Empirical Correlation For Nusselt Number Research Articles

Investigation on flow and heat transfer in various channels based on triply periodic minimal surfaces (TPMS)

Heat exchangers are one of the key components to ensure the safe and efficient operation of nuclear energy systems. Additive manufacturing offers the processing solutions of advanced heat exchangers based on triply periodic minimal surfaces (TPMS). TPMS has superior mechanical and thermal–hydraulic performance that provides excellent energy-saving potential in the energy systems. In this study, I-WP, Neovius, Fischer-Koch S, Primitive surface-based heat transfer channels with different volume shares are constructed in three dimensions. The enhanced heat transfer mechanisms of TPMS topologies are identified and parametric analysis on the thermal–hydraulic performance is performed. The results indicate that the secondary flows, periodic flow acceleration/deceleration and constant changes in flow directions play key roles in convective heat transfer of TPMS topologies. Based on a large amount of simulation data, empirical correlations for Nusselt number and friction factor in the turbulent regime are established. This study provides a database for the design and application of TPMS-based heat exchangers, which contributes to the energy-saving and sustainable future target.

Optimization of elliptical pin-fin microchannel heat sink based on artificial neural network

Conjugate fluid-solid heat transfer in a pin-fin microchannel heat sink is an effective way to dissipate heat from the heating surface with high heat flux. The introduction of fins increases the heat exchange area and enhances flow turbulence, while it increases the flow resistance at the mean time. The thermal-hydraulic performance of heat sink is affected by fin shape, density and flow parameters. In this paper, contrived numerical simulations of the flow and heat transfer process in elliptical pin-fin microchannel heat sink are carried out, including 2033 cases with different fin sizes, numbers and flow velocities. The simulation results show that the flow velocity and fin transverse width are the main factors affecting heat transfer and fluid flow. Three artificial neural networks are established to predict the average temperature, the temperature non-uniformity of heating surface and the pressure drop of microchannel. The predicted results show that the pump power and heating surface temperature are contradictory objectives. A microchannel with the optimal thermal-hydraulic performance is selected. It has numerous fins which are longer in the flow direction. The empirical correlations for Nusselt number and friction coefficient of the optimal microchannel are proposed.

Saturation flow boiling characteristics of R290 (propane) inside a brazed plate heat exchanger with offset strip fins

An inclusive experimental study was conducted to explore the saturated flow boiling heat transfer coefficient (HTC) and frictional pressure drop (PDf) features of R290 in a brazed plate heat exchanger embedded with offset strip fins with an offset length of 2 mm, fin thickness of 0.3 mm, and fin height of 2 mm. The experiment was conducted at four different saturation temperatures (Ts = 5–20 °C), three mass fluxes (G =20–60 kg m−2 s−1), four heat fluxes (q = 7.5–15 kW m−2), and eight mean vapor qualities (Xm) at increasing inlet vapor quality (0.1–0.8). The findings revealed that nucleate boiling vanquished at lower Xm values, irrespective of the working conditions, despite the fact that at higher Xm, the boiling process was dominated by convection. There was a dry-out condition inside the heat exchanger at Xm = 0.42–0.63, except when G = 60 kg m−2 s−1. The result suggested that the HTC of R290 strongly depended on Xm and Ts compared with G and q. The PDf of R290 shows a strong dependence on Ts, G, and Xm, whereas it is less dependent on q. Moreover, PDf increases with an increase in G, Xm, and q values, and decreases with an increase in Ts. Furthermore, empirical correlations for Nusselt number and friction factor, which were developed for R290, accounted for the influence of equivalent and liquid Reynolds numbers and the liquid and vapor densities with a mean absolute error of 10% and 14%, respectively.

Experimental evaluation on heat/mass transfer and pressure drop of a microchannel membrane‐based desorber for compact and efficient H2O/LiBr absorption refrigeration

• Microchannel membrane-based desorber using H 2 O/LiBr is experimentally studied. • The lower channel performs better in heat/mass transfer but worse in pressure drop. • Nu and Sh increase with Re and inlet temperature but decrease with concentration. • f increases with inlet concentration but decreases with Re and inlet temperature. • Prediction accuracies of Nu, Sh , and f are improved by 38.83%, 62.76%, and 78.18%. Microchannel membrane-based desorber plays a vital role in compact and efficient absorption refrigeration systems to utilize renewable and waste energy. However, its existing models have certain errors because they are based on the empirical correlations that developed for other processes. In this study, experiments are carried out to evaluate the heat/mass transfer and solution pressure drop characteristics of a H 2 O/LiBr microchannel membrane-based desorber (1 mm width, 250 mm length, 0.15 and 1 mm height, and 100 channel numbers) with mass concentration ranging between 50 and 60 wt% and inlet temperature between 65 and 85 °C. The desorber with a lower channel height has a higher overall heat transfer coefficient, a higher desorption rate, and a greater pressure drop. But when the inlet temperature reaches 85 °C, the higher channel yields an unexpected higher desorption rate (0.00645 kg/(m 2 ⋅s)) than the lower channel (0.00615 kg/(m 2 ·s)). The experimental results show that both heat and mass transfer processes are strengthened by a higher solution flow rate, higher inlet temperature, and lower concentration, while the solution pressure drop is significantly reduced by a lower flow rate, lower concentration, and higher inlet temperature. Based on the experimental data, empirical correlations for Nusselt number, Sherwood number, and friction factor are obtained with errors of ± 40%, ± 20%, and ± 25% with prediction accuracies improvement of 38.83%, 62.76% and 78.18% compared to the correlations from the literature, facilitating the evaluation and design of compact and efficient absorption refrigeration systems.

Study of Mixed Convection and Surface Radiation in Flush Mounted Vented Cavities

In the present work, a computational study of mixed convection in air-filled vented cavities is presented. The experimental work is also introduced in this study in order to enrich the computational results. The parametric study of the enclosure is presented for different ranges of Reynolds numbers, ; Richardson numbers, ; and vent ratio, , and the heat input provided to the right wall, . The continuity, momentum, and energy equations are discretized by the finite volume method and solved using SIMPLEC algorithm. In the present study, optimization of the cavity vent ratio, heat source size, and location found as a novelty in the present work is introduced based on the combined numerical and experimental investigation to achieve better cooling. Empirical correlations for Nusselt number and maximum right wall temperature are developed as functions of , , and .

Experimental investigation of heat transfer and pressure drop characteristics of internal finned tubes

This study investigates experimentally laminar flow in a water-to-water double pipe heat exchanger for counter flow arrangement. The hot water flows in inner pipe and cold water in the outer annulus. The test section, which has a length of 1400 mm, is a horizontal annular passage formed by aluminum alloy tube with an inner diameter 20.9 mm and outer diameter 35 mm. Three different finned tubes with four, six, and eight longitudinal trapezoidal fins, which have length 1400 mm, height 5.23 mm, and thickness 3.63 mm at base and 1 mm at the tip, attached to the wall surface of the inner tube. For comparison, the heat transfer and pressure drop characteristics are also studied for a smooth inner tube. The results show that the differences in Nu are insignificant among the internal finned tubes with four, six, and eight fins at a smaller Re, whereas the inner tube with more fins has a larger Nu at a larger Re. At a fixed Reynolds number, the friction factor of tube with eight fins is the largest, followed by tube with six fins, tube with four fins and smooth tube for Re< 1000; however, the differences in friction factors of the four heat exchangers are not pronounced for Re >1500. In addition, the heat transfer benefit tends to decrease as the pressure drop increases for internal finned tubes. Finally, empirical correlations of Nusselt number and the friction factor with the Reynolds number are proposed.

Thermal and hydraulic characteristics of multiple row spiral finned tube heat exchangers

An experimental investigation for the thermal and hydraulic characteristics of a spiral finned-tube heat exchanger was performed to understand its cooling performance for a developed novel defrosting technique. Two identical spiral finned-tube heat exchangers were manufactured; one having four rows and other having five rows. Both heat exchangers tubes were arranged inline. The heat exchangers had a tube diameter of 9.36 mm, spiral fins of 23.4 mm outer diameter, and 3.6 mm fin pitch (277 fins/m). The overall heat transfer coefficient was calculated using the measured temperatures and flow rates of each stream, and utilizing the logarithmic mean temperature difference method. The air-side heat transfer coefficient was determined using the calculated overall heat transfer coefficient and the tube-side heat transfer coefficient. The air-side pressure drop across the heat exchanger was also measured using a differential pressure digital manometer. The experimental data covered Reynolds number range of 1500 to 6000 and a Prandtl number of 0.7. Empirical correlations of Nusselt number, Colburn factor and friction factor versus Reynolds number were developed using least squares regression. The results showed that there is no significant variation in air-side heat transfer coefficient for the four and five rows spiral finned-tube heat exchanger and their Colburn factor is almost constant over the tested range of Reynolds number.

Heat transfer augmentation for turbulent flow in circular tubes using inserts with multiple curved vortex generator elements

Measurements of local heat transfer coefficients on the circumference of a circular tube, fitted with two modified versions of an already existing axially inline curved Vortex Generator (VG) element insert are reported in this study. Measurements for average pressure drop are also presented and the air was used as the working fluid. The first modified insert is manufactured with a pair of two VG elements spaced symmetrically 180° apart but with the subsequent pairs along the axis staggered at an angle of 90°. The geometric features for the staggered insert were identical to the optimal one for the existing inline one. The staggered insert gives a more uniform circumferential and axial Nusselt number distribution. The ratio of the highest and lowest Nusselt number values for the staggered and inline case is equal to approximately 1.3 and 1.6 respectively. The average Nusselt number ratio at constant Reynolds number (10,000 < Re < 45,000) and constant pumping power however remained the same at about 2.6 and 1.5 respectively. The second modified insert was manufactured with three vortex generators placed symmetrically 120°apart at each axial location with all subsequent locations in line with one another. Two angles of attack 30°and 45° were used for the vortex generator elements and the pitch to projected length ratio of the VGs was varied between 1.6 and 12.2. The average heat transfer coefficient augmentation ratio using this insert at the equal Reynolds number and constant pumping power was obtained in the range of 1.5–5.5 and 1.0 - 1.8, respectively. The experimental data is presented in the form of empirical correlations for Nusselt number, and friction factor as a function of tube flow parameters, and non-dimensional geometrical parameters of VG inserts, which predict the data with an accuracy equal to ±20 %.

Thermohydraulic performance and second law analysis of a tube embedded with multiple helical tape inserts

ABSTRACT The present investigation deals with the analysis of the heat exchanger tube by inserting the multiple helical tape geometry to determine the heat transfer, friction factor, thermal performance, and entropy generation experimentally. The helical tapes designed for current investigation are analyzed in terms of geometrical parameters namely number of tape (1,2,3), twist ratio (2,3,4), and width ratio (0.4). The experiments are conducted in the range of Reynolds number lying in turbulent region from 5000 to 29000. The experimentation affirms an enhancement of the thermal performance. The experimental data reveal that there is 3.95 times enhancement in the heat transfer for twist ratio of 2 and number of tapes of 3. The thermal performance factor is enhanced by 1.23 times over smooth tube for the twist ratio of 2 and number of tapes of 1. It is observed that the maximum heat transfer enhancement is found for low and high values of twist ratio and number of tapes, respectively. The rate of entropy generation is less for the tube equipped with helical tape inserts for all possible cases than smooth tube. The minimum entropy generation value of 0.27 is observed for twist ratio of 2 and number of tapes 3. The developed empirical correlations for Nusselt number, friction factor, and thermal performance factor are in good agreement with experimental results.

Investigation of the flow and heat transfer characteristics of helium gas in printed circuit heat exchangers with asymmetrical airfoil fins

This work presents a numerical investigation on the flow and heat transfer performance of printed circuit heat exchangers with asymmetrical airfoil fins, and the influence of the arrangements, attack angles, horizontal spacings, and staggered spacings of fins are studied. Then an orthogonal experiment is designed to optimize the comprehensive performance of these printed circuit heat exchangers. Finally, empirical correlations of Nusselt number and friction factor for these heat exchangers with the inlet Reynolds number ranging from 2000 to 10,000 are proposed based on our numerical results. The results show that the printed circuit heat exchangers with a consistent layout of fins show better comprehensive performance than those with a reverse layout. The comprehensive performance of these printed circuit heat exchangers with asymmetrical airfoil fins increases as the horizontal fin spacing and fin attack angle decrease. The staggered spacing has little influence on the comprehensive performance of printed circuit heat exchangers. In the present work, the printed circuit heat exchanger with the values of the normalized horizontal spacing, staggered spacing, and attack angles of 4, 1.0, and 1.269, respectively, exhibits the best comprehensive performances.

Convection Heat Transfer and Pressure Drop for Dilute Polymer Solutions Flow Inside Multi- Channels Flat Tube (Dept.M)

Convection heat transfer and pressure drop is investigated experimentally, for the flow of dilute polymer solutions (polyacrylamide) inside multi-channels flat tube and compared with water. An experimental apparatus equipped with the required measuring devices is designed and constructed to assess the effects of the operating parameters on convection heat transfer and pressure drop. The flat Aluminum multi-channels extruded tube composed of 22 parallel rectangular mini-channels (3.6 mm x 3.85 mm) with hydraulic diameter of 3.72 mm. Different polymer concentrations are considered; 10, 20, 50 and 100 ppm. This work covers a range of Reynolds number from 300 to 1200 and heat flux from 15 to 41kW/m2. The experimental measurements for flow rate, temperature, pressure, and pressure drop are taken to perform the required analysis. Therefore, the average value of convection heat transfer coefficient and friction factor for different operating parameters are computed. The obtained experimental results show that, the laminar-turbulent transition occurs in the range of Re=1100-2000. Pressure drop and in turn friction factor takes higher values for laminar flow of polymer solutions compared with water. Friction factor decreases with increasing Reynolds number for both polymer solutions and water flow inside the flat tube. Surface temperature of flat tube decreases with increasing Reynolds number for both polymer solutions and water. Accordingly, convection heat transfer coefficient and in tum Nusselt number are increased. When using polymer solutions, the surface temperature of flat tube increases compared with water. Therefore, Nusselt number is decreased. The reduction value in Nu increases with increasing concentration of polymer solution. The average value for this reduction in Nu was about 15%. An empirical correlation for Nusselt number is obtained in the range of the studied operating parameters. Comparison between the obtained experimental results with the previous data is done and gives the same trend.

Investigation of the thermal-hydraulic characteristics in the shell side of heat exchanger with quatrefoil perforated plate

Quatrefoil perforated plate (QPP) is a kind of whole circular support plate for the shell side of shell-and-tube heat exchanger (STHX), and the design and optimization of heat exchanger with this support structure are the key technologies to study and improve the performance of heat exchanger. The influences of the hole height and plate spacing of the QPP on the thermal-hydraulic performance of the heat exchanger were studied mainly by using computational fluid dynamics (CFD) method. And the reliability and accuracy of the numerical results were verified by compared with experimental results. With Reynolds number varying from 5000 to 20,000, the results show that the heat transfer coefficient and pressure drop in the shell side of the heat exchanger both increase with the decrease of the hole height and the plate spacing of the QPP, but the shell side heat transfer coefficient per unit pressure drop h/Δp decreases. Under the conditions of the same fluid flow rate and same plate spacing, compared with segmental baffle heat exchanger, the comprehensive performance h/Δp of heat exchanger with QPPs is improved by 27%–41%. The empirical correlations for Nusselt number and pressure drop in the shell side of heat exchanger with QPPs were obtained and the calculation deviation of correlations both are within ±10%, which can be used to guide engineering design and practice.

Modelling and Evaluation of the Thermohydraulic Performance of Finned-Tube Supercritical Carbon Dioxide Gas Coolers

This paper investigates the thermohydraulic performance of finned-tube supercritical carbon dioxide (sCO2) gas coolers operating with refrigerant pressures near the critical point. A distributed modelling approach combined with the ε-NTU method has been developed for the simulation of the gas cooler. The heat transfer and pressure drop for each evenly divided segment are calculated using empirical correlations for Nusselt number and friction factor. The model was validated against test results and then used to investigate the influence of design and operating parameters on local and overall gas cooler performance. The results show that the refrigerant heat-transfer coefficient increases with decreasing temperature and reaches its maximum close to the pseudocritical temperature before beginning to decrease. The pressure drop increases along the flow direction with decreasing temperature. Overall performance results illustrate that higher refrigerant mass flow rate and decreasing finned-tube diameter lead to improved heat-transfer rates but also increased pressure drops. Design optimization of gas coolers should take into consideration their impact on overall refrigeration performance and life cycle cost. This is important in the drive to reduce the footprint of components, energy consumption, and environmental impacts of refrigeration and heat-pump systems. The present work provides practical guidance to the design of finned-tube gas coolers and can be used as the basis for the modelling of integrated sCO2 refrigeration and heat-pump systems.

Thermohydraulic characteristics of inline and staggered angular cut baffle inserts in the turbulent flow regime

In the present work, heat transfer and pressure drop characteristics in flow through a tube with inline and staggered baffles having angular cut at the edge are reported for various operating conditions. An experimental test rig is designed and developed to investigate heat transfer and pressure drop behavior for different conditions. Effects of different geometrical parameters, i.e., pitch ratios, baffle arrangement and cutting angle of baffles on heat transfer rate and pressure drop characteristics, have been investigated for turbulent flow regime. Reynolds number ranging from 10,000 to 52,000 has been considered in the present study. The maximum heat transfer rate has been observed for staggered arrangement with pitch ratio of 0.1 and cutting angle of 60°, while minimum heat transfer rate has been observed for inline arrangement with pitch ratio of 0.2 and cutting angle of 30°. Empirical correlations for Nusselt number and friction factor have been developed as a function of geometrical and flow parameters. The deviations between experimental and predicted values of Nusselt number and friction factor for staggered arrangements have been observed as ± 10%, ± 4%, respectively, whereas for inline arrangement the deviation has been observed as ± 12%, ± 5%, respectively. Results from empirical correlations are well agreed with the experimental data.

A comprehensive analysis and empirical correlations for Nusselt number, friction factor and exergy destruction of helical tube equipped with spring-wire

Although different kinds of turbulators are employed through the straight tubes, spring-wire is the only applicable turbulator for helical tubes which has been recently proposed by some researchers. The geometrical characteristics of spring-wire (including wire-diameter, spring-diameter and spring-pitch) severely affect the thermal, frictional and exergetic behavior of fluid flow through the helical tubes. In this research, spring-wire (with different geometries) is employed as a turbulator for helical tube to provide empirical correlations of Nusselt number, friction factor and exergy destruction for spring wire through the helical tubes (as the functions of flow parameters and geometric characteristics) which have not been provided before. It is noted that, the correlations of the straight tubes (equipped with turbulator) cannot be employed for helical tubes. Notable thermal/exergetic behaviors were observed for spring-wire though helical tubes. Larger wire-diameter of turbulator provided higher heat transfer coefficient and higher Nusselt number. Smaller spring-pitch provided higher heat transfer coefficient but lower Nusselt number. Indeed, higher heat transfer coefficient does not necessarily mean higher Nusselt number for spring-wire turbulators which is explained in detail in this study.

Compound thermal performance of an arc-shaped inner finned tube equipped with Y-branch inserts

A novel arc-shaped inner finned tube with Y-branch inserts was proposed to further enhance the tube side’s thermal performance. The compound thermal performances of the arc-shaped inner finned tube with Y-branch inserts were experimentally studied by comparing with the smooth tube and the arc-shaped inner finned tube. Experimental results indicate that the Nusselt number of the arc-shaped inner finned tube with Y-branch inserts is enhanced by ∼3.7 times that of the smooth tube and is approximately 15.7–86.2% higher than that of the arc-shaped inner finned tube depending on Reynolds number and space length (S). The friction factor of arc-shaped inner finned tube with Y-branch inserts with S = 10 cm, 15 cm and 20 cm are respectively 2.22–3.11, 2.1–2.73, 2.07–2.34 times as that of the arc-shaped inner finned tube. It is also found that the Nusselt number, friction factor and performance evaluation criterion of the arc-shaped inner finned tube with Y-branch insert increases with decreasing of the space length. Moreover, the performance evaluation criterion for the arc-shaped inner finned tube with Y-branch insert is about 1.02–2.22 while it is approximately 1.17–1.55 for the arc-shaped inner finned tube, which means that the arc-shaped inner finned tube with Y-branch inserts yields excellent overall thermal performance. Compared with other single and compound enhanced structures, the novel arc-shaped inner finned tube with Y-branch inserts can exchange more heat at the same pumping power. Finally, the empirical correlations for Nusselt number and friction factor are proposed according to the experimental results.

Experimental Study of Forced Convection Heat Transfer Porous Media inside a Rectangular Duct at Entrance Region

This work presents experimental investigation of flow and heat transfer characteristics for entry length of turbulent flow in a rectangular duct fitted with porous media and air as the working fluid. Rectangular duct (300×30 mm) with a hydraulic diameter (54.54 mm) was subjected to constant heat flux from lower surface (1.5 ×102 –1.8 ×102 w/m2) and Reynolds number ranged (3.3x104 up to 4.8x104). Copper mesh inserts (as porous media) with screen diameter (54.5 mm) for vary distance between two adjacent screens of (10 mm), (15 mm) and (20 mm) in the porosity range of (0.98 - 0.99) are considered for experimentation. The effect of porous height ratio (full and partial) are also considered. It is observed that the enhancement of heat transfer by using mesh inserts when compared to a plain surface is more by a factor of (2.2) times where the skin fraction coefficient is about (5) times. An Empirical correlation for Nusselt number and friction factor are developed for the mesh inserts from the obtained results.

An experimental investigation on heat transfer and friction factor of Silicon Carbide/water nanofluids in a circular tube

The Silicon Carbide (SiC)/water nanofluids are experimentally investigated and compared to understand the effect of weight concentration and size of the SiC nanoparticles in the base fluid i.e., distilled water (DIW). The Nusselt number and friction factors are presented for different Reynolds numbers ranging from 3000 – 16000. A combination of nanofluids at 0.04 wt. %, 0.08 wt.% and 0.1 wt.% concentrations containing SiC nanoparticles obtained after 5 hrs, 10 hrs and 15 hrs of ball milling are considered in the present study. The results show that the heat transfer coefficient and friction factor are more than that of the base fluid for all combinations of nanofluids. The Nusselt number enhancement varies from 3.38% to 36.74%, where the friction factor increase varies from 2.1% - 13.5% with that of the base fluid for all nanofluids. The SiC nanofluid at 0.1 wt.% of nanoparticles obtained after 5hrs of ball milling dispersed in the base fluid is observed to give better results. The obtained results are compared with the standard liquid correlations and also empirical correlations for Nusselt number and friction factor as a function of particle size and weight concentration are established.

Experimental and numerical study on forced convection heat transport in eccentric annular channels

In the process of drilling, the tubing-casing annulus are easily to be eccentric. Heat transport phenomenon occurring in such tubes and annulus can be complex, and this paper investigates forced convection in a vertical eccentric annulus with different radius ratios and eccentricity (normalized by the radius difference). Physical experiments and numerical simulation have been conducted with constant inner tube inlet temperature and flow rate of hot water. Results show that with the increase of radius ratios, the convection heat transport coefficient increases. For a radius ratio of 1.875, the heat transport coefficient increases as the eccentricity increases when the Re > 2000 and it decreases when the Re < 2000. For a radius ratio of 2.25 and Re < 1500, the influence of eccentricity is trivial, but for Re > 1500, the increase of eccentricity strengthens the heat convection. For a radius ratio of 3.06, the heat transport coefficient increases as the eccentricity increases. An empirical correlation for Nusselt number is derived as a function of Reynolds number, Prandtl number and eccentricity.

Enhanced heat transfer and frictional losses in heat exchanger tube with modified helical coiled inserts

The application of compact heat exchangers in any thermal system improves overall performance with a considerable reduction in size and weight. Inserts of different geometrical features have been used as turbulence promoting devices to increase the heat transfer rates. The present study deals with the experimental investigation of heat transfer and fluid flow characteristics of a tubular heat exchanger fitted with modified helical coiled inserts. Experiments have been carried out for a smooth tube without insert, tube fitted with helical coiled inserts, and modified helical coiled inserts. The helical coiled inserts are tested by varying the pitch ratio and wire diameter ratio from 0.5–1.5, and 0.063–0.125, respectively for the Reynolds number range of 1400 to 11,000. Experimental data have also been collected for the modified helical coiled inserts with gradually increasing pitch (GIP) and gradually decreasing pitch (GDP) configurations. The Nusselt number and friction factor values for helical coiled inserts are enhanced in the range of 1.42–2.62, 3.4–27.4, relative to smooth tube, respectively. The modified helical coiled insert showed enhancements in Nusselt number and friction factor values in the range of 1.49–3.14, 11.2–19.9, relative to smooth tube, respectively. The helical coiled and modified helical coiled inserts have thermo-hydraulic performance factor in the range of 0.59–1.29, 0.6–1.39, respectively. The empirical correlations of Nusselt number and friction factor for helical coiled inserts are proposed.