Field synergy equation for turbulent heat transfer and its application

A field synergy equation with a set of specified constraints for turbulent heat transfer developed based on the extremum entransy dissipation principle can be used to increase the field synergy between the time-averaged velocity and time-averaged temperature gradient fields over the entire fluid flow domain to optimize the heat transfer in turbulent flow. The solution of the field synergy equation gives the optimal flow field having the best field synergy for a given decrement of the mean kinetic energy, which maximizes the heat transfer. As an example, the field synergy analysis for turbulent heat transfer between parallel plates is presented. The analysis shows that a velocity field with small eddies near the boundary effectively enhances the heat transfer in turbulent flow especially when the eddy height which are perpendicular to the primary flow direction, are about half of the turbulent flow transition layer thickness. With the guide of this optimal velocity field, appropriate internal fins can be attached to the parallel plates to produce a velocity field close to the optimal one, so as to increase the field synergy and optimize the turbulent heat transfer.     

Two energy conservation principles in convective heat transfer optimization

Improving heat transfer performance is very beneficial to energy conservation because heat transfer processes widely existed in energy utilization systems. In this contribution, in order to effectively optimize convective heat transfer, such two principles as the field synergy principle and the entransy dissipation extremum principle are investigated to reveal the physical nature of the entransy dissipation and its intrinsic relationship with the field synergy degree. We first established the variational relations of the entransy dissipation and the field synergy degree with the heat transfer performance, and then derived the optimization equation of the field synergy principle and made comparison with that of the entransy dissipation extremum principle. Finally the theoretical analysis is then validated by the optimization results in both a fin-and-flat tube heat exchanger and a foursquare cavity. The results show that, for prescribed temperature boundary conditions, the above two optimization principles both aim at maximizing the total heat flow rate and their optimization equations can effectively obtain the best flow pattern. However, for given heat flux boundary conditions, only the optimization equation based on the entransy dissipation extremum principle intends to minimize the heat transfer temperature difference and could get the optimal velocity and temperature fields.     

Field synergy optimization and enhanced heat transfer by multi-longitudinal vortexes flow in tube

The field synergy equation for steady laminar convection heat transfer was derived by conditional variation calculus based on the least dissipation of heat transport potential capacity. The optimum velocity field with the best heat transfer performance and least flow resistance increase can be obtained by solving the synergy equation. The numerical simulation of laminar convection heat transfer in a straight circular tube shows that the multi-longitudinal vortex flow in the tube is the flow pattern that enhances the heat transfer enormously. Based on this result, a novel enhanced heat transfer tube, the discrete double-inclined ribs tube (DDIR-tube), is developed. The flow field of the DDIR-tube is similar to the optimal velocity field. The experimental results show that the DDIR-tube has better comprehensive heat transfer performance than the current heat transfer enhancement tubes. The present work indicates that new heat transfer enhancement techniques could be developed according to the optimum velocity field.     

Experimental study of laminar forced convective mass transfer and pressure drop in microtubes

The investigation of laminar convective mass transfer and friction factor was performed experimentally for the circular tubes with the diameter of 0.20 mm and the L/d values in the range of 100–500 for a Reynolds number range of 40–1400. The pressure drop experiments were conducted with distilled water, and the mass transfer experiments were carried out with an electrochemical solution by using the electrochemical limiting diffusion current technique. The friction factor results showed good agreement with the classical Poiseuille flow theory, while Sherwood numbers are smaller than those obtained by conventional correlations.     

Discussion on the convective heat transfer and field synergy principle

The convective “heat” transfer is actually mainly carried out by the motion of hotter or colder particles from one system into another system. Therefore, the best convective “heat” (strictly speaking, internal energy) transfer is the case where velocity vectors are always perpendicular to the isothermal surfaces (or isotherm in 2D cases). This conclusion has been named “field synergy principle”. In this paper, some field synergy exact solutions are presented to further develop the principle. The concrete physical meanings of the derived analytical solutions are analyzed. The method of separating variables with addition and other extraordinary approaches are adopted in the derivation.     

The application of field synergy number in shell-and-tube heat exchanger optimization design

In the present work the field synergy principle is applied to the optimization design of the shell-and-tube heat exchanger with segmental baffles. The field synergy number which is defined as the indicator of the synergy between the velocity field and the heat flow is taken as the objective function. The genetic algorithm is employed to solve the heat exchanger optimization problems with multiple design variables. The field synergy number maximization approach for heat exchanger optimization design is thus formulated. In comparison with the initial design, the optimal design leads to a significant cost cut on the one hand and an improvement of the heat exchanger performance on the other hand. The comparison with the traditional heat exchanger optimization design approach with the total cost as the objective function shows that the field synergy number maximization approach is more advantageous.     

CFD study on local fluid-to-wall heat transfer in packed beds and field synergy analysis

To reach the target of smaller pressure drop and better heat transfer performance, packed beds with small tube-to-particle diameter ratio (D/d _p<10) have now been considered in many areas. Fluid-to-wall heat transfer coefficient is an important factor determining the performance of this type of beds. In this work, local fluid- to-wall heat transfer characteristic in packed beds was studied by Computational Fluid Dynamics (CFD) at different Reynolds number for D/d _p=1.5, 3.0 and 5.6. The results show that the fluid-to-wall heat transfer coefficient is oscillating along the bed with small tube-to-particle diameter ratio. Moreover, this phenomenon was explained by field synergy principle in detail. Two arrangement structures of particles in packed beds were recommended based on the synergy characteristic between flow and temperature fields. This study provides a new local understanding of fluid-to-wall heat transfer in packed beds with small tube-to-particle diameter ratio.     

Hall effects on the hydromagnetic free convective flow and mass transfer through a porous medium bounded by an infinite vertical porous plate with constant heat flux

Effects of Hall current on free convection and mass transfer flow through a porous medium bounded by a vertical surface when a uniform magnetic field acts in a plane which makes an angle x with the plane transverse to the plate have been analysed. An analytic solution of the problem is obtained and the effects of the Hall parameter and the permeability parameter, as well as the other parameters entering into the problem, are discussed and shown graphically.     

Numerical study of fluid flow and heat transfer in a flat-plate channel with longitudinal vortex generators by applying field synergy principle analysis

Three dimensional numerical simulations are performed on laminar heat transfer and fluid flow characteristics of a flat-plate channel with longitudinal vortex generators (LVGs). The effects of two different shaped LVGs, rectangular winglet pair (RWP) and delta winglet pair (DWP) with two different configurations, common-flow-down (CFD) and common-flow-up (CFU), are studied. The numerical results indicate that the application of LVGs effectively enhances heat transfer of the channel. According to the performance evaluation parameter, (Nu/Nu₀)/(f/f₀), the channel with DWP has better overall performance than RWP; the CFD and CFU configurations of DWP have almost the same overall performance; the CFD configuration has a better overall performance than the CFU configuration for RWP. The basic mechanism of heat transfer enhancement by LVGs can be well described by the field synergy principle.     

A numerical study of laminar convective heat transfer in microchannel with non-circular cross-section

Three-dimensional numerical simulations of the laminar flow and heat transfer of water in silicon microchannels with non-circular cross-sections (trapezoidal and triangular) were performed. The finite volume method was used to discretize the governing equations. Numerical results were compared with experimental data available in the literature, and good agreements were achieved. The effects of the geometric parameters of the microchannels were investigated, and the variations of Nusselt number with Reynolds number were discussed from the field synergy principle. The simulation results indicate that when the Reynolds numbers are less than 100, the synergy between velocity and temperature gradient is much better than the case with Reynolds number larger than 100. There is an abrupt change in the intersection angle between velocity and temperature gradient around Re=100. In the low Reynolds number region the Nusselt number is almost proportional to the Reynolds number, while in the high Reynolds number region, the increasing trend of Nusselt number with Reynolds number is much more mildly, which showed the applicability of the field synergy principle. In addition, for the cases studied the fully developed Nusselt number for the microchannels simulated increases with the increasing Reynolds number, rather than a constant.     

Theoretical and numerical analysis of convective heat transfer in the rotating helical pipes

In terms of the tensor analysis technique, the relative N-S equations and the energy equation in a rotating helical coordinate system are presented in this paper. Convective heat transfer in the rotating helical pipes with circular cross-section is investigated employing theoretical and numerical method. A perturbation solution up to the secondary order is obtained for a small Dean number. Variations of the temperature distribution with the force ratio (the ratio of the Coriolis force to the centrifugal force), the curvature and the torsion are discussed in detail. Present studies also show the natures of the Nusselt number, as well as the effects of the force ratio, the curvature, and the torsion. This study explores many new characteristics of convective heat transfer in the rotating helical pipes and covers wide ranges of parameters.     

Study on the convective heat transfer and pressure drop in the micro-channel heat sink

Experiments have been performed to investigate the heat transfer characteristics and pressure drop in the micro-channel heat sinks under constant heat flux conditions. The experiments are performed for the Reynolds number and heat flux in the ranges of 200–1000 and 1.80–5.40 kW/m², respectively. The micro-channel heat sink with two different channel heights and two different channel widths are accomplished by wire electrical discharge machine. Effects of different geometrical configurations parameters of the micro-channel and heat flux on the heat transfer characteristics and pressure drop are considered. The micro-channel geometry configuration has significant effect on the enhancement heat transfer and pressure drop. The results of this study are expected to lead to guidelines that will allow the design of the micro-channel heat exchangers with improved heat transfer performance of the electronic devices.     

水平管降膜蒸发中强迫对流传质过程实验研究

对水平横管束降膜吸收器中,溴化锂溶液表面自然对流和强迫对流传质现象,分别在常压和负压下进行了实验研究。以惠特曼提出的双膜模型为基础,对实验结果做出了分析;以图线的方式,直观的比较了传质系数与压力,溶液表面对流情况的关系。得出了强迫对流对传质系数有很大提升的结论。     

An experimental investigation of convective mass transfer characterization in two configurations of electrolysers

This work is devoted to the study of hydrodynamics behavior and mass transfer performance in water electrolysis processes, two configurations of containers and electrodes are studied in laboratory experiments under different current densities, the platinum (0.2 mm in diameter) in an acidic environment (36% CH₃COOH) as electrode material, surrounds the sides of the container in horizontal mode. The system is studied using particle image velocimetry (PIV), microscope enhanced visualization. The experimental results show that the velocity distribution in most regions of electrolyser is dominated by two asymmetry bubble buoyancy induced flow patterns. The greater reaction rate of water electrolysis and better mass transfer arise in the smaller space of electrodes. By comparing hydrodynamic behavior in two containers with different current densities, hydrogen production, bubble-driven convection and convective mass transfer increase at higher current densities, however, this increase is not linear, the interaction mechanisms are analyzed on mass transfer, electrochemical reaction and bubble effect. Results facilitate the understanding and the design of the transport phenomena in electrolyser.     

Analysis of the heat and mass transfer processes in solar stills - The validation of a model

The outcome of the earlier systematic research work on the theoretical modeling of the complex transport phenomena occurring in solar stills was the development of the fundamental Dunkle’s model, already known almost four decades ago. Although it has been based on several simplified assumptions, this model has extensively been employed over the years as a convenient and sufficiently accurate predictive tool for solar stills working under ordinary operating conditions. However, it has occasionally been reported that it fails under unusual operating conditions, mainly corresponding to higher average temperatures, usually leading to higher distillate yields. The aim of the present investigation was to relax the initially established simplified assumptions of the fundamental Dunkle’s model and to evaluate the comparative accuracy of both, the refined and the earlier fundamental models against an extensive body of previously reported measurements from the literature, both field and laboratory. The comparative presentation of results indicates that although both models are impressively correct for ordinary low temperature operating conditions where the humid air thermophysical properties are close to those of dry air, the saturation vapor pressure at the brine and condensing plate temperatures are negligible compared to barometric pressure and the familiar Jakob’s dimensionless Nusselt-Rayleigh correlation for natural convection heat transfer appears to be valid, they both fail at higher operational temperatures. It appears that as far as Dunkle’s simplified model is concerned, this occurs not only owing to the first two counteracting effects but also to the effect of the dimensionless convective heat transfer correlation affecting also the accuracy of the refined model, which fails to predict precisely the natural convection conditions at higher Rayleigh numbers representing conditions of strong turbulence in the solar still cavity. Assuming a constant asymptotic value of the exponent n = 1/3 which persists over a broad region of high Rayleigh numbers relevant to solar still operation, an improved value of the proportionality constant C around the value of 0.05 was estimated for the accurate prediction of measurements, at least as far as the available data from the literature is concerned.     

Electrochemical experimental method for natural convective heat and mass transfer in porous media

Natural convection driven by combined thermal and solutal buoyant forces in a fluid-saturated porous enclosure was studied experimentally. An electrochemical method was employed to establish the concentration gradients. The inside temperature profiles and heat and mass transfer coefficients on the vertical walls were determined experimentally. The effects of dimensionless parameter Ra, Le, N on flow, heat, and mass transfer are discussed in detail. © 1999 Scripta Technica, Heat Trans Asian Res, 28(4): 266–277, 1999     

Numerical investigation and analysis of heat transfer enhancement in channel by longitudinal vortex based on field synergy principle

3-D numerical simulations were presented for laminar flow and heat transfer characteristics in a rectangular channel with vortex generators. The effects of Reynolds number (from 800 to 3 000), the attack angle of vortex generator (from 15° to 90°) and the shape of vortex generator were examined. The numerical results were analyzed based on the field synergy principle. It is found that the inherent mechanism of the heat transfer enhancement by longitudinal vortex can be explained by the field synergy principle, that is, the second flow generated by vortex generators results in the reduction of the intersection angle between the velocity and fluid temperature gradient. The longitudinal vortex improves the field synergy of the large downstream region of longitudinal vortex generator (LVG) and the region near (LVG); however, transverse vortex only improves the synergy of the region near vortex generator. Thus, longitudinal vortex can enhance the integral heat transfer of the flow field, while transverse vortex can only enhance the local heat transfer. The synergy angle decreases with the increase of Reynolds number for the channel with LVG to differ from the result obtained from the plain channel, and the triangle winglet performs better than the rectanglar one under the same surface area condition. __________ Translated from Journal of Xi’an Jiaotong University, 2006, 40(9): 996–1000 [译自: 西安交通大学学报]     

Pressure drop and point mass transfer in a rectangular microchannel

This paper describes the pressure drop and local mass transfer in a rectangular microchannel having a width of 3.70 mm, height of 0.107 mm and length of 35 mm. The pressure measurements were carried out with distilled water as working fluid at Reynolds numbers in the range of 100–845, while mass transfer measurements with a chemical solution at Reynolds numbers in the range of 18–552 by using the electrochemical limiting diffusion current technique (ELDCT). Experimental friction factors were slightly higher than those calculated by theoretical correlation. The Sherwood number correlation was also obtained.     

Numerical and experimental analysis of moisture transfer for convective drying of some products

Numerical and experimental results of moisture transfer in drying process for apple and potato slices are compared in this study. Experimental results are obtained using a cyclone type dryer. Two-dimensional analysis of heat and moisture transfer during drying of objects is carried out solving heat and mass equations using finite-volume approach. Thus, moisture distributions inside the moist objects are obtained at different time steps. Comparison of results showed that there is a considerably high agreement between experimentally measured data and predicted values. Moist distribution also presented inside the products at different time periods.     

Laminar fluid flow and mass transfer in a standard field and laboratory emission cell

The field and laboratory emission cell (FLEC) is becoming a standard method of characterizing pollutant emissions from building materials. Based on this method, the material and the inner surface of the FLEC cap form a cone-shaped cavity. The airflow is distributed radially inward over the test surface through a slit in a circular-shaped channel at the perimeter of the chamber. After mass transfer, the air is exhausted through an outlet in the center. Usually, emission rate profiles are obtained using such cells. However, the local convective mass transfer coefficients are now needed. In this study, laminar fluid flow and mass transfer in a standard FLEC are investigated. The velocity field and moisture profiles are obtained by solving Navier-Stokes equations numerically. The whole geometry, including the air inlet and outlet, channel, air slit, and emission space, are included in the numerical modeling domain. The mean convective mass transfer coefficients are calculated and compared with the experimental data. In the test, distilled water is used in the FLEC lower chamber to substitute the emission surface. Mass transfer data are obtained by calculating humidity differences between the inlet and outlet of a gas stream flowing through the FLEC. The study concentrates on assessing the variations of velocity and humidity profiles, as well as convective mass transfer coefficients, in the cell.