT Adjoint Solver, is currently not possible, because the current FLUENT Adjoint Solver does not provide access to the adjoint functions it computes. Therefore, the results produced by the FLUENT Adjoint Solver can only be verified indirectly, by comparing temperature sensitivities computed using the FLUENT Adjoint Solver to the exact results obtained from the analytical expression of the corresponding benchmark sensitivities. This situation further underscores the need for developing additional thermal-hydraulics benchmark problems that admit exact solutions.

Research on the effect of boundary pressure on the boundary heat transfer coefficients between hot stamping die and boron steel

Boundary heat transfer coefficient (BHTC) between the hot stamping die and boron steel is one of the most important thermal physical parameters in the hot stamping. A software of inverse heat conduction problem (IHTP) was developed based on the optimization method and finite element method. NiCr–NiSi thermocouples were used to measure the temperature of sample, and the high speed data collection device was used to acquisite the electrical signal from the thermocouples. The BHTC between hot stamping die and boron steel was calculated by the IHTP software according to the temperature curve. Main factors affecting the evaluation accuracy of BHTC were discussed, such as surface temperature of test device, surface temperature of sample, height to diameter ratio (H/D) of sample, boundary pressure between the test device and sample. The research results show that, the surface temperatures of test device and sample have little effect on the BHTC. The heat conduction of sample with thermal insulation material can be simplified into one-dimensional process if H/D is not more than 0.6. The boundary pressure has a significant effect on the BHTC. The relationship between the BHTC and boundary pressure is approximately linear.

Solution of boundary heat transfer coefficients between hot stamping die and cooling water based on FEM and optimization method

The thermal physical parameters have significant effects on the calculation accuracy of physical fields, and the boundary heat transfer coefficient between the die and water is one of the most important thermal physical parameters in the hot stamping. In order to attain the boundary heat transfer coefficient, the testing devices and test procedures are designed according to the characteristic of heat transfer in the hot stamping die. A method of estimating the temperature-dependent boundary heat transfer coefficient is presented, and an inverse heat conduction software is developed based on finite element method, advance-retreat method and golden section method. The software is used to calculate the boundary heat transfer coefficient according to the temperatures measured by NiCr–NiSi thermocouples in the experiment. The research results show that, the convergence of the method given in the paper is well, the surface temperature of sample has a significant effect on the boundary heat transfer coefficient between the die and water. The boundary heat transfer coefficient increases as the surface temperature of sample reduces, and the variation is nonlinear.

Interferometric study of nanofluid-based heat transfer phenomena in compact channels

The present work is concerned with the interferometric measurements of dilute nanofluid-based heat transfer enhancement in compact rectangular channels. The heat transfer experiments have been conducted in forced convection regime for a range of Reynolds number. Simultaneously developing flow regimes have been considered. Al2O3-based dilute nanofluids with volume concentrations of 0.01% and 0.05% have been employed with deionized water as the base fluid. A Mach–Zehnder interferometer has been used to record the line-of-sight images of the convective fields inside the channel. Interferometry experiments have been performed in infinite as well as wedge fringe-setting mode of the interferometer. The images recorded in infinite fringe setting mode have been qualitatively interpreted to understand the effect of increasing volume concentration of nanofluids on phenomena like disruption of thermal boundary layer, temperature gradients etc. The interferograms corresponding to the wedge fringe-setting mode have been quantitatively analyzed to retrieve the whole field temperature distribution inside the compact channel, local variation of heat transfer coefficient for the range of volume concentration of nanofluids and Reynolds numbers studied in the present work. Results have been presented in the form of interferometric images, the contours of two-dimensional temperature distribution, local variation of thermal boundary layer thicknesses and heat transfer coefficients along the length of the channel and percentage enhancement in heat transfer rates due to increasing volume concentration of nanofluids for each Reynolds number. The experimental study clearly reveals a reduction in the thickness of the thermal boundary layer with increasing volume concentration of nanofluids and hence the increasing strength of the thermal gradients. An overall enhancement of heat transfer coefficient by a factor of about 1.7–2 in the case of nanofluid is observed in comparison with that obtained with the base fluid.

Experimental and numerical heat transfer studies on quenching of Inconel 600 probe

The effect of heat transfer coefficient and quench start temperature on cooling behaviour of Inconel 600 quench probe was assessed by numerical experiments. A quantitative model that relates the mean cooling rate and quench start temperature of the probe with the boundary heat transfer coefficient was proposed. Computed aided cooling curve analysis was carried out by heating Inconel 600 probe to temperatures varying from 100 to 850 °C followed by quenching in water. The results of quenching experiments and the data available in the literature were used to validate the proposed model. A good agreement between the measured and estimated value was observed. The results showed that the film and transition boiling of cooling stages were significantly influenced by quench start temperature of the material while nucleate boiling and convective cooling stages were strongly dependent on the boundary heat transfer coefficient.

Assessment of the Effect of Quench Probe Parameters on Cooling Behavior by Numerical Simulation

The cooling severity of liquid quenchants is generally assessed by measuring the cooling rate inside a metallic probe. In the present study, numerical simulation of heat transfer was carried out to assess the effect of quench probe parameters on the cooling behavior. Simulations were carried out for different combinations of size, geometry, material and boundary heat transfer coefficients. Factorial experiments were carried out to assess the significance of probe parameters on mean cooling rate of the probe during quenching. Factorial analysis results showed significant influence of size and material of the probe on the mean cooling rate during quenching. The percentage contribution of the size and material parameters to the overall effect of various parameters on the mean probe cooling rate were about 45 and 16 pct. respectively. Among the interaction effects of various parameters, the interaction among probe material and size was found to be most significant. Factorial experiments showed that the effect of probe geometry on the mean cooling rate was insignificant particularly for probes of higher thermal conductivity. It was found that for a given geometry, the cooling parameter (L2CR/α) increased exponentially with increase in Biot number (Bi). The effect of probe geometry on mean cooling rate was significant when Bi was greater than 0.8.

Dimensionless Cooling Performance Parameter for Characterization of Quench Media

The effect of varying thermal properties and boundary heat transfer coefficients on temperature profiles inside cylindrical quench probes was simulated during immersion cooling. The results of simulation indicated that, for assessment of the cooling performance of the quench media, the ratio of the quench probe diameter to its thermal conductivity should be less than 0.0005 m2K/W. A simple dimensionless cooling parameter (D2CR/αΔT) was proposed to assess the cooling performance of quench media.

Effect of Boundary Heat Transfer Coefficient and Probe Section Size on Cooling Curves During Quenching

In the present work the effect of boundary heat transfer coefficient and section size of quench probe material on cooling curves was investigated by using finite difference heat transfer based SolidCast software. Simulations were carried out at different combinations of heat transfer coefficient and quench probe diameter and thermal history at the geometric center of the probe was estimated to generate cooling curves. Simulation results show that both boundary heat transfer coefficient and quench probe diameter had a significant effect on the average cooling rate. A relationship between Grossmann quench severity (H), thermal conductivity of material, size of the probe, and average cooling rate was established. By using this model, for a known quench medium, probe size, and material it is possible to predict the average cooling rate of the probe. On the other-hand, for a given material and required cooling rate, cooling severity required from the quench media could be predicted and accordingly an appropriate quench medium can be selected.

Heat transfer during solidification of chemically modified Al–Si alloys around a copper chill

The solidifying metal/chill contour will significantly affect the boundary heat transfer coefficients, and solidification modellers should be aware of the casting conditions for which the heat transfer coefficients are determined. The previous work carried out on solidification of Al–Si alloys in a metallic mould and solidification against bottom/top chills has shown that modification and chilling have synergetic effect resulting in a significant increase in the heat flux transients at the casting/chill interface. In the present work, the heat transfer during solidification of unmodified and chemically modified Al–Si alloys around a cylindrical copper chill was investigated. Heat flux transients were estimated using lumped heat capacitance method. Lower peak heat flux was obtained with chemically modified alloy. This is in contrast to the results reported for alloys solidifying against chills and in metallic moulds. The chill thermal behaviour and heat transfer to the chill material when surrounded by modified and unmodified alloys were explained on the basis of the decrease in the degree of undercooling in the case of modified alloy as compared to unmodified alloy and the change in contact condition and shrinkage characteristics of the alloy due to the addition of chemical modifiers.

A variational Bayesian method to inverse problems with impulsive noise

We propose a novel numerical method for solving inverse problems subject to impulsive noises which possibly contain a large number of outliers. The approach is of Bayesian type, and it exploits a heavy-tailed t distribution for data noise to achieve robustness with respect to outliers. A hierarchical model with all hyper-parameters automatically determined from the given data is described. An algorithm of variational type by minimizing the Kullback–Leibler divergence between the true posteriori distribution and a separable approximation is developed. The numerical method is illustrated on several one- and two-dimensional linear and nonlinear inverse problems arising from heat conduction, including estimating boundary temperature, heat flux and heat transfer coefficient. The results show its robustness to outliers and the fast and steady convergence of the algorithm.

Improved performance of diode-end-pumped Nd:GdVO4 912 nm laser property with indium solder technology

A novel indium-solder technology is demonstrated to deal with the serious thermal dissipation problem in the 912 nm Nd:GdVO4 laser operation. By use of indium-solder between the laser rod and the heat-sink, the contact resistance is reduced by removing the air bubble and heat conducting silicon and the boundary heat transfer coefficient is raised. After the indium-solder was used, it is found that the temperature in the laser rod and the deformation in the pumping end surface are eased remarkably based on a simulation of finite element analysis. Experimental results show that the continuous-wave 912 nm laser performance is improved obviously, both in a plano-plano cavity and a plano-concave cavity.

Kinetic simulation of methane hydrate formation and dissociation in porous media

The vast amount of hydrocarbon gas deposited in the earth's crust as gas hydrates has significant implications for future energy supply and global climate. A 3-D simulator for methane hydrate formation and dissociation in porous media is developed for designing and interpreting laboratory and field hydrate experiments. Four components (hydrate, methane, water and salt) and five phases (hydrate, gas, aqueous-phase, ice and salt precipitate) are considered in the simulator. The intrinsic kinetics of hydrate formation or dissociation is considered using the Kim–Bishnoi model. Water freezing and ice melting are tracked with primary variable switch method (PVSM) by assuming equilibrium phase transition. Mass transport, including two-phase flow and molecular diffusions, and heat transfer involved in formation or dissociation of hydrates are included in the governing equations, which are discretized with finite volume difference method and are solved in a fully implicit manner. The developed simulator is used here to study the formation and the dissociation of hydrates in laboratory-scale core samples. In hydrate formation from the system of gas and ice ( G + I ) and in hydrate dissociation systems where ice appears, the equilibrium between aqueous-phase and ice ( A – I ) is found to have a “blocking” effect on heat transfer when salt is absent from the system. Increase of initial temperature (at constant outlet pressure), introduction of salt component into the system, decrease of outlet pressure, and increase of boundary heat transfer coefficient can lead to faster hydrate dissociation.

Simulation and verification of ohmic heating in static heater using MRI temperature mapping

Mathematical modeling of ohmic heating of liquid–particulate mixtures allows insight into the heating behavior, but model verification that uses only a selected number of points in an ohmic heating system is inadequate because of the unknown temperature distribution within the heated food materials, including the locations of hot and cold spots. In this study, ohmic heating of liquid–particulate mixtures was simulated using the finite-element analysis with the commercial software FEMLAB, and the model predictions were verified against temperature maps obtained using magnetic resonance imaging (MRI). A factor ignored by the previous modeling works, the electricity-to-heat conversion efficiency, was considered in the model, resulting in an improved model performance. The electrical conductivity and its temperature dependence for all the materials used in the simulation were determined under consistent electric field strength as the simulated ohmic heating processes. Other factors/parameters affecting model prediction, such as the boundary conditions and heat transfer coefficients, were also determined in situ for an accurate parametric input. The model predictions yielded good agreement with the MRI temperature maps. Results showed that the electrical conductivity of the materials is the most critical factor causing heating rate variations between the particulate phase and the liquid phase. The heating rate variations could be overcome by adjusting the electrical conductivity of the food materials before ohmic heating. This modeling procedure can be used for designing and controlling ohmic heating processes to ensure thermal sterilization and safety of ohmically heated food products.