Estimation Of Heat Transfer Coefficient Research Articles

Sequential particle filter estimation of a time-dependent heat transfer coefficient in a multidimensional nonlinear inverse heat conduction problem

In the applied mathematical modelling of heat transfer systems, the heat transfer coefficient (HTC) is one of the most important parameters. This paper proposes a combination of the Method of Fundamental Solutions (MFS) with particle filter Sequential Importance Resampling (PF-SIR) to estimate the time-dependent HTC in two-dimensional transient inverse heat conduction problems from non-standard boundary integral measurements. These measurements ensure the unique solvability of the boundary coefficient identification problem. Numerical results show high performance on several test cases with both linear and nonlinear Robin boundary conditions, supporting the synergy between the MFS and simulation-based particle filter sequential analysis methods.

Intelligent Control Based Estimation of Heat Transfer Coefficient from Four Flat Tubes with Different Attack Air Angles

Intelligent Control Based Estimation of Heat Transfer Coefficient from Four Flat Tubes with Different Attack Air Angles

Special Section: Memorial Festschrift for the Late Professor Frank Kreith Sunrise Delayed but the Sun Shines Brightly: The Energy-Sustainability Quandary and Legacy of Professor Frank Kreith

Special Section: Memorial Festschrift for the Late Professor Frank Kreith Sunrise Delayed but the Sun Shines Brightly: The Energy-Sustainability Quandary and Legacy of Professor Frank Kreith

A Criterion of Heat Transfer Deterioration for Supercritical Organic Fluids Flowing Upward and Its Heat Transfer Correlation

The main objective of this study was to develop the supercritical heat transfer correlation applicable for organic fluids when flowing upward in smooth tubes based on the available experimental data. The organic fluids contain R-22, R-134a, R-245fa and Ethanol and the associated heat transfer characteristics were compared with non-organic fluids like water and carbon-dioxide (CO2). It was found that the limit heat flux may result in heat transfer deterioration (HTD) of organic fluid and the corresponding values are much smaller than water or CO2. A new criterion to predict the HTD was developed and this criterion yields the best predictive ability against database. It was found that HTD occurs can be well described by the acceleration parameter evaluated at the wall condition rather than at bulk condition. For estimation of the supercritical heat transfer coefficient (HTC) for organic fluid, the present study proposes a new correlation with a physically based correction factor, which gives satisfactory predictions against the HTC of supercritical organic fluid. The new correlation can offer the smallest average deviation of 0.007 and standard deviation of 0.181 among the existing correlations.

Cooling of porous metal surfaces by droplet impact

An experimental study was conducted on the impact of droplets of pure water and n-heptane on impervious and porous (5 µm and 100 µm pore size) stainless steel surfaces. Surface porosity, roughness and thermal conductivity were measured. Droplet diameter (2.5 mm) and impact velocity (0.9 m/s) were kept constant while surface temperature was varied from room temperature to 300 °C. Droplet impact was observed using a high-speed video camera. Droplet evaporation times were measured by recording the change in weight of the surface on which the droplet was deposited and surface temperature variation during droplet impact measured using a fast response surface thermocouple.Droplets spread out on porous surfaces during impact to form a thin film that was then drawn into pores by capillary forces. The rate of droplet spread decreased with greater surface roughness. The Leidenfrost temperature of n-heptane droplets increased with surface porosity while water droplets did not go into film boiling on the porous surfaces. A one-dimensional heat conduction model was used to estimate heat transfer coefficients between the impacting droplets and substrates. Heat transfer coefficients increased with surface temperature until sufficient vapor was generated at the liquid-solid interface to inhibit contact. Heat transfer coefficients then decreased with further increases in temperature.

Modeling of adsorption heat pump system based on experimental estimation of heat and mass transfer coefficients

This paper presents a zero-dimensional model for predicting the performance of adsorption heat pumps. In particular, the overall heat and mass transfer coefficients at the adsorbers are experimentally estimated. Two materials are used as adsorbents: A-type silica gel, and a natural mesoporous material termed Wakkanai siliceous shale (WSS) impregnated with 20 wt% LiCl. Corrugated fin-type heat exchangers are filled with each adsorbent at different filling densities: 223 and 305 g/L for A-type silica gel, and 233 and 329 g/L for the WSS + LiCl 20 wt%. Experiments performed to estimate the overall mass transfer coefficient are based on the large pressure jump method and are conducted at various adsorbent temperatures in the range of 30–60 °C. Furthermore, the overall heat transfer coefficients of the adsorbers are experimentally estimated when the inlet water temperature changes from 80 to 30 °C to elucidate the actual working condition of adsorption heat-pump systems. Finally, according to the adsorption time, the cooling capacity, specific cooling power (SCP), and coefficient of performance (COP) are analyzed via a dynamic model. The results indicate that the COP of the heat exchanger using the WSS composite material are improved by 6–17% compared with the heat exchanger using the A-type silica gel.

Thermal and Rheological Properties of Juices and Syrups during Non-centrifugal Sugar Cane (Jaggery) Production

This work focused on the physicochemical characterization of sugarcane juices and syrups obtained during non-centrifugal cane sugar (NCCS) production. Samples were collected from two different factories that use steam or combustion gases as heating medium during the open evaporation process. Juices and syrups contained sucrose as the predominant sugar (>90%), followed by reducing sugars (i.e. glucose and fructose), and the sugars profile remained invariable during processing. Viscosities of the solutions ranged from 1.4 and 165.8 mPa s, and a large dependence on temperature and solids content was observed. Heat capacities of the liquid mixtures ranged from 2.4 to 3.8 kJ/kgK, and the densities were barely constant, ranging from 1.12 to 1.35 g/ml. The thermal conductivity of the liquid solutions was in between 0.26 and 0.46 W/mK. Correlations were obtained for all properties as function of temperature, and the sugars concentration or the solids content (i.e. °Brix). A comparison with reported data, and models for juices, syrups, and sucrose solutions, as well as with predictive equations for saccharides mixtures is presented. Regressed equations enabled to estimate heat transfer coefficients of the boiling liquid during the concentration process. Convective heat transfer coefficients around 160-290 W/m2K were estimated for nucleate boiling. Comparatively, values around 70-200 W/m2K were estimated for film boiling conditions.

Estimation of time-dependent heat transfer coefficient in unidirectional casting using a numerical model coupled with solidification analysis and data assimilation

We have recently developed a method to estimate the heat transfer coefficient based on data assimilation. To understand its usefulness for estimating the time-dependent heat transfer coefficient, herein we performed unidirectional casting experiments of Al-1mass%Si alloy and obtained the cooling curves during solidification. The experimental data were then used to validate the estimated time-dependent heat transfer coefficient. Consequently, the measured cooling curves could be accurately simulated, and the average errors between measured and simulated cooling curves were below 0.8%. The estimated time-dependent heat transfer coefficient was 29461.5 Wm−2K−1 at the initial stage of cooling, which rapidly decreased to about 6000 Wm−2K−1 and then gradually decreased to about 1000 Wm−2K−1. These values are reasonable as the heat transfer coefficients for castings of Al base alloys. Additionally, the effect of the setting parameters of the data assimilation were evaluated. It was found that the position of the cooling curve(s) used in the estimation was the most important factor and a cooling curve measured at the position near the surface of the mold should be utilized. This method allows the reasonable estimation of the time-dependent heat transfer coefficient between the mold and molten alloy for unidirectional castings without using trial and error, and experimentally measured cooling curves can be accurately reproduced by solidification analysis.

Quantitative Estimation of Leaf Heat Transfer Coefficients by Active Thermography at Varying Boundary Layer Conditions.

Quantifying heat and mass exchanges processes of plant leaves is crucial for detailed understanding of dynamic plant-environment interactions. The two main components of these processes, convective heat transfer, and transpiration, are inevitably coupled as both processes are restricted by the leaf boundary layer. To measure leaf heat capacity and leaf heat transfer coefficient, we thoroughly tested and applied an active thermography method that uses a transient heat pulse to compute τ, the time constant of leaf cooling after release of the pulse. We validated our approach in the laboratory on intact leaves of spring barley (Hordeum vulgare) and common bean (Phaseolus vulgaris), and measured τ-changes at different boundary layer conditions.By modeling the leaf heat transfer coefficient with dimensionless numbers, we could demonstrate that τ improves our ability to close the energy budget of plant leaves and that modeling of transpiration requires considerations of convection. Applying our approach to thermal images we obtained spatio-temporal maps of τ, providing observations of local differences in thermal responsiveness of leaf surfaces. We propose that active thermography is an informative methodology to measure leaf heat transfer and derive spatial maps of thermal responsiveness of leaves contributing to improve models of leaf heat transfer processes.

Simultaneous estimation of heat flux and heat transfer coefficient in irregular geometries made of functionally graded materials

Abstract A numerical inverse analysis based on explicit sensitivity coefficients is developed for the simultaneous estimation of heat flux and heat transfer coefficient imposed on different parts of boundary of a general irregular heat conducting body made of functionally graded materials with spatially varying thermal conductivity. It is assumed that the thermal conductivity varies exponentially with position in the body. The body considered in this study is an eccentric hollow cylinder. The heat flux is applied on the cylinder inner surface and the heat is dissipated to the surroundings through the outer surface. The numerical method used in this study consists of three steps: 1) to apply a boundary-fitted grid generation (elliptic) method to generate grid over eccentric hollow cylinder (an irregular shape) and then solve for the steady-state heat conduction equation with variable thermal conductivity to compute the temperature values in the cylinder, 2) to propose a new explicit sensitivity analysis scheme used in inverse analysis, and 3) to apply a gradient-based optimization method (in this study, conjugate gradient method) to minimize the mismatch between the computed temperature on the outer surface of the cylinder and simulated measured temperature distribution. The inverse analysis presented here is not involved with an adjoint equation and all the sensitivity coefficients can be computed in only one direct solution, without the need for the solution of the adjoint equation. The accuracy, efficiency, and robustness of the developed inverse analysis are demonstrated through presenting a test case with different initial guesses.

Parameter estimation for heat transfer analysis during casting processes based on ensemble Kalman filter

It is very important for production of casts with high quality to predict and control the solidification processes of the alloy. Heat transfer analysis has been utilized for understanding solidification processes. However, it is often difficult to obtain values of all input parameters such as thermal conductivity and heat transfer coefficient precisely. In this study, a parameter estimation method in heat transfer analysis is developed based on data assimilation. In the authors’ previous study, the particle filter, a method of data assimilation, was applied to estimation of thermal conductivity and heat transfer coefficient in heat transfer analysis for mold casting, and its applicability was systematically investigated. It was shown that the particle filter is very effective in estimating these parameters. However, the particle filter suffers from a shortcoming called sample degeneracy which often prevents accurate estimation of parameters in phenomena of interest. The present study focuses on a different method of data assimilation called the ensemble Kalman filter and its applicability to the estimation of heat transfer coefficient and thermal conductivity is investigated based on twin experiments. It is shown that thermal conductivity and constant or time-dependent heat transfer coefficient can be accurately estimated independently with three and two cooling curves, respectively. Furthermore, the thermal conductivity and time-dependent heat transfer coefficient can be estimated simultaneously with high accuracy.

Estimation of the Possibility to Equalize the Fluid Temperature in a Hydrolevelling System by Mixing

Measurement systems that are based on the hydrostatic leveling method under ideal conditions allow one to determine vertical displacements with accuracy on the order of a micron. Heterogeneous and time-varying environmental conditions have a significant effect on the measurement error. One method to increase the accuracy of results is to equalize the temperature of the fluid in the hydrostatic level by mixing the liquid inside it before taking measurements. In this paper, the possibility to perform this operation by forced circulation of the fluid is estimated. For this purpose, a model problem of the circulation flow created by a pump in a simplified analog of the hydrostatic level with allowance for the heat transfer through the hose wall is solved. The fluid dynamics is described by the Reynolds averaged Navier-Stokes equations which are closed by the Menter shear stress transport model. The analytically obtained estimates of heat transfer coefficients on the lateral surface of the hose are refined based on experiments at two values of the flow rate of water flowing through the pipe. The evolution of the temperature field is found from the numerical solution of the coupled heat transfer problem by the finite volume method. In a test example, in which two parts of the hydrostatic level are located in areas with markedly different temperature, the spatial inhomogeneity of the temperature field at different times is calculated. The mixing time sufficient to achieve a temperature distribution close to the homogeneous distribution of the flowing fluid in the hose at different volumes of the mixer joint with the hydrostatic level is determined. The proposed approach can be used under real external conditions for the selection of optimal operation parameters: the pump flow rate, mixing time, and mixing tank volume. The temperature field obtained in the calculation can serve as a basis for estimating the achievable accuracy of the measurement system.

Heat transfer to a stationary cubic particle in a laminar tube flow: Computational fluid dynamics simulations and experiments

In continuous aseptic processing involving liquid food suspensions, the suspended particles must receive sufficient heat treatment without affecting their nutritional or sensory qualities. Optimal process design for the sterilization of particulates in liquid food therefore requires good estimates of convective heat transfer coefficient at the fluid to particle interface. Relatively few studies have been reported involving coarse non-spherical particles in a confined flow. In this work, we have used a combination of computational fluid dynamics (CFD) simulations and experiments to investigate the heat transfer rate to a coarse cubic particle suspended in a laminar fluid flow within a circular tube. We carried out the simulations using ANSYS Fluent software, whereas for the experimental investigations, we used the stationary particle method, employing a thermocouple to measure the particle temperature at the centre. We conducted all tests using a sugar solution as the heat-carrying fluid, and we employed two types of cubic particles, one fabricated from peach fruit and one from polycarbonate plastic. We varied the particle orientation, the fluid flow rate, and the radial position of the particle in the tube. For all the above parameters, we validated the time-temperature profiles of the particle obtained from the simulations against the values measured in the experiments. The temperature data from the simulations for the polycarbonate particle showed fairly good agreement with the experimental data (within 5%) for all flow rates and particle orientations. However, for the peach fruit particle, the agreement between the simulated and experimental data was unacceptable, especially for non-central positions in the tube, with obvious deviations between the simulated and experimental data, where the maximum deviations were between 15% and 25%. The evaluated average fluid-particle heat transfer coefficients for polycarbonate particles were compared with the values obtained from correlations in the literature. The comparison resulted in either overestimation (up to 50%) or underestimation (up to 35%) of the average fluid-particle heat transfer coefficients.

Numerical estimation of the external convective heat transfer coefficient for buildings in an urban-like setting

Current external convective heat transfer coefficient estimation methods are known to introduce significant uncertainty in energy consumption evaluations for building with complex surrounding conditions. In this study, the impact of built area density (aggregation or rarefaction) on convective heat transfer from buildings is numerically investigated in an urban-like setting. Arrays of cubical buildings with twelve different packing density in different flow regimes including three isolated, five wake interference and four skimming flow regimes, and an isolated cube case for comparison have been investigated. Reynolds stress turbulence model (RSM) is used for closure of the steady Reynolds averaged momentum and energy equations. The results indicate that the behavior of convective heat transfer varies from one flow regime to another. The convective heat transfer coefficient (CHTC) trends in the isolated flow regimes are characterized by sharp changes with density; whereas in the interference and skimming flow regimes the CHTC gently decreases with the increase of built area density. New correlations for estimating CHTC in these three regimes are proposed. The proposed correlations are expected to enable estimation of CHTC for buildings located in urban neighborhoods based on the built area density.

3D coupled conduction-convection problem using in-house heat transfer experiments in conjunction with hybrid inverse approach

Purpose Many a times, the information about the boundary heat flux is obtained only through inverse approach by locating the thermocouple or temperature sensor in accessible boundary. Most of the work reported in literature for the estimation of unknown parameters is based on heat conduction model. Inverse approach using conjugate heat transfer is found inadequate in literature. Therefore, the purpose of the paper is to develop a 3D conjugate heat transfer model without model reduction for the estimation of heat flux and heat transfer coefficient from the measured temperatures. Design/methodology/approach A 3 D conjugate fin heat transfer model is solved using commercial software for the known boundary conditions. Navier–Stokes equation is solved to obtain the necessary temperature distribution of the fin. Later, the complete model is replaced with neural network to expedite the computations of the forward problem. For the inverse approach, genetic algorithm (GA) and particle swarm optimization (PSO) are applied to estimate the unknown parameters. Eventually, a hybrid algorithm is proposed by combining PSO with Broyden–Fletcher–Goldfarb–Shanno (BFGS) method that outperforms GA and PSO. Findings The authors demonstrate that the evolutionary algorithms can be used to obtain accurate results from simulated measurements. Efficacy of the hybrid algorithm is established using real time measurements. The hybrid algorithm (PSO-BFGS) is more efficient in the estimation of unknown parameters for experimentally measured temperature data compared to GA and PSO algorithms. Originality/value Surrogate model using ANN based on computational fluid dynamics simulations and in-house steady state fin experiments to estimate the heat flux and heat transfer coefficient separately using GA, PSO and PSO-BFGS.

Inverse Approach Using Bio-Inspired Algorithm Within Bayesian Framework for the Estimation of Heat Transfer Coefficients During Solidification of Casting

Abstract In any parameter estimation problem, it is desirable to obtain more information in one single experiment. However, it is difficult to achieve multiple objectives in one single experiment. The work presented in this paper is the simultaneous estimation of heat transfer coefficient parameters, latent heat, and modeling error during the solidification of Al–4.5 wt %Cu alloy with the aid of Bayesian framework as an objective function that harmoniously matches the mathematical model and measurements. A 1D transient solidification problem is considered to be the mathematical model/forward model and numerically solved to obtain temperature distribution for the known boundary and initial conditions. Genetic algorithm (GA) and particle swarm optimization (PSO) are used as an inverse approach and the estimation of unknown parameters is accomplished for both pure and noisy temperature data. The use of Bayesian framework for the estimation of unknown parameters not only provides the information about the uncertainties associated with the estimates but also there is an inherent regularization term in which the inverse problem boils down to well-posed problem thereby plethora of information is extracted with less number of measurements. Finally, the results of this work open up new prospects for the solidification problem so as to obtain a feasible solution with the present approach.

Estimation of time-dependent thermal boundary conditions and online reconstruction of transient temperature field for boiler membrane water wall

The thermal boundary conditions of membrane water wall include local radiant heat flux on the fire side, fluid temperature inside the tube, and the convective heat transfer coefficient. Obtaining the above thermal boundary conditions has an important impact on the safe operation of modern power station boilers. When the above thermal boundary conditions have time-varying characteristics, the heat transfer system shows obvious nonlinearity. In view of the fact that they are difficult to measure directly and accurately, a multiple model adaptive inverse scheme based on boundary condition transfer (BCT-MMAI) is proposed. In this scheme, the estimation of convective heat transfer coefficient in the tube is transferred to the estimation of adiabatic boundary condition on the back side of water wall, that is, the local radiative heat flux on the fire side, the fluid temperature in the tube and the adiabatic boundary condition on the back side are simultaneously estimated. Firstly, according to the given discrete points of convective heat transfer coefficient (characteristic variable), the non-linear heat transfer system is divided into several linear subspaces, and the temperature prediction sub-model corresponding to each linear subspace is established. Secondly, according to the predicted and measured temperatures at the measurement points, the estimated results of the three variables are obtained by rolling optimization. Further, the weighting coefficient of each linear sub-model is constructed based on the accuracy of inversion results of adiabatic boundary condition on the back side by each linear sub-model. Finally, by weighting the inversion results of each sub-model, the estimation results of local radiant heat flux on the fire side and the fluid temperature in the tube are directly obtained. Meanwhile, the discrete values of characteristic quantity are comprehensively weighted, and the identification results of time-varying convective heat transfer coefficient are indirectly generated.

Exergy and sensibility analysis of each individual effect in a kraft multiple effect evaporator

The multiple effect evaporator (MEE) is an energy intensive step in the kraft pulping process. The exergetic analysis can be useful for locating irreversibilities in the process and pointing out which equipment is less efficient, and it could also be the object of optimization studies. In the present work, each evaporator of a real kraft system has been individually described using mass balance and thermodynamics principles (the first and the second laws). Real data from a kraft MEE were collected from a Brazilian plant and were used for the estimation of heat transfer coefficients in a nonlinear optimization problem, as well as for the validation of the model. An exergetic analysis was made for each effect individually, which resulted in effects 1A and 1B being the least efficient, and therefore having the greatest potential for improvement. A sensibility analysis was also performed, showing that steam temperature and liquor input flow rate are sensible parameters.

Experimental design for estimation of the distribution of the convective heat transfer coefficient for a bubbly impinging jet

In this study, a two-dimensional inverse algorithm is developed to determine the heat transfer coefficient distribution of a two-phase air–water bubbly jet impinging on a steel cylindrical thermal mass. All procedures of thermal mass heating and cooling are simulated by solving two-dimensional, transient heat conduction equations using finite difference method. Afterward, the nonlinear inverse heat conduction problem is implemented to directly predict the local convective heat transfer coefficient of the bubbly jet. The sum of squared differences between calculated and measured temperature data is the objective function. Conjugate gradient method is employed sequentially in every time step to optimize the objective function at four gas Reynolds numbers which represent four different two-phase jets. The inverse scheme is validated using exact temperature data without noise. Local heat transfer coefficients are then estimated by inverse technique at five data acquisition times and four initial temperatures of thermal mass in the presence of noise. Furthermore, the effects of uncertainties due to indefinite lateral boundary conditions, temperature dependency of thermal conductivity, and the non-uniformity of the initial temperature distribution are investigated. A satisfactory agreement between exact and estimated heat transfer coefficients is achieved. However, the results show a greater sensitivity to the highest value of initial temperature, the shortest data acquisition time, and the lowest gas Reynolds number allowing a better estimation of heat transfer distribution for the bubbly jet.

Air side heat transfer coefficient in plate finned tube heat exchangers

ABSTRACTIn order to establish a reliable procedure for estimation of heat transfer coefficient, experiments on plate finned tube heat exchangers have been conducted on five exchangers. Using own and previously published experimental data databank of 969 working regimes, a new correlation was formed. Correlation is based on hydraulic diameter and porous velocity and on the ratio of characteristic surfaces of the finned tube bundle. Statistical parameters of a new correlation for estimation of heat transfer coefficient are very good, and correlation covers a wide range of geometrical and other parameters of heat exchangers that are industrially important.