Physical quantity synergy in laminar flow field and its application in heat transfer enhancement

On the basis of field synergy principle for heat transfer enhancement, physical quantity synergy in laminar flow field of convective heat transfer is analyzed according to physical nature of convective heat transfer between fluid and solid wall. Synergy regulation among physical quantities is revealed by mathematical expressions reflecting mechanism of heat transfer enhancement. Characteristic of heat transfer enhancement, which is directly associated with synergy angles α, β and γ, is also analyzed. Numerical simulation is made to verify the principle of physical quantity synergy developed in the paper.     

Heat transfer analysis of peristaltic flow in a curved channel

We investigate the effects of heat transfer on peristaltic flow of a viscous fluid in a curved channel. Governing equations for flow and heat transfer are derived using long wavelength and small Reynolds number assumptions. Exact solution is obtained for stream function. The temperature field is obtained numerically by a shooting method using Runge–Kutta algorithm. Effects of curvature parameter and Brinkman number are analyzed on various features of peristaltic motion and temperature field. It is found that peristaltic pumping rate increases in going from straight to curved channel. It is further noted that the symmetry of trapped bolus is destroyed in the curved channel and upper bolus pushes the lower bolus toward the lower wall. Moreover, the rate of heat transfer decreases in a curved channel in comparison with the case of straight channel.     

Field synergy analysis and optimization of decontamination ventilation designs

The field synergy principle has been validated to be an effective tool for enhancing convective heat transfer capability. Since convective mass transfer is analogous to convective heat transfer, the field synergy principle has been extended to convective mass transfer analyses to enhance the overall decontamination rate of indoor ventilation systems. According to the field synergy principle, the overall decontamination capability and the utilization efficiency of the air are both influenced by the synergy between the velocity vectors and the contaminant concentration gradients. Furthermore, in order to derive a method to improve the synergy based on the essence of convective mass transfer, the mass transfer potential capacity dissipation function is defined, and then the convective mass transfer field synergy equation is obtained by seeking the extremum of the mass transfer potential capacity dissipation function for a set of specified constraints. The convective mass transfer field synergy equation can be solved to find the optimized air velocity distribution to increase the field synergy and the overall decontamination capability. The optimized air velocity field provides guidance for optimizing ventilation system designs.     

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.     

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 principle analysis on fully developed forced convection in porous medium with uniform heat generation

In the presence of uniform heat source, the energy equation for forced convective heat transfer in porous medium between two parallel plates is solved for fully developed flow. Field synergy analysis is performed with emphasis on the intersection angle between the velocity vector and temperature gradient vector with the inclusion of heat generation. Maximum local intersection angle corresponds to location with the highest resistance to heat convection. Relationship between Nusselt number and field synergy for forced convection in the presence of heat generation is studied. It is necessary to define a modified intersection angle in order to compare the wall heat transfer coefficient for convective heat transfer processes with uniform heat source.     

Numerical study on laminar convection heat transfer in a rectangular channel with longitudinal vortex generator. Part A: Verification of field synergy principle

This study presents numerical computation results on laminar convection heat transfer in a rectangular channel with a pair of rectangular winglets longitudinal vortex generator punched out from the lower wall of the channel. The effect of the punched holes and the thickness of the rectangular winglet pair to the fluid flow and heat transfer are numerically studied. It is found that the case with punched holes has more heat transfer enhancement in the region near to the vortex generator and lower average flow frictional coefficient compared with the case without punched holes. The thickness of rectangular winglet can cause less heat transfer enhancement in the region near to the vortex generator and almost has no significant effect on the total pressure drop of the channel. The effects of Reynolds number (from 800 to 3000), the attack angle of vortex generator (15°, 30°, 45°, 60° and 90°) were examined. The numerical results were analyzed from the viewpoint of field synergy principle. It was found that the essence of heat transfer enhancement by longitudinal vortex can be explained very well by the field synergy principle, i.e., when the second flow generated by vortex generators results in the reduction of the intersection angle between the velocity and fluid temperature gradient, the heat transfer in the present channels will be enhanced. Longitudinal vortices (LVs) improve the synergy between velocity and temperature field not only in the region near LVG but also in the large downstream region of longitudinal vortex generator. So LVs enable to enhance the global heat transfer of channel. Transverse vortices (TVs) only improve the synergy in the region near VG. So TVs can only enhance the local heat transfer of channel.     

泡沫铝通道内瞬态流动的平均换热系数

针对泡沫铝金属填充矩形通道内的对流换热开展了瞬态实验研究,分析了泡沫铝孔径(孔隙率)、流体流量(流速)等关键参数的影响。为了有效地处理实验数据,重新定义并推导了平均换热系数的计算公式,得到了泡沫铝通道内流动的平均换热系数,并引入了基于渗透率的雷诺数和达西数,确定了相关换热、流动准则数关系。实验研究表明,流速的增大有利于对流换热的强化:而平均换热系数对泡沫金属孔径较敏感;对于低孔隙率泡沫金属,渗透率成为影响换热强度的主要因素,相同或接近的孔隙率下,孔径越大,渗透率和达西数越大,越有利于换热,且压损减小。     

NUMERICAL DESIGN OF EFFICIENT SLOTTED FIN SURFACE BASED ON THE FIELD SYNERGY PRINCIPLE

In this article, a numerical investigation of the flow and heat transfer in a three-row finned-tube heat exchanger is conducted with a three-dimensional laminar conjugated model. Four types of fin surfaces are studied; one is the whole plain plate fin, and the other three are of slotted type, called slit 1, slit 2, and slit 3. All four fin surfaces have the same global geometry dimensions. The three slotted fin surfaces have the same numbers of strips, which protrude upward and downward alternatively and are positioned along the flow direction according to the rule of “front coarse and rear dense.” The difference in the three slotted fins is in the degree of “coarse” and “dense” along the flow direction. Numerical results show that, compared to the plain plate fin, the three types of slotted fin all have very good heat transfer performance in that the percentage increase in heat transfer is higher than that in the friction factor. Among the three slotted fin surfaces, slit 1 behaves the best, followed by slit 2 and slit 3 in order. Within the Reynolds number range compared ( from 2,100 to 13,500), the Nusselt number of slit 1 is about 112–48% higher than that of the plain plate fin surface under the identical pumping constraint. An analysis of the essence of heat transfer enhancement is conducted from the field synergy principle, which says that the reduction of the intersection angle between the velocity and the temperature gradient is the basic mechanism for enhancing convective heat transfer. It is found that for the three comparison constraints the domain-average synergy angle of slit 1 is always the smallest, while that of the plain plate fin is the largest, with slit 2 and slit 3 being somewhat in between. The results of the present study once again show the feasibility of the field synergy principle and are helpful to the development of new types of enhanced heat transfer surfaces.     

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]     

关于管内单相对流换热强化的极限问题

从场协同理论出发,分析了通道内表面全部为射流冲击换热表面时的极限换热率;将全射流冲击管内换热与普通流动管内换热进行了比较。给出了层流和紊流工况下全射流冲击换热可能达到的最大强化比。针对相同R e,分析得出:在层流充分发展段,全射流冲击通道的强化极限是16.9倍;在紊流充分发展段是3.5倍。综合现有各种通道内强化换热的研究结果进行比较,其换热率均低于全射流冲击管内换热率,其中层流工况以折流翅片式通道和交叉缩放椭圆管的换热率与极限换热率最为接近;紊流工况以内插螺旋丝强化管最为接近。     

An analytical solution for thermally fully developed combined pressure – electroosmotically driven flow in microchannels

An analytical solution is presented to study the heat transfer characteristics of the combined pressure – electroosmotically driven flow in planar microchannels. The physical model includes the Joule heating effect to predict the convective heat transfer coefficient in two dimensional microchannels. The velocity field, which is a function of external electrical field, electroosmotic mobility, fluid viscosity and the pressure gradient, is obtained by solving the hydrodynamically fully-developed laminar Navier–Stokes equations considering the electrokinetic body force for low wall zeta potentials. Then, assuming a thermally fully-developed flow, the temperature distribution and the Nusselt number is obtained for a constant wall heat flux boundary condition. The fully-developed temperature profile and the Nusselt number depend on velocity field, channel height, solid/liquid interface properties and the imposed wall heat flux. A parametric study is presented to evaluate the significance of various parameters and in each case, the maximum heat transfer rate is obtained.     

Three-dimensional numerical study of wavy fin-and-tube heat exchangers and field synergy principle analysis

In this paper, 3-D numerical simulations were performed for laminar heat transfer and fluid flow characteristics of wavy fin-and-tube heat exchanger by body-fitted coordinates system. The effect of four factors were examined: Reynolds number, fin pitch, wavy angle and tube row number. The Reynolds number based on the tube diameter varied from 500 to 5000, the fin pitch from 0.4 to 5.2 mm, the wavy angle from 0° to 50°, and the tube row range from 1 to 4. The numerical results were compared with experiments and good agreement was obtained. The numerical results show that with the increasing of wavy angles, decreasing of the fin pitch and tube row number, the heat transfer of the finned tube bank are enhanced with some penalty in pressure drop. The effects of the four factors were also analyzed from the view point of field synergy principle which says that the reduction of the intersection angle between velocity and fluid temperature gradient is the basic mechanism for enhance convective heat transfer. It is found that the effects of the four factors on the heat transfer performance of the wavy fin-and-tube exchangers can be well described by the field synergy principle.     

Convective heat transfer of gaseous solid suspension flow in a curved tube

Experimental study was performed on the convective heat transfer of gaseous solid suspension flow within helically coiled circular tube. The results show that the increase in heat transfer is greater than that due to the simple contribution of the increased heat capacity as the flowing media. This suggests that the addition of the suspended phase into the flows with curved stream lines can bring about the substantial reduction in the convective heat transfer resistance in the vicinity of the channel walls of the outer curvature portion. However, slight decrease in mixture Stanton number is also observed at the slight loading ratio region and the sublayer disturbing effect is seen to be gradually saturated at the higher loading region. Accordingly, overall reduction in the turbulence level also exists in the turbulent core of the flow and it is expected that there is an optimum solid loading ratio at which the viscous sublayer disturbing effect on the overall heat transfer performance is most effective.     

Unified field synergy and heatline visualization of forced convection with thermal asymmetries

Forced convection between two parallel plates imposed with thermal asymmetric boundary condition is analyzed by employing a unified field synergy and heatline visualization technique. The heatline visualization is incorporated in the field synergy analysis through the introduction of an included angle between the heatline and the streamline, which is comparable to the well-established synergy angle of the field synergy principle. Inherently, both angles present the common intrinsic characteristics with each other. The heatline plot provides a more explicit visualization of heat flow in convection heat transfer compared to the isotherm plot, which is widely used in the existing field synergy study. Similar to the synergy angle, it is observed that the decrease of the included angle between the heatline and the streamline enhances the synergy between the heat and fluid flow, resulting in higher Nusselt number and field coordination number. The variations of the heat flux ratio induce changes on the field synergy of the flow due to the effects of thermal asymmetries, which concurrently alter the heatline patterns.     

Analysis of the heat transfer in the entrance region of optimised corrugated wall channel

In this work the analysis of the heat transfer in the entrance region of a channel composed by a corrugated profile and a flat wall is presented. The laminar and incompressible flow of a Newtonian fluid is assumed inside the channel, and an uniform heat flux is imposed on the external surface of the corrugated wall. The governing equations are solved with the help of a finite-element method, and the results are compared with the heat transfer coefficient in the entrance region of a flat channel. In order to investigate the sensitivity of the convective heat transfer coefficient to the Reynolds number under laminar conditions, the analysis have been performed for different values of the flow rate. The effect on the flowfield of the of the corrugated profile amplitude is also discussed.     

A unified analysis on enhancing single phase convective heat transfer with field synergy principle

Numerical simulations were conducted to reveal the inherent relation between the filed synergy principle and the three existing mechanisms for enhancing single phase convective heat transfer. It is found that the three mechanisms, i.e., the decreasing of thermal boundary layer, the increasing of flow interruption and the increasing of velocity gradient near a solid wall, all lead to the reduction of intersection angle between velocity and temperature gradient. It is also revealed that at low flow speed, the fin attached a tube not only increases heat transfer surface but also greatly improves the synergy between the velocity and the temperature gradient.     

Differentially heated cubical cavity using energy pathlines and field synergy

The article deals with the natural convective flow of air in a cubical cavity which is analyzed numerically. Isothermal temperature is maintained on the vertical walls where the temperature of the left wall is more than the right wall and all other walls are assumed to be kept insulated. In this present article, upwind, QUICK, SUPERBEE, and self‐filtered central differencing schemes are compared based on their accuracy and computational time with a numerical example. An attempt has been made to analyze the flow behavior inside the cavity using vortex corelines, streamlines, isotherms energy pathlines, and field synergy by varying the Rayleigh number (Ra) from 10³ to 10⁶. In the vicinity of isothermal vertical walls, the velocity, and temperature boundary layers become thinner as Ra increases. The energy pathlines are in oscillating nature when Ra increases to 10⁵ and above. The field synergy principle implies by improving the synergy between the velocity and temperature, the heat transfer gets enhanced with the less increased flow resistance.     

REDUCED PUMPING POWER AND WALL TEMPERATURE IN MICROCHANNEL HEAT SINKS WITH FRACTAL-LIKE BRANCHING CHANNEL NETWORKS

Comparisons are made of the maximum channel wall temperature along, and total pressure drop across, a heat sink with a fractal-like branching channel network with those in a heat sink having a straight channel array. The total channel lengths are identical between the heat sinks, as are the applied heat fluxes. The hydraulic diameter of the straight channel array is equal to that of the terminal branch of the branching channel network. The number of branches per level, number of branching levels, and channel dimensions in the fractal-like network remain fixed. Minor losses are neglected and both hydrodynamic and thermal boundary layers are assumed to reinitiate following each channel bifurcation in the branching flow network. With identical total convective surface areas for both configurations and maintaining a heat sink surface area equal to that of the convective surface area, the fractal-like channel network yielded a 60% lower pressure drop for the same total flow rate and a 30°C lower wall temperature under identical pumping power conditions. The two heat sinks were also compared under identical pressure drop conditions. Channel packing densities in which the convective surface area in the fractal-like channel network is 50% less than that in the straight channel array yield approximately the same pressure drop and maximum wall temperature for fixed-flow-rate conditions.     

Field synergy principle for enhancing convective heat transfer--its extension and numerical verifications

The concept of enhancing parabolic convective heat transfer by reducing the intersection angle between velocity and temperature gradient is reviewed and extended to elliptic fluid flow and heat transfer situation. Five examples of elliptic flow are provided to show the validity of the new concept (field synergy principle). Two further examples are supplemented to demonstrate the importance of the concept in the design of the enhanced surfaces.