Mechanistic Heat Transfer Model Research Articles

Study of the Effect of the Reduced Pressure on a Mechanistic Heat Transfer Model for Flow Boiling of CO2 in Macroscale and Microscale Tubes

The effect of the reduced pressure on flow boiling of CO2 in macroscale- and microscale-tubes was analyzed in this paper. First, flow boiling heat transfer at high and low reduced pressures were simulated using a general mechanistic heat transfer model for flow boiling CO2 to analyze the heat transfer mechanisms. Then, the simulated heat transfer coefficients were compared to an experimental database at the reduced pressure from 0.1332 to 0.9082 (the corresponding saturation temperature from -40.6 to 26.77 °C), the tube diameter from 0.529 to 9.52 mm, the heat flux from 2 to 72 kW/m2 and the mass flux from 100 to 1500 kg/m2s. The model predicts 81.3% of the data before the dryout inception within ±30% while it only predicts 21% of data in the dryout and mist flow regimes within ±30%. The poor prediction of the heat transfer in these two regimes are because the model does not capture the dryout inception and completion. Furthermore, the heat transfer mechanisms are discussed from the standpoint of the flow regime variations and unstable flow boiling phenomena in macroscale and microscale tubes. It is recommended that the model should be improved by considering the mechanisms at low and high reduced pressures.

Mechanistic model of combined pressure drop and heat transfer for the entire growth stage of an elongated bubble in a rectangular microchannel

A one-dimensional flow-boiling model for the slug-flow regime is formulated to describe the pressure drop and heat transfer mechanism in a microchannel of rectangular cross-section. The pressure drop model considers three stages of bubble growth namely: (i) partial confinement, (ii) full confinement and (iii) vapour venting. The heat transfer coefficient at any particular location is obtained by assuming the periodic passage of four zones: (i) liquid slug zone, (ii) elongated bubble zone, (iii) partially dryout zone, and (iv) fully dryout zone. The model is evaluated using constant fluid properties, to study the parametric variation of channel pressure drop and heat transfer coefficient. The effects of variation in channel dimension, flow velocity, heat flux and properties of working fluid on pressure drop and heat transfer coefficient have been studied using the model. The model is capable of simulating all the transport processes for a single bubble from its inception till it leaves the microchannel and thereby it can estimate the pressure drop in the channel along with the heat transfer coefficient i.e. spatially averaged over the channel length and at any location from channel upstream to the downstream end.

Model-based assessment of boiling heat transfer enhanced by coatings

The present study aims to investigate boiling heat transfer enhancement on coated surfaces, based on mechanistic models. An electrochemical deposition method was used to fabricate coatings on copper surfaces which enhance critical heat flux and heat transfer coefficient of deionized water by 35.5% and 40.1%, respectively, compared with a smooth surface. Bubble dynamics indicates that regardless of surfaces, scaling laws of Db*∝t*0.5 and Db*∝t*0.2 are followed in the inertia-controlled growth stage and the heat-diffusion-controlled growth stage, respectively, concerning normalized bubble diameter (Db*) and normalized bubble time (t*). The coating decreases the bubble departure diameter to one-third to half of that on the smooth surface and increases the departure frequency to three times that on the smooth surface. In addition, the coated surface provides more active nucleation sites which are 1, 2 order magnitude higher than the smooth surface. With these insights, a mechanistic heat transfer model was established by quantifying natural convection, transient heat conduction, and microlayer evaporation, which matches well with the measured pool boiling curve. In the end, critical heat flux was explored experimentally and theoretically. Inspired by the coalesced bubble behavior at high heat flux and the Kandlikar force model, a new force-balance model was proposed by incorporating a surface-dependent surface tension force and adding a new capillary wicking force. The present model presents a better prediction of critical heat flux, verified by the current measurement and the literature.

Experimental study on heat transfer of dense phase flow through a horizontal tube under constant wall flux conditions

A novel application of particles is utilization as dense phase flow for heat capture, transportation and storage. The use of horizontal dense phase flow as heat transfer fluid in solar systems is discussed with respect to current technologies. The investigation aims to analyze the heat transfer behavior of a horizontal dense phase flow under the condition of uniform surface heat flux. The proposed technologies transport particles as semi-continuous plug flow with a bottom layer, particles at the bottom layer will regularly renew once plugs pass by. Tests were conducted in a self-pilot scale-up platform. The measured wall-to-mixture heat transfer coefficient varies from ∼303 to 813 W/m2K in the particle mass flux range from 125 to 777 kg/m2s. Three heat transfer equations will be provided with the experimental data. A heat transfer equation describes the wall-to-mixture heat transfer coefficient linearly increases with particle mass flux. Then, a general empirical correlation in a dimensionless form predicted results well with experimental data of the present work and other data reported in the literature. Furthermore, a mechanistic heat transfer model is proposed according to a partial penetration mechanism and multi-layer flow model. The predicted results agree with experimental results within 12% of the average error. Considering the findings in this paper, researchers may have ideas to improve the heat transfer of horizontal dense phase flow to utilize this technology to the parabolic concentrator for the solar thermal industry.

Mechanistic modeling of flow and heat transfer in vertical upward two-phase slug flows

Two-phase slug flow exhibits intrinsically stochastic and statistically periodic flow behaviors. Understanding the mechanisms of flow and heat transfer of upward two-phase slug flow is important. This paper develops a mechanistic model of flow and heat transfer for upward two-phase slug flow in vertical pipes. First, a hydrodynamic model of two-phase slug flow in regular-sized channels is developed based on the hypothesis of the slug unit cell. Each slug unit cell is hypothesized to be composed of a liquid slug and a Taylor bubble region. Second, a mechanistic heat transfer model is derived based on the hydrodynamic model. The overall heat transfer coefficient is integrated by using the local heat transfer coefficients of liquid slug and the Taylor bubble region. Third, the proposed mechanistic model is validated by the experimental void fraction, pressure drop, and two-phase heat transfer coefficient from different sources. Finally, the effect of flow geometry and parameters—such as superficial gas and liquid velocities, void fraction, slug frequency, pressure drop, and the ratio of slug length to unit cell length—on heat transfer in two-phase slug flow is comprehensively investigated. The enhancement in heat transfer in two-phase slug flow compared with that of single-phase flow can be attributed to an increase in the turbulence of the liquid due to the injection of air and a reduction in the thermal boundary layer owing to the frequent alternation between liquid slug and the Taylor bubble.

Evolution of Temperature Field around Underground Power Cable for Static and Cyclic Heating

Power transmission covering long-distances has shifted from overhead high voltage cables to underground power cable systems due to numerous failures under severe weather conditions and electromagnetic pollution. The underground power cable systems are limited by the melting point of the insulator around the conductor, which depends on the surrounding soils’ heat transfer capacity or the thermal conductivity. In the past, numerical and theoretical studies have been conducted based on the mechanistic heat and mass transfer model. However, limited experimental evidence has been provided. Therefore, in this study, we performed a series of experiments for static and cyclic thermal loads with a cylindrical heater embedded in the sand. The results suggest thermal charging of the surrounding dry sand and natural convection within the wet sand. A comparison of heat transfer for dry, unsaturated and fully saturated sand is presented with graphs and colour maps which provide valuable information and insight of heat and mass transfer around an underground power cable. Furthermore, the measurements of thermal conductivity against density, moisture and temperature are presented showing positive nonlinear dependence.

Bubble dynamics and mechanistic boiling heat transfer prediction on a scored copper surface

In this study, pool boiling heat transfer of de-ionized water was experimentally studied on a scored copper surface at a heat-flux range of 0 - 60 W/cm2. Bubble dynamics in an isolated bubble region were carefully investigated, including bubble departure diameters, bubble departure frequencies, and active nucleation site densities. The bubble dynamics were compared with available models, indicating the suitable models regarding the present experimental results. Then, based on the bubble dynamics, a mechanistic heat transfer model, developed in our previous studies, was employed to predict the present boiling curve. In the mechanistic model, heat fluxes from natural convection, transient heat conduction, and microlayer evaporation were incorporated.

Investigation of Heat Transfer in a Large-Scale External Heat Exchanger with Horizontal Smooth Tube Bundle

In the research work, energy transport between a dense fluidized bed and submerged horizontal tube bundle is analyzed in the commercial external heat exchanger (EHE). In order to investigate the heat transfer behavior, the authors carried out eight performance tests in a fluidized bed heat exchange chamber with a cross-section of 2.7 × 2.3 m in depth and width and a height of 1.3 m. The authors have been developing a mechanistic model for the prediction of the average heat transfer coefficient, which includes the effect of the geometric structure of the tube bundle and the location of the heat transfer surface on the heat transfer rate. The computational results depict that the average heat transfer coefficient is essentially affected by superficial gas velocity and suspension density rather than bed particle size. The empirical correlations have been proposed for predicting heat transfer data since the existing literature data is not sufficient for industrial fluidized bed heat exchangers. On the basis of the evaluated operating conditions of an external heat exchanger, the optimal conditions where heat transfer occurs could be deduced. The developed mechanistic heat transfer model is validated by experimental data under the examined conditions.

Mechanistic modeling of flow and heat transfer in turbulent–laminar/turbulent gas–liquid stratified flow

Two-phase gas–liquid stratified flow is characterized by a structure in which the gas and liquid phases are separated from each other by a continuous interface. Adequately understanding its flow mechanism and heat transfer is important for analyzing two-phase stratified flow. This paper develops a mechanistic model of flow and heat transfer in turbulent–laminar/turbulent two-phase stratified flow in horizontal and slightly inclined pipes. First, a hydrodynamic model of two-phase stratified flow is developed by using the concept of two-fluid model. Second, a mechanistic model of heat transfer is derived based on the hydrodynamic model. The overall heat transfer coefficient is integrated by using the coefficients of local heat transfer of the liquid film and the gas core. Third, the effect of such flow geometries and parameters as the superficial Reynolds numbers for liquid and superficial gas, void fraction, pressure drop, and inclination angle of the pipe on heat transfer in two-phase stratified flow is comprehensively investigated. Finally, the relationships between the two-phase heat transfer multiplier and the overall void fraction and pressure drop multipliers are quantified. A simple correlation of the heat transfer multiplier for two-phase stratified flow is developed by using the void fraction as the input parameter serving as a quick but rough prediction of the heat transfer multiplier in two-phase stratified flow.

Flow and heat transfer for a two-phase slug flow in horizontal pipes: A mechanistic model

In view of the practical importance of gas–liquid two-phase flow in many applications, such as chemical engineering, petroleum engineering, nuclear engineering, etc., a reliable model of flow and heat transfer for two-phase flow is of practical importance in the two-phase flow analysis. Among various two-phase flow regimes, slug flow is most complicated due to the intrinsic randomness and intermittency. This paper aims at developing a novel mechanistic model of flow and heat transfer for two-phase slug flow in horizontal pipes. First, a hydrodynamic model of two-phase slug flow is developed using the concept of slug unit cell. Then, a heat transfer model is deduced based on the hydrodynamic model. The overall heat transfer coefficient is integrated by the local heat transfer coefficients of liquid slug, liquid film, and elongated bubble. The newly developed mechanistic model is well validated by the experimental results. Finally, the dependence of the heat transfer performance on the overall flow parameters, such as superficial liquid velocity and superficial gas velocity, and the local flow parameters, such as slug frequency, pressure drop, void fraction, and ratio of slug length to unit cell length, is comprehensively investigated. The heat transfer enhancement of two-phase slug flow compared with single-phase flow is mainly attributed to the turbulence increase in liquid by the injection of air and the decrease in thermal boundary layer by the frequent alternation between the liquid slug and the elongated bubble.

Control of asymmetric track geometry in printed parts of stainless steels, nickel, titanium and aluminum alloys

In powder bed fusion, distorted temperature fields and deposit dimensions, undesirable surface features, and defects have been attributed to asymmetry in track geometry. It is also thought to affect sensing and control. While data on the asymmetry have been widely reported in the literature for many commonly used alloys, the origin of the asymmetry and the role of alloy composition and process variables are not known. Here we examine the role of local differences in heat transfer from the fusion zone as the origin of asymmetry in the track geometry. We use a mechanistic model of heat transfer and experimental data to examine the role of main process variables and alloy composition on the extent of asymmetry and provide easy-to-use process maps. We show that high laser power and slow scanning speed decreases asymmetry. Marangoni, Fourier and Peclet numbers can be used for controlling asymmetry. Among the four alloys examined, stainless steel 316 and AlSi10Mg are the most and least susceptible to asymmetry because of their lowest and highest thermal diffusivity, respectively.

Heat transfer characteristic in an external heat exchanger with horizontal tube bundle

In this research article, experimental study was carried out to obtain the heat transfer characteristics between a submerged horizontal tube bundles and a fluidized bed in a large-scale circulating fluidized bed (CFB) boiler with an external heat exchanger (EHE). Authors used operating conditions of fluidized bed heat exchanger to predict the average heat transfer coefficient (HTC) making use of an existing calculation method based on the packed renewal theory. The operational parameters in the tube EHE were measured during performance tests at variable load conditions. The heat transfer characteristics are considered in terms of heat transfer mechanisms such as emulsion phase convection, gas convection and also thermal radiation. The obtained heat transfer data exhibits a maximum value with variation mean bed particle size irrespective of pressure. The results showed that the average HTC increases with a decrease of the Sauter mean particle diameter and with the increase of the fluidizing number as a result of good mixing dynamics in emulsion phase (i.e. emulsion wall contact time, bubble fraction in the bed). Based on the heat transfer data, empirical correlations are proposed for predicting a heat transfer coefficient from fluidized bed to horizontal tube bundle. The mechanistic heat transfer model predicted the average HTC in sufficient good agreement with accessible literature data. The predictions were as accurate refer to experimental data at the examined conditions.

A heat transfer model development for CHF prediction with consideration of dry patch characteristics

This study develops an observation-based mechanistic heat transfer model that can be extended to the whole boiling curve to reflect real physical phenomena on a heated surface. In addition to hot spot formation, this study focuses on dry patch behaviors, which actually directly trigger CHF occurrences. For that purpose, hot spot distribution and the critical number of hot spots are further considered to determine the kinds of dry patches, whether reversible (quenchable) or irreversible (unquenchable). To assess the prediction performance, CHF data that include combined effects are used for data comparisons. The developed model predicts well for large dimensions at a vertical orientation, suggesting potential applications to large-scale facilities.

Saturated pool boiling heat transfer of acetone and HFE-7200 on modified surfaces by electrophoretic and electrochemical deposition

Boiling heat transfer intensification is of big relevance to energy conversion and conservation, materials and resources saving, and electronics cooling. This work aims to enhance saturated pool boiling of well-wetting liquids, i.e., acetone and HFE-7200 on nanoparticles-deposited surfaces by electrophoretic deposition and on microporous foam surfaces by electrochemical deposition. The electrophoretic-deposited surfaces enhance the heat transfer coefficient of acetone and HFE-7200 by up to 70% and 190%, respectively. However, the critical heat flux is not improved on electrophoretic-deposited surfaces. The electrochemical-deposited surfaces increase the boiling heat transfer coefficient by up to 370% and the critical heat flux by more than 30%. Bubble dynamics were visualized simultaneously. The bubble departure diameter from experiments can be predicted by a dynamic force balance model within a ±20% error band. A mechanistic heat transfer model was proposed for modified porous surfaces, including not only the heat fluxes from microlayer evaporation and transient conduction but also the heat flux from micro-convection due to liquid agitation and entrainment by growing and departing bubbles. The mechanistic heat transfer model can predict experimental pool boiling curves of acetone and HFE-7200 on electrophoretic-deposited and electrochemical-deposited surfaces relatively well, especially for the isolated bubble regime where most bubbles are isolated and bubble coalescence is not intensive. Besides, the critical heat flux of a modified surface can be estimated if the initial (maximum) wicked volume flux on the structured surface relative to the smooth surface is considered.

Nucleate pool boiling heat transfer of acetone and HFE7200 on copper surfaces with nanoparticle coatings

Nucleate pool boiling performance of two well-wetting liquids, i.e., acetone and HFE7200, on three nanoparticle-coated surfaces were experimentally studied and compared with that of the smooth surface. Electrophoretic deposition was used to fabricate nano-porous surfaces. Surface roughness, static and advancing contact angles, capillarity of the smooth and coated surfaces were characterized. Compared to the smooth surface, the nanoparticle-coated surfaces decreased the wall superheat by more than 50% for acetone and 65% for HFE7200 at the same heat flux level, and accordingly enhanced the heat transfer coefficient by up to 85% for acetone and up to 200% for HFE7200. Bubble departure diameters were measured and correlated with the advancing contact angle, the capillary length and the Jacob number. A new mechanistic heat transfer model was proposed based on the heat flux partition method. The advancing contact angle was suggested to be used for calculation of the active nucleation site density. Based on the mechanistic model, transient heat conduction on and around nucleation sites over the whole bubble cycle contributes the most (>70%) to the total heat flux, while microlayer evaporation contributes around 10-30% to the total heat flux, with negligible natural convection. The critical heat flux was not enhanced for the two well-wetting liquids.

Heat transfer characteristics of an external tube heat exchanger in a 1296t/h circulating fluidized bed boiler

In this research article, experimental study was carried out to obtain the heat transfer characteristics between a submerged horizontal tube bundle and a fluidized bed in a large-scale circulating fluidized bed (CFB) boiler with an external heat exchanger (EHE). The operational parameters in the tube EHE were measured during performance tests at variable load conditions. The average heat transfer coefficient (HTC) was calculated using a mechanistic heat transfer model based on packed renewal theory. The heat transfer characteristics are considered in terms of heat transfer mechanisms such as emulsion phase convection, gas convection and also thermal radiation. The obtained heat transfer data exhibit a maximum value with variation mean bed particle size irrespective of pressure. The results showed that the average HTC increases with a decrease of the Sauter mean particle diameter and with the increase of the fluidizing number as a result of good mixing dynamics in emulsion phase (i.e. emulsion wall contact time, bubble fraction in the bed). Based on the heat transfer data, empirical correlations are proposed for predicting a heat transfer coefficient from fluidized bed to horizontal tube bundle. The mechanistic heat transfer model predicted the average HTC in sufficiently good agreement with CFB boiler data accessible in the literature.

Heat transfer characteristics in a large-scale bubbling fluidized bed with immersed horizontal tube bundles

This work investigates heat transfer characteristics in a bubbling fluidized bed with a submerged superheater tube bundles under conditions of an integrated fluidized bed heat exchanger (Integrated Recycle Heat Exchanger, Intrextm) of a large-scale circulating fluidized bed boiler. The effect of mean bed particle size, normalized suspension density, and fluidizing number on the average heat transfer coefficient between the immersed horizontal tubes and the bed was evaluated. The physical parameters of bed particles and fluidizing air in the external heat exchanger were measured at different CFB unit loads. Bubble fraction and contacting time of emulsion phase on the heat transfer surface were calculated on the basis of operating data of fluidized bed heat exchanger. A mechanistic heat transfer model was used to predict the heat transfer coefficient. Depending on emulsion density and the local dynamics of gas and bed particles, the average heat transfer coefficient (havg) varied in a range of 255–381 W/(m2K), showing an increasing trend with the decrease in bed particle size. Moreover, havg decreased with increasing emulsion contact time on the tube surface with the reduction of the solids mixing. Obtained results were compared with literature data.

A pressure drop model for condensation accounting for non-equilibrium effects

A mechanistic pressure drop model is proposed in this paper for condensation in horizontal smooth round tubes in order to account for the non-equilibrium effects. The model makes use of a flow regime map and void fraction correlation as well as a mechanistic heat transfer model that are all developed for condensation of superheated vapor in a vapor-compression system. The model provide seamless transition between single-phase and two-phase regions including the superheated, condensing-superheated, two-phase, condensing-subcooled and subcooled regions. Diabatic flow visualizations are used to analyze the effects on pressure drop from the formation of waves. An enhancement factor to represent the frequency and magnitude of the waves is established using Kelvin-Helmholtz and Rayleigh-Taylor instability. The two-phase pressure drop is modeled based on the single-phase pressure drop correlations, the flow regimes, void fractions as well as the enhancement factor. Data obtained from R134a, R32, R1234ze(E), R1233zd(E) and R245fa with mass fluxes from 100 kg m−2s−1 to 400 kg m−2s−1and heat fluxes from 5 kW m−2 to 15 kW m−2 inside two different tubes of 4 and 6 mm are used to validate the model.

A mechanistic model of heat transfer for gas\u2013liquid flow in vertical wellbore annuli

The most prominent aspect of multiphase flow is the variation in the physical distribution of the phases in the flow conduit known as the flow pattern. Several different flow patterns can exist under different flow conditions which have significant effects on liquid holdup, pressure gradient and heat transfer. Gas–liquid two-phase flow in an annulus can be found in a variety of practical situations. In high rate oil and gas production, it may be beneficial to flow fluids vertically through the annulus configuration between well tubing and casing. The flow patterns in annuli are different from pipe flow. There are both casing and tubing liquid films in slug flow and annular flow in the annulus. Multiphase heat transfer depends on the hydrodynamic behavior of the flow. There are very limited research results that can be found in the open literature for multiphase heat transfer in wellbore annuli. A mechanistic model of multiphase heat transfer is developed for different flow patterns of upward gas–liquid flow in vertical annuli. The required local flow parameters are predicted by use of the hydraulic model of steady-state multiphase flow in wellbore annuli recently developed by Yin et al. The modified heat-transfer model for single gas or liquid flow is verified by comparison with Manabe’s experimental results. For different flow patterns, it is compared with modified unified Zhang et al. model based on representative diameters.

Effect of bed particle size on heat transfer between fluidized bed of group b particles and vertical rifled tubes

The effect of bed particle size on the local heat transfer coefficient between a fluidized bed and vertical rifled tubes (38mm-O.D.) has been determined in a large-scale circulating fluidized bed (CFB) reactor. Bed particles with different Sauter mean particle diameter within the range of 0.219–0.411mm and particle density in the range of 2650–2750kg/m3 were used as bed material in this heat transfer study. A gas fluidized bed furnace with 27.6×10.6m cross-section above refractory line and 48m in height was used. Air coal firing conditions at the membrane wall in the form of water tubes welded with lateral fins corresponded to a suspension density covering the range of 1.36–6.22kg/m3, furnace temperatures in the range of 1080–1164K, a superficial gas velocity varied from 2.99 to 5.11m/s and solids circulation flux covered a range of 23.3–26.2kg/(m2s). For these operating conditions, the heat transfer analysis of CFB reactor with detailed analysis of bed-to-wall heat transfer coefficient along furnace height was investigated. In this work, the overall heat transfer coefficient was estimated using a mechanistic heat transfer model based on cluster renewal approach. The experimental results show that: (i) higher heat transfer coefficients along furnace height were found under finer bed particles size dp<0.241mm, (ii) heat transfer data confirms strong dependency of the overall heat transfer coefficient on suspension density and also hydrodynamic conditions within CFB furnace, (iii) for small bed particles, dp<0.233mm, the particle convection component plays dominant role in heat transfer mechanism, (iv) for large bed particles, dp>0.366mm, the effect of particle size on relative contribution of radiation from dispersed phase become essential with particle diameter increasing, and (v) for all bed particles with diameters in the range of 0.240–0.411mm, the gas convection heat transfer coefficient between the fluidized bed (Geldart B particles) and the rifled tubes increased as the bed particles size increased.