A Review and Correlations for Convection Heat Transfer and Pressure Losses in Toroidal and Helically Coiled Tubes

The conducted review of the experiments for pressure losses and convection heat transfer in toroidal and coiled tubes yielded 2,410 pressure losses data for water, air, and ethylene glycol flows in 62 different coiled tubes. These data are used to develop a friction factor correlation, in terms of a modified Dean number. The compiled Nusselt number database of 176 data points for flows of water, air, and water–10% and 43.5% glycerol mixtures and additional 17 data points for flows of ethylene glycol, n-amyl alcohol, n-butanol, and n-amyl acetate, with higher Prandtl numbers of 15–175, is correlated in terms of the modified Reynolds number. The friction factor and Nusselt number correlations span the entire range of the data, and agree with the data to within ±20%. In addition, the experimental data of the critical Reynolds number are correlated to within ±10%. The developed correlations are compared to those reported previously. The comparison of the calculated results for a coiled tube and a straight tube, of the same diameter and total length, quantifies the relative heat transfer enhancement and increase in pressure losses. A review of the thermal development in toroidal and coiled tubes indicates that the value and the oscillatory behavior of the local Nusselt number depend on the angular location.     

Prediction of thermal and fluid flow characteristics in helically coiled tubes using ANFIS and GA based correlations

This study introduces the ability of Adaptive Neuro-Fuzzy Inference System (ANFIS) and genetic algorithm (GA) based correlations for estimating the hydrodynamics and heat transfer characteristics in coiled tubes. The experimental data related to the heat transfer and pressure drop in helically coiled tubes with deferent geometrical parameters (coil diameter and pitch) were used. In the experiments, hot water was passed in the coiled tubes, which were placed in a cold bath. Two ANFIS models were developed for predicting the Nusselt number (Nu) and friction factor (f) in the coiled tubes and the geometric parameters were employed as input data. Moreover, empirical correlations for estimating the Nu and f were developed by a phenomenological argument in the form of classical power–law correlations and their constants were found using the GA technique. The mean relative errors (MRE) of the developed ANFIS models for estimation of Nu and f are 6.24% and 3.54%, respectively. On the other hand, for empirical correlations, a MRE of 8.06% was found for prediction Nu while MRE of 5.03% was obtained for f. The results show that the ANFIS models can predict Nu and f with the higher accuracy than the developed correlations.     

Experimental investigation on the convective heat transfer of nanofluid flow inside vertical helically coiled tubes under uniform wall temperature condition

In this study, heat transfer enhancement of a nanofluid flow inside vertical helically coiled tubes has been investigated experimentally in the thermal entrance region. The temperature of the tube wall was kept constant at around 95 °C to have isothermal boundary condition. Experiments were conducted for fluid flow inside straight and helical tubes. In these experiments, the effects of a wide range of different parameters such as Reynolds and Dean numbers, geometrical parameters and nanofluid weight fractions have been studied. In order to investigate the effect of the fluid type on the heat transfer, pure heat transfer oil and nanofluids with weight concentrations of 0.1, 0.2 and 0.4% were utilized as the working fluid. The thermo-physical properties of the working fluids were extremely temperature dependent; therefore, rough correlations were proposed to predict their properties. Based on the experimental data, utilizing helical coiled tubes instead of straight ones enhances the heat transfer rate remarkably. Besides, nanofluid flows showed much higher Nusselt numbers compared to the base fluid flow. Finally, it was observed that combination of the two enhancing methods has a noticeably high capability to the heat transfer rate.     

Fluid flow and heat transfer of liquid-liquid two phase flow in microchannels: A review

The fluid flow and heat transfer behavior of liquid–liquid two phase flows have led to significantly improve the heat transfer rates in microchannels. Both numerical and experimental studies are reviewed in this paper to gain useful insights into the effect of a number of parameters such as film thickness, Peclet number, working fluid and flow geometry on hydrodynamic and thermal behavior of microchannels using liquid-liquid two phase flow. In addition, the paper summarises information about common correlations proposed to predict the pressure drop and heat transfer coefficient in the form of Nusselt number (Nu). The present study shows that there is little agreement across the literature between measured pressure drop and Nusselt number and predictions based on these correlations. Finally, the conclusions and important summaries, and some possible future development of this field are presented.     

Laminar convective heat transfer in chaotic configuration

The convective heat transfer in chaotic configuration of circular cross-section under laminar flow regime at different values of Dean number and Prandtl number is investigated numerically. The chaotic configuration is the combination of 90° bends and coils. The insertion of equidistant 90° bends between the two consecutive coil produces the phenomenon of flow inversion. The hydrodynamics and heat transfer under laminar flow conditions in the chaotic configuration with constant wall flux as a boundary condition is studied. The control-volume finite difference method with second-order accuracy is used. The chaotic configuration shows a 25–36% enhancement in the heat transfer due to chaotic mixing while relative pressure drop is 5–6%. The effect of Prandtl number on fully developed heat transfer coefficient is also reported. It is observed that heat transfer increases with increase in Prandtl number. The stretching and folding phenomenon in chaotic configuration is observed and discussed for heat transfer coefficient and pressure drop in the chaotic configuration. The cyclic oscillation behavior in the heat transfer coefficient with downstream distance in the chaotic configuration and coiled tube is also observed and discussed. It appeared that heat transfer is strongly influenced by flow inversion. The effect of boundary conditions on heat transfer performance in the chaotic configuration as well as in the coiled tube is also carried out. The study is further extended to predict hydrodynamics and heat transfer with temperature-dependent viscosity in the chaotic configuration. A comparative study for heat transfer and friction factor is also carried out for constant and temperature-dependent viscosity in coiled tube and chaotic configuration. It was observed that the heat transfer under heating condition with temperature-dependent viscosity is higher as compared to the constant viscosity result while friction factor shows the reverse phenomenon in the chaotic configuration.     

Experimental investigation of turbulent flow and convective heat transfer characteristics of alumina water nanofluids in fully developed flow regime

In this paper the convective heat transfer and friction factor of the nanofluids in a circular tube with constant wall temperature under turbulent flow conditions were investigated experimentally. Al₂O₃ nanoparticles with diameters of 40 nm dispersed in distilled water with volume concentrations of 0.1–2 vol.% were used as the test fluid. All physical properties of the Al₂O₃–water nanofluids needed to calculate the pressure drop and the convective heat transfer coefficient were measured. The results show that the heat transfer coefficient of nanofluid is higher than that of the base fluid and increased with increasing the particle concentrations. Moreover, the Reynolds number has a little effect on heat transfer enhancement. The experimental data were compared with traditional convective heat transfer and viscous pressure drop correlations for fully developed turbulent flow. It was found that if the measured thermal conductivities and viscosities of the nanofluids were used in calculating the Reynolds, Prandtl, and Nusselt numbers, the existing correlations perfectly predict the convective heat transfer and viscous pressure drop in tubes.     

水滴形管换热与阻力特性的数值研究

为提高换热管的综合性能,设计并研究了一种新型水滴形换热管,采用CFD软件,在相同管横截面积的前提下,对圆形、椭圆形及水滴形换热管单管和管束的换热与阻力特性进行了模拟计算。研究表明:水滴形管可以明显减小换热管背流面的回流;在相同的进口流速下,水滴形管管束努塞尔数Nu较圆管和椭圆管分别增大了28%和18. 5%,而进出口压降相较于椭圆形及圆形管分别减小了45. 5%及90%,相较于圆形管及椭圆形管,水滴型管具有更好的换热流动特性。     

Thermally dependent viscosity and non-Newtonian flow in a double-pipe helical heat exchanger

A double-pipe helical heat exchanger was numerically studied to determine the effects of thermally dependent viscosity and non-Newtonian flows on heat transfer and pressure drop for laminar flow. Thermally dependent viscosities were found to have very little effect on the Nusselt number correlations for Newtonian fluids; however significant effects on the pressure drop in the heat exchanger were predicted. Changing the flow rate in the annulus can significantly affect the pressure drop in the inner tube, since the average viscosity of the fluid in the inner tube would change due to the change in the average temperature.The effects of non-Newtonian power law fluids on the heat transfer and the pressure drop were determined for laminar flow in the inner tube and in the annulus. The Nusselt number was correlated with the Péclet number for heat transfer in the inner tube. For the annulus, the Nusselt number was found to correlate best with the Péclet number and the curvature ratio. Pressure drop data were compared by using ratios of the pressure drop of the non-Newtonian fluid to a Newtonian fluid at identical mass flow rates and consistency indices.     

Prediction of heat transfer and flow characteristics in helically coiled tubes using artificial neural networks

In this study, Artificial Neural Network (ANN) models were developed to predict the heat transfer and friction factor in helically coiled tubes. The experiments were carried out with hot fluid in coiled tubes which placed in a cold bath. Coiled tubes with various curvature ratios and coil pitches (nine Layouts) were used. The output data of the ANNs were Nusselt number and friction factor. The validity of the method was evaluated through a test data set, which were not employed in the training stage of the network. Moreover, the performance of the ANN model for estimating the Nusselt number and friction factor in the coiled tubes was compared with the existing empirical correlations. The results of this comparison show that the ANN models have a superior performance in predicting Nusselt number and friction factor in the coiled tubes.     

Effect of fluid thermal properties on the heat transfer characteristics in a double-pipe helical heat exchanger

Heat transfer characteristics of a double-pipe helical heat exchanger were numerically studied to determine the effect of fluid thermal properties on the heat transfer. Two studies were performed; the first with three different Prandtl numbers (7.0, 12.8, and 70.3) and the second with thermally dependent thermal conductivities. Thermal conductivities of the fluid were based on a linear relationship with the fluid temperature. Six different fluid dependencies were modeled. Both parallel flow and counterflow configurations were used for the second study.Results from the first study showed that the inner Nusselt number was dependent on the Prandtl number, with a greater dependency at lower Dean numbers; this was attributed to changing hydrodynamic and thermal entry lengths. Nusselt number correlations based on the Prandtl number and a modified Dean number are presented for the heat transfer in the annulus. Results from the second part of the study showed that the Nusselt number correlated better using a modified Dean number. The counterflow configuration had higher heat transfer rates than the parallel flow, but the ratio of these differences was not different when comparing thermally dependent properties and thermally independent properties.     

An Experimental Study of Condensation Heat Transfer in Sub-Millimeter Rectangular Tubes

The characteristics of local heat transfer and pressure drops were experimentally investigated using condensing R134a two-phase flow, in single rectangular tubes, with hydraulic diameter of 0.494, 0.658, and 0.972 mm. New experimental techniques were used to measure the in-tube condensation heat transfer coefficient especially for the low heat and mass flows. Tests were performed for a mass flux of 100, 200, 400, and 600 kg/m2s, a heat flux of 5 to 20 kW/m2, and a saturation temperature of 40℃. In this study, effect of heat flux, mass flux, vapor qualities, and hydraulic diameter on flow condensation were investigated and the experimental local condensation heat transfer coefficients and frictional pressure drop are shown. The experimental data of condensation Nusselt number are compared with previous correlations, most of which are proposed for the condensation of pure refrigerant in a relatively large inner diameter round tubes.     

A geometric study on shell side heat transfer and flow resistance of a six-start spirally corrugated tube

Heat transfer enhancement is of great importance for energy efficiency improvement. The utilization of spirally corrugated tubes is one of the efficient ways to strengthen heat transfer. In this article, based on a validated numerical model, the effects of geometric parameters of a six-start spirally corrugated tube, including the pitch p and the corrugation depth e, on the shell side heat transfer and flow resistance performance are numerically investigated, in high Reynolds number conditions ranging from 10,000 to 60,000. The shell side secondary flow velocity distribution, longitudinal vortex distribution, and temperature distribution of a six-start spirally corrugated tube are presented, respectively. In addition, the heat transfer and flow resistance characteristics are evaluated by comparing the Nusselt number and the flow resistance coefficient with these of smooth tubes. Results show that the utilization of six-start spirally corrugated tubes can enhance the heat transfer performance at the expense of an increase of the flow resistance. However, with the same geometric parameters, the Nusselt number increases and the flow resistance coefficient decreases as Reynolds number increases. With the pitch increasing, the Nusselt number and the flow resistance coefficient decrease at a fixed Reynolds number. In contrast, as the corrugation depth increasing, the Nusselt number changes irregularly, and the flow resistance coefficient increases. Finally, correlations for the shell side Nusselt number and flow resistance coefficient of the six-start spirally corrugated tube are established. This work is of significance for engineers and scientists focusing on the heat transfer and the flow resistance characteristics of spirally corrugated tubes and their applications.     

Thermal Performance of Coiled Square Tubes at Large Temperature Differences for Heat Exchanger Application

In many heat exchanger applications, working fluid inside the tubes is subjected to considerable temperature changes. Coiled tubes are used widely in heat exchanger applications due to the enhanced heat transfer rate caused by secondary flows. This study examines the thermal performance of three configurations of coiled tubes of square cross-section, namely, in-plane, helical, and conical coiled tubes, subjected to a large temperature difference between the fluid and the wall and compares it with that of a straight tube of identical cross-section area and length. The concept of figure of merit (FoM) is introduced to compare the heat transfer performance of the various configurations tested. The results indicate that FoM increases as the wall temperature is increased. In addition, the combination of temperature-induced buoyant flow and curvature-induced secondary flow significantly affects the flow behavior and heat transfer performance inside the tubes. The coil pitch in helical and conical tubes has an adverse effect on the heat transfer performance due to shift in vortices generation. The in-plane spiral tube operates at a higher wall temperature and lower Reynolds number, which gives rise to a higher FoM. The highest Nusselt number is obtained for the in-plane spiral tube at higher wall temperature and higher Reynolds number, which shows potential for practical applications.     

Heat Transfer and Pressure Drop Characteristics of Nanofluid Flows Inside Corrugated Tubes

An experimental investigation is carried out to study the heat transfer and pressure drop characteristics of multiwalled carbon nanotubes (MWCNTs)/heat transfer oil nanofluid flows inside horizontal corrugated tubes under uniform wall temperature condition. To provide the applied nanafluids, MWCNTs are dispersed in heat transfer oil with mass concentrations of 0.05, 0.1, and 0.2 wt%. The Reynolds number varies between 100 and 4,000. Three tubes with hydraulic diameters of 11.9, 13.2, and 15.5 mm are applied as the test section in the experimental setup. Tubes are corrugated four times on the cross section; that is, there are four different helices around the tube. Depths of the corrugations are chosen as 0.9, 1.1, and 1.3 mm, and pitch of corrugation is 14 mm. The acquired data confirm the increase of heat transfer rate as a result of utilizing nanofluids in comparison with the base fluid flow. However, corrugating the tubes decreases the heat transfer rate at low Reynolds numbers. The highest increase in heat transfer rate is observed for the Reynolds numbers for which the smooth tube is in the transition regime and the corrugated tube reaches the turbulent flow, that is, Reynolds number in the range of 1,000 to 3,000. Rough correlations are proposed to predict the Nusselt number and friction factor.     

Refrigerant Condensation Flow Regimes in Enhanced Tubes and Their Effect on Heat Transfer Coefficients and Pressure Drops

Flow regimes influence the heat and mass transfer processes during two-phase flow, implying that any statistically accurate and reliable prediction of heat transfer and pressure drop during flow condensation should be based on the analysis of the prevailing flow pattern. Many correlations for heat transfer coefficient and pressure drop during flow condensation completely ignored flow regime effects and treated flows as either annular or non-stratified flow or as stratified flow. This resulted in correlations of poor accuracy and limited validity and reliability. Current heat transfer coefficient, pressure drop, and void fraction models are based on the local flow pattern, though, resulting in deviations of around 20% from experimental data. There are, however, several inconsistencies and anomalies regarding these models, which are discussed in this paper. A generalized solution methodology for two-phase flow problems still remains an elusive goal, mainly because gas-liquid flow systems combine the complexities of turbulence with those of deformable vapor-liquid interfaces. The paper focuses on the state of the art in correlating flow condensation in micro-fin tubes and proposes flow regime-based correlations of heat transfer coefficient and pressure drop for refrigerant condensation in smooth, helical micro-fin, and herringbone micro-fin tubes.     

A Numerical Study of Flow and Heat Transfer in Internally Finned Rotating Curved Pipes

In this article, the effects of internal fins on an incompressible viscous flow and heat transfer inside rotating curved pipes are numerically studied under the hydrodynamically and thermally fully developed conditions. The fins are assumed to have negligible thickness with the same conditions as the pipe walls. Two thermal boundaries including constant wall temperature and constant heat flux are considered at the pipe wall. First the accuracy of the numerical code written by a finite-volume method based on the SIMPLE algorithm is verified by the available data for the finless rotating curved pipes. Then, the numerical results for the internally finned rotating pipes are investigated in both positive and negative rotation numbers affecting remarkably on the flow and temperature field patterns. Also, the Dean number (K_LC) effects on the friction factor, Nusselt number, and other nondimensional parameters are studied in detail. Analyzing the numerical results by the Colburn factor, two optimum fin heights consisting of the four-fifth of the pipe radius at the lower Dean numbers and one-third of the pipe radius at higher Dean numbers are determined in the curved rotating pipe with six internal fins.     

Forced convection heat transfer and pressure drop for a horizontal cylinder with vertically attached imperforate and perforated circular fins

In this study, the effect of holes placed on perforated finned heat exchangers on convective heat transfer experimentally investigated. Six millimeter-diameter holes were opened on each circular fin on a heating tube in order to increase convective heat transfer. These holes were placed on the circular fins in such a way as to follow each other at the same chosen angle. The holes created turbulence in a region near the heating tube surface on the bottom of the fin. Some experiments were then performed to analyze the effect of this turbulence on heat transfer and pressure drop. These experiments were carried out at six different angular locations in order to determine the best angular location. In addition, a perforated finned heater was compared with an imperforate finned heater to observe the differences. In the cases of the Re above the critical value, Nusselt numbers for the perforated finned positions are 12% higher than the Nusselt numbers for the imperforate state. Moreover, a correlation has been obtained between the Re and Nu in the Re number above the critical value and the Re below the critical value. Meanwhile, correlations regarding pressure drops in the flow areas have been obtained.     

Characterization of sodium flow over hexagonal fuel subassemblies

Steady flow of liquid sodium over a bundle of heat generating hexagonal subassemblies has been investigated. The cross flow pressure drop and heat transfer are characterized using the general purpose CFD code STAR-CD. Analysis has been carried out for both laminar and turbulent regimes of interest to liquid metal fast reactors. Turbulence has been modeled using low Reynolds number (Re) k-ε model. The estimated pressure drop and heat transfer coefficients are compared against that of a straight parallel plate channel. It is seen that in the low Reynolds number range, the pressure drop for the hexagonal path is nearly equal to that of the parallel plate channel for the same length. However, in the high Reynolds number range, the pressure drop of the hexagonal path is much higher than that in the parallel plate channel, the ratio being 2 at Re = 2000 while it is 3.6 at Re = 20,000. Two competing factors, viz., (i) jet impingement/flow development effect and (ii) flow separation effect are found to influence the average Nusselt number (Nu). In the laminar regime, the latter effect dominates leading to a decrease of the Nusselt number with an increase in the Reynolds number. However, in the turbulent regime, the former effect dominates leading to an increase in the Nusselt number with Reynolds number. The Nusselt number in the hexagonal path is about twice that of the parallel plate channel due to under development of velocity/temperature profiles and the recirculation associated with the hexagonal path due to the changes in flow direction. Detailed correlations for both the pressure drop and the average Nusselt number have been proposed.     

An experimental investigation of convection heat transfer to supercritical carbon dioxide in miniature tubes

Experimental results of convection heat transfer to supercritical carbon dioxide in heated horizontal and vertical miniature tubes are reported in this paper. Stainless steel circular tubes having diameters of 0.70, 1.40, and 2.16 mm were investigated for pressures ranging from 74 to 120 bar, temperatures from 20 to 110 °C, and mass flow rates from 0.02 to 0.2 kg/min. The corresponding Reynolds numbers and Prandtl numbers ranged from 10⁴ to 2×10⁵ and from 0.9 to 10, respectively. It is found that the buoyancy effects were significant for all the flow orientations, although Reynolds numbers were as high as 10⁵. The experimental results reveal that in downward flow, a significant impairment of heat transfer was discerned in the pseudocritical region, although heat transfer for both horizontal and upward flow was enhanced. The experimental results further indicate that in all the flow orientations, the Nusselt numbers decreased substantially as the tube diameter shrunk to <1.0 mm. Based on the experimental data, correlations were developed for the axially-averaged Nusselt number of convection heat transfer to supercritical carbon dioxide in both horizontal and vertical miniature heated tubes.     

Thermally Developing Forced Convection of Non-Newtonian Fluids Inside Elliptical Ducts

Laminar-forced convection inside tubes of various cross-section shapes is of interest in the design of a low Reynolds number heat exchanger apparatus. Heat transfer to thermally developing, hydrodynamically developed forced convection inside tubes of simple geometries such as a circular tube, parallel plate, or annular duct has been well studied in the literature and documented in various books, but for elliptical duct there are not much work done. The main assumptions used in this work are a non-Newtonian fluid, laminar flow, constant physical properties, and negligible axial heat diffusion (high Peclet number). Most of the previous research in elliptical ducts deal mainly with aspects of fully developed laminar flow forced convection, such as velocity profile, maximum velocity, pressure drop, and heat transfer quantities. In this work, we examine heat transfer in a hydrodynamically developed, thermally developing laminar forced convection flow of fluid inside an elliptical tube under a second kind of a boundary condition. To solve the thermally developing problem, we use the generalized integral transform technique (GITT), also known as Sturm-Liouville transform. Actually, such an integral transform is a generalization of the finite Fourier transform, where the sine and cosine functions are replaced by more general sets of orthogonal functions. The axes are algebraically transformed from the Cartesian coordinate system to the elliptical coordinate system in order to avoid the irregular shape of the elliptical duct wall. The GITT is then applied to transform and solve the problem and to obtain the once unknown temperature field. Afterward, it is possible to compute and present the quantities of practical interest, such as the bulk fluid temperature, the local Nusselt number, and the average Nusselt number for various cross-section aspect ratios.