Semi-empirical Heat Transfer Correlation Research Articles

Numerical Modelling of Rapid Decrease in Water Flow Rate in a Plate-and-Tube Heat Exchanger

In this article, a mathematical simulation of a plate-fin and tube heat exchanger (PFTHE) is presented. Water flows in the tubes and air flows perpendicular to the tube axis. The general numerical model was developed to perform the transient operation of the heat exchanger. The Reynolds number on the waterside ranged from 4,000 to 12,000. The transient response of the PFTHE was modeled for a rapid decrease in the water volume flow rate in time. The heat transfer correlation for the air side was established using the empirical data. Unknown parameters present in the power-type relationship for the airside Nusselt number were estimated using the least-squares method. The waterside heat transfer coefficients in the transitional and turbulent flow ranges were calculated using the semi-empirical heat transfer correlation. The results of the mathematical simulations of the investigated PFTHE were compared with the measurement data. The agreement between computation and measurement results, i.e., between the calculated and measured air and water temperatures at the outlets of the PFTHE, was very satisfactory.

Numerical investigation of supercritical methane in helically coiled tube on regenerative cooling of liquid rocket electromechanical actuator

A numerical model employing the SST k-ω turbulent model is built to predict the turbulent flow and heat transfer of supercritical methane in helically coiled tube for the heat dissipation of high-power electromechanical actuator. The heat transfer mechanism and the crucial influence factors viz. pressure and heat flux are discussed, and the comparison between the semi-empirical heat transfer correlations and the simulation results are performed. The calculation results indicate that: (1) before the pseudo-critical point of supercritical methane in helically tube, the effect of the buoyancy caused by the thermophysical properties cannot be neglected; (2) the domination of the centrifugal force on the heat transfer after the pseudo-critical point of supercritical methane can be confirmed obviously, contributed to the non-uniform distribution of flow and heat transfer coefficient in cross sections; (3) pressure and heat flux both exhibit significant effects on heat transfer of supercritical methane in helically coiled tube; (4) the semi-empirical heat transfer correlation from Zhang et al. shows the best agreement against the simulation result in the present paper.

Ice formation prediction and heat transfer analysis of LNG in serpentine tube under supercritical pressure

A numerical model employing the SST k-ω turbulent model and Shell Conduction model is established to predict the ice layer formation and thermal performance of serpentine tube in submerged combustion vaporizer (SCV) under supercritical pressure. The affecting factors on the heat transfer and ice layer formation such as pressure and heat flux are analyzed. A new semi-empirical heat transfer correlation is proposed taking account of the flow acceleration, thermophysical properties, buoyancy force and geometrical factor on the serpentine tube of supercritical LNG. The simulation results reveal that: (1) the interactive effect of centrifugal force, chaotic mixing fluid and buoyancy force are implied from the complicated flow structure and thermal performance of LNG in serpentine tube, and the centrifugal force dominates on heat transfer in the bend region resulting from the strengthening of cross flow and rotational flow; (2) the deviation of thermal performance between ice layer formation or not becomes slighter in the bend region than that in the straight sections due to the interaction of flow acceleration, reverse flow and secondary flow; (3) pressure and heat flux exhibit significant effects on thermal performance and ice layer formation; (4) the semi-empirical heat transfer correlation proposed in present paper can predict the heat transfer of LNG in serpentine tube under supercritical pressure accurately.

Experimental investigation on non-boiling heat transfer of two-component air-oil and air-water slug flow in horizontal pipes

Gas-liquid slug flow in horizontal pipes occurs frequently in industrial applications and its heat transfer characteristics are very important but complicated due to the intermittent flow structures. This paper aims at investigating the heat transfer mechanism of both air-oil and air-water slug flow in horizontal pipes. An experimental setup was fabricated to investigate the flow and heat transfer characteristics of air-oil and air-water slug flow under cooling conditions in horizontal pipes. The test section was made of a copper pipe with I.D. of 26 mm and a polyvinyl chloride pipe with I.D. of 63 mm using concentric geometry. The effect of flow parameters, such as liquid flow rate, gas flow rate, two-phase pressure drop multiplier, void fraction and slug frequency on heat transfer of gas-liquid slug flow was comprehensively investigated. The heat transfer coefficient of two-phase flow was significantly improved by the introduction of air and the maximum two-phase heat transfer enhancement ratio for air-water and air-oil flow were 150% and 300%, respectively. The circumferential temperature distribution and local heat transfer coefficient were also investigated. The local heat transfer coefficient at the bottom was around 25% higher than that at the top due to the uneven distribution of liquid and gas inside the pipe. Finally, a semi-empirical heat transfer correlation for gas-liquid slug flow was developed based on Reynolds and Chilton–Colburn analogies. The newly developed correlation predicts 96% of the present experimental two-phase heat transfer data within ±20% error and the mean relative deviations of the correlations are estimated to be -2.02% and +2.85% for Ref ≤ 2300 and Ref > 2300, respectively. This research helps researchers and engineers to better understand the heat transfer mechanism of gas-liquid slug flow.

Study on heat transfer performance of steam-cooled ribbed channel using neural networks and genetic algorithms

This work aims to optimize the steam-cooled ribbed channels to achieve the best heat transfer performance. The combined effects of channel aspect ratio (W/H = 0.25–4), rib angle (α = 30–90°) and Reynolds number (Re = 10,000–100,000) on the heat transfer characteristics of steam-cooled ribbed channels were analyzed. The semi-empirical heat transfer correlation related to W/H, α and Re was developed. The back propagation neural network (BPNN) combined with genetic algorithm (GA) was used to predict the heat transfer coefficients and optimize the structural parameters of steam-cooled ribbed channels based on 90 groups experimental data, and an excellent BPNN model with a maximum prediction error of 1.9% was obtained. Flow fields in the steam-cooled ribbed channels were numerically calculated to explore the heat transfer enhancement mechanism of optimized channels. The results show that the average heat transfer coefficients of steam-cooled ribbed channels increase at first and then decrease with the increase of W/H and α. The optimized neural network has better prediction accuracy than that of the fitted empirical correlation. Reynolds number has a great influence on the optimal aspect ratio and rib angle of the steam-cooled ribbed channel. The optimal W/H and the optimal α increase from 2.23 to 3.35 and 41.12° to 60.89°, respectively, with the increase of Re. Large α within the range of 41.12–60.89° should be selected for cooling channels with relatively larger W/H in the range of 0.25–4. The enhancement of longitudinal secondary flows and the suppression of main secondary flows result in the heat transfer enhancement of the optimized channels.

The buoyancy force and flow acceleration effects of supercritical CO2 on the turbulent heat transfer characteristics in heated vertical helically coiled tube

Numerical simulations are performed to investigate the turbulent heat transfer characteristics of supercritical CO2 in heated vertical helically coiled tube, and primary focus is to analyze the mechanism of buoyancy force and flow acceleration on the heat transfer. The results show similar effect from buoyancy force and centrifugal force, and both forces induce a secondary flow in the cross section that improves the heat transfer efficiency. The buoyancy parameter ϕ2 and flow acceleration parameter q+ are established with reasonably good validation against numerical results. On the basis of the two parameters, the buoyancy factor Fb and the acceleration factor FAc are proposed to quantify buoyancy and flow acceleration effect, respectively. Furthermore, a temperature difference correction factor Ft is introduced to consider variation of thermo-physical properties. A new semi-empirical heat transfer correlation is proposed for supercritical CO2 in function of Fb, FAc and Ft for the vertical helically coiled tube.

Semi-empirical heat transfer correlations for turbulent tube flow of liquid metals

PurposeThe purpose of this paper is to develop new semi-empirical heat transfer correlations for turbulent flow of liquid metals in the tubes, and then to compare these correlations with the experimental data. The Prandtl and Reynolds numbers can vary in the ranges: 0.0001 ≤ Pr ≤ 0.1 and 3000 ≤ Re ≤ 106.Design/methodology/approachThe energy conservation equation averaged by Reynolds was integrated using the universal velocity profile determined experimentally by Reichardt for the turbulent tube flow and four different models for the turbulent Prandtl number. Turbulent heat transfer in the circular tube was analyzed for a constant heat flux at the inner surface. Some constants in different models for the turbulent Prandtl number were adjusted to obtain good agreement between calculated and experimentally obtained Nusselt numbers. Subsequently, new correlations for the Nusselt number as a function of a Peclet number was proposed for different models of the turbulent Prandtl number.FindingsThe inclusion of turbulent Prandtl number greater than one and the experimentally determined velocity profile of the fluid in the tube while solving the energy conservation equation improved the compatibility of calculated Nusselt numbers, with Nusselt numbers determined experimentally. The correlations proposed in the paper have a sound theoretical basis and give Nusselt number values that are in good agreement with the experimental data.Research limitations/implicationsHeat transfer correlations proposed in this paper were derived assuming a constant heat flux at the inner surface of the tube. However, they can also be used for a constant wall temperature, as for the turbulent flow (Re > 3,000), the relative difference between the Nusselt number for uniform wall heat flux and uniform wall temperature is very low.Originality/valueUnified, systematic approach to derive correlations for the Nusselt number for liquid metals was proposed in the paper. The Nusselt number was obtained from the solution of the energy conservation equation using the universal velocity profile and eddy diffusivity determined experimentally, and various models for the turbulent Prandtl number. Four different relationships for the Nusselt number proposed in the paper were compared with the experimental data.

Heat transfer in the rectangular cross-flow flat-sheet membrane module for vacuum membrane distillation

This paper presents a study of heat transfer coefficients of boundary layers in a laboratory-scale rectangular cross-flow flat-sheet membrane module by using distilled water vacuum membrane distillation (VMD) experiments. Results show that the traditional heat transfer correlations, which are mostly employed in the membrane distillation literature, are not suitably used to predict the heat transfer process in the VMD system for the Reynolds numbers ranging from 300 to 1090. This study formulates a new semi-empirical heat transfer correlation by suggesting Knudsen-viscous mechanism governs the water vapour across the membrane. Compared to the feed flow rate, the feed temperature is the limit to the heat transfer. The heat transfer coefficients are strongly dependent on the physical properties of the feed solution, but less relied on the design of the membrane module.

Heat Transfer to Supercritical Water in a Horizontal Pipe: Modeling, New Empirical Correlation, and Comparison Against Experimental Data

Abstract Enhancement of heat transfer to supercritical fluids has drawn the attentions of many researchers within the past few decades. Modeling and predicting heat transfer to turbulent flow of supercritical fluids, however, are very complicated due to severe variations of fluid properties near the critical point. Large discrepancies between available heat transfer data are greatly due to confusion of forced convection and mixed convection data. The data unaffected by buoyancy have been selected cautiously from a large database generated in this study. Such data have been used to develop a 1D numerical model as well as a semi-empirical correlation to predict forced convection heat transfer to turbulent flow of supercritical water. In the numerical model, radial variations of heat flux and shear stress are taken into account. Modifications to turbulent Prandtl number and wall shear stress formulations have been applied to a law of the wall type of model to fit supercritical conditions. The model shows good agreement with experiments. In the experimental part, the extensive database obtained on a full-scale test facility in the present study, plus a new conceptual approach, has been employed together to develop a semi-empirical heat transfer correlation. It accurately predicts the experiments.

Modeling of Molten Metal/Water Interactions

A theoretical model has been developed for molten metal/water interactions by using a semiempirical heat transfer correlation and a mass transfer analogy to predict the metal ignition threshold tem...