Empirical Correlation For Nusselt Number Research Articles

Investigation friction factor and heat transfer characteristics of turbulent flow inside the corrugated tube inserted with typical and V-cut twisted tapes

In present paper the effects of using typical twisted tape (TT) and V-cut twisted tape (VTT) on Nusselt number (Nu), friction factor (f) and thermal performance factor (η) inside corrugated tube in the turbulent flow are experimentally investigated despite the fact that the wall is under uniform heat flux. The experiments are conducted by twisted tapes with different twist ratio (y = 4.5, 6.07), depth and width ratios ranging (0.285–0.5) and Reynolds number varied from 5300 to 25,700 and water was as a working fluid. The obtained results show that the Nusselt number for corrugated tube that equipped with twisted tapes increases with increasing Reynolds number and is remarkable at high Reynolds Number while the friction factor is low. Moreover, the thermal performance factor for fluid increases with increasing Reynolds number and also the thermal performance factor for all states of VTT are higher than of TT. The new empirical correlations for Nusselt number, friction factor and thermal performance factor are predicted and compared with experimental data.

Application of response surface method and multi-objective genetic algorithm to configuration optimization of Shell-and-tube heat exchanger with fold helical baffles

A kind of shell-and-tube heat exchangers with fold baffles was proposed to eliminate the triangular leakage zones between adjacent baffles. An effective algorithm combing second-order polynomial response surface method and multi-objective genetic algorithm was adopted to study the effect of fold baffle configuration parameters on the performance of flow and heat transfer. The helical angle, overlapped degree and shell-side inlet velocity were chosen as design parameters, and the Nusselt number and shell-side pressure drop were considered as objective functions. The results show that both the Nusselt number and shell-side pressure drop increase with the decrease of helical angle and shell-side inlet velocity, and increase with the increasing overlapped degree. A set of Pareto-optimal points were obtained, and the optimization results illustrate a good agreement with CFD simulation data with the relative deviation less than ±3%. And the empirical correlations of Nusselt number and friction coefficient were obtained based on response surface method, the helical angle and overlapped degree were fitted into empirical correlations as correction factors for the first time. It is found that the adjusted coefficient of determination of the Nusselt number and friction coefficient is 0.943 and 0.999, respectively, which illustrate the fitting is correct and reliable.

Experimental investigation on convective heat transfer of supercritical RP-3 in vertical miniature tubes with various diameters

This article presents convective heat transfer of hydrocarbon fuel RP-3 at supercritical pressures in vertical micro-tubes with inner diameters of 0.538mm, 1.09mm and 1.82mm under heating conditions. Effects of system pressure, heat flux, mass flow rate and flow direction were experimented and analyzed with wide range of supercritical status. Also, inner diameter effect on heat transfer were compared at identical conditions. The results indicate that sharp variation of thermal properties with temperature is the key factor to influence heat transfer. Normal, deterioration and enhancement heat transfer phenomena generally occur in turn along with dimensionless position. Moreover, Nusselt number variation shows good agreement when the contrast temperature Tb/Tpc is lower than 0.80 and Bo∗=1.0×10−8 could be the critical point to evaluate buoyancy influence. At last, two well-predicted empirical correlations of Nusselt number are proposed for downward and upward flow heat transfer in 1.09mm tube.

Heat transfer enhancement of internal flow by inserting punched delta winglet vortex generators with various attack angles

Effects of punched delta winglet vortex generator inserts (PDWVGs) on single-phase forced convection heat transfer and friction loss of internal flow were experimentally investigated. The PDWVGs were manufactured by punching directly on aluminum strips with different attack angles (α) of 30°, 50° and 70°. Winglet-pitch ratio (Rp) and a winglet-width ratio (Rb) of PDWVGs were 1.05 and 0.42, respectively. Longitudinal strip and plain tube were also tested for comparison. The experiments were carried out under the conditions of Reynolds number from 5500 to 14500. Experimental results reveal that the PDWVG insert in a tube provided considerably higher heat transfer coefficient than the tube without the insert through pressure loss was also increased. The Nusselt number and friction factor increased with the increasing of α. The heat transfer enhancement by the PDWVGs with α of 30°, 50° and 70° provided higher than the plain tube in the range of 110–131%, 157–188% and 218–264%, respectively. The average friction factors in the inner tube generated by the PDWVGs with α of 30°, 50° and 70° were about 8.80, 10.21 and 11.87 times above the plain tube, respectively. The thermal enhancement factor was in the range of 0.91–1.22 for PDWVGs and 0.88–0.99 for L-S. In addition, the empirical correlations of Nusselt number, friction factor and thermal performance factor for PDWVGs were developed from the experimental results.

Experimental study on effect of heat transfer enhancement for single-phase forced convective flow with twisted tape inserts

In this paper, experimental investigation on heat transfer and friction characteristics of dual-pipe heat exchanger for single-phase forced convective flow with alternation of clockwise and counterclockwise twisted tape (ACCT tape) and typical twisted tape (TT tape) inserted in the inner tube has been carried out. And effects of different lengths of twisted tapes on heat transfer enhancement were studied through a circular tube using water as testing fluid in turbulent conditions with a range of Reynolds number between 3000 and 9000. In the dual-pipe heat exchanger, hot water was cooled in the inner tube and cold water was as cooling fluid between the inner tube and the outer tube. The results showed that the ACCT tapes performed better on heat transfer enhancement than the typical twisted tapes and the best effect appeared with the full-length (l=2400mm) ACCT tape insert in comparison with the twisted tapes of other lengths. The maximum values of PEC (performance evaluation criteria) with the full-length ACCT tape insert reached 1.42 in experimental flowing conditions. Empirical correlations for Nusselt number and friction factors were established and found to fit the experimental data with a deviation within 8%.

Experimental investigation and CFD analysis of rectangular profile FINS in a square channel for forced convection regimes

Steady-state heat transfer from rectangular fin arrays is examined experimentally and numerically for turbulent fully developed flow. The effects of geometrical parameters on heat transfer coefficient and Nusselt number are investigated. For different inter fin ratios, Reynolds number and Nusselt number dependence of the results is investigated. A generalized empirical correlation for Nusselt number is developed for rectangular fins for a Reynolds number range of 17 × 107 < Re < 2.47 × 108, and an aspect ratio of 0.089 < d/w < 0.0625, 0.24875 < t/L < 0.729. The correlation can predict the results with a relative rms error of 11.14%.

Heat transfer augmentation in a circular tube with perforated double counter twisted tape inserts

The present study explored the effects of perforated double counter twisted tapes on heat transfer and fluid friction characteristics in a heat exchanger tube. The twisted tapes with four different porosities of Rp=1.2, 4.6, 10.4 and 18.6% were used as counter-swirl flow generators in the test section. The experiments were conducted in a circular tube in turbulent flow regime with Reynolds number ranging from 7200 to 50,000 using air as the working fluid under uniform wall heat flux boundary condition. The experimental results demonstrated that the Nusselt number, friction factor and thermal enhancement efficiency were increased with decreasing porosity except porosity of 1.2%. The results also revealed that the heat transfer rate of the tube fitted with tapes were significantly increased with corresponding increase in friction factor. In the range of the present investigation, heat transfer rate and friction factor were obtained to be around 80 to 290% and 111 to 335% higher than those of the plain tube values, respectively. Based on constant blower power, the highest thermal enhancement efficiency of 1.44 was achieved. In addition, the empirical correlations of Nusselt number, friction factor and thermal enhancement efficiency were developed based on the experimental data.

Experimental investigation of forced convective heat transfer enhancement of γ-Al2O3/water nanofluid in a tube

The effect of nanofluids on heat transfer inside circular tubes under uniform constant heat flux boundary condition was investigated. The working nanofluid was a suspension of γ-Al2O3 nanoparticles of average diameter 20 nm. The heat transfer coefficients were calculated experimentally in the range of 1057 < Re < 2070 with different particle volume concentrations of 0.1%, 0.3% and 0.9%. Increasing the particle volume fraction led to enhancement of the convective heat transfer coefficient. The results show that the average heat transfer coefficient increased 16.8% at 0.9% volume concentration and Reynolds number of 2070 compared with distilled water. In addition, the enhancement of the convective heat transfer was particularly significant in the entrance region and decreased with axial distance. Finally, an empirical correlation for Nusselt number has been proposed for the present range of nanofluids. The mean deviation between the predicted Nusselt number and experimental values for the new correlation is 3.57%.

Moving-orientation and position effects of the piezoelectric fan on thermal characteristics of the heat sink partially filled in a channel with axial flow

This study experimentally investigated the heat transfer and fluid flow behaviors of the heat sink partially filled in a rectangular channel with the axial mainstream interacted by the oscillating movement of the upstream piezoelectric fan. Total eight heat sinks, including square pin–fin heat sinks (Models A–C), plate-fin heat sinks (Models D–F) and aluminum-foam heat sinks (Models G and H), were employed. The relevant parameters were the Reynolds number of the mainstream (Re), the oscillating-movement orientation of the piezoelectric fan and the location of the piezoelectric fan (the relative horizontal distance S/L=0.25 and the relative vertical distance Hp/L=0.22–0.62). The smoke flow visualizations demonstrate that the oscillating movement of the piezoelectric fan did strengthen the turbulent intensity of the mainstream at low Reynolds number, giving the additional disturbance momentum to the mainstream and making the fluid flow through the heat sink with turbulent flow characteristic. The heat transfer results indicate that the heat sink gained more heat transfer enhancement at smaller Re when the piezoelectric fan was operating. For example, when the piezoelectric fan was operating with transverse oscillation at Re=850, S/L=0.25 and Hp/L=0.62, the Nu/Nu0 (Nu and Nu0 separately mean the Nusselt number of the case with and without the piezoelectric fan) of square pin–fin heat sink Model C would exceed 2. The values of Nu/Nu0 for various heat sinks would drop and approach to unity as increasing Re. In general, under the oscillating condition, the square pin–fin heat sink gained the best heat transfer enhancement; the longitudinal plate-fin heat sink gained slightly less heat transfer enhancement than the square pin–fin heat sink did; the aluminum-foam heat sink gained poor heat transfer enhancement. In addition, the transverse oscillation promoted slightly more heat transfer enhancement than the axial oscillation did. Finally, this study proposed reasonable and accurate empirical correlations of Nusselt number in view of the pure axial-flow, the pure piezoelectric-fan and the both-combined conditions.

Comparative Studies on Thermal Performance of Conic Cut Twist Tape Inserts with SiO2 and TiO2 Nanofluids

This paper presents a comparison study on thermal performance conic cut twist tape inserts in laminar flow of nanofluids through a constant heat fluxed tube. Three tape configurations, namely, quadrant cut twisted tape (QCT), parabolic half cut twisted tape (PCT), and triangular cut twisted (VCT) of twist ratio y = 2.93 and cut depth de = 0.5 cm were used with 1% and 2% volume concentration of SiO2/water and TiO2/water nanofluids. Typical twist tape with twist ratio of y = 2.93 was used for comparison. The results show that the heat transfer was enhanced by increasing of Reynolds number and nanoparticles concentration of nanofluid. The results have also revealed that the use of twist tape enhanced the heat transfer coefficient significantly and maximum heat transfer enhancement was achieved by the presence of triangular cut twist tape insert with 2% volume concentration of SiO2 nanofluid. Over the range investigated, the maximum thermal performance factor of 5.13 is found with the simultaneous use of the SiO2 nanofluid at 2% volume concentration VCT at Reynolds number of 220. Furthermore, new empirical correlations for Nusselt number, friction factor, and thermal performance factor are developed and reported.

Heat transfer enhancement by helical screw tape coupled with rib turbulators

The influence of helical screw tape coupled with rib turbulators (HST-R) on thermohydraulic characteristics in a circular tube has been experimentally investigated. The experiments were performed under constant heat flux condition for Reynolds number between 6,000 and 20,000. The rib-pitch ratio (p/D) was varied from 1.0 to 3.0 while rib-height ratio (e/W) was varied from 0.5 to 1.5. The experimental results revealed that heat transfer and friction factor increase with increasing rib-height ratio (e/W) and decreasing rib-pitch ratio (p/D). For the range examined, the HST-Rs with moderate rib-pitch ratio (p/D = 2) and the largest rib-height ratio (e/W = 1.5) gave the maximum thermal performance factor while HST possessed thermal performance factor around average value of those of the tubes with HSTRs. The developed empirical correlations for Nusselt number, friction factor and thermal performance factor gave the predictions within ±4.4%, ±13% and ±4.2%, respectively as compared to the experimental data.

Investigation of heat transfer enhancement by perforated helical twisted-tapes

Influence of perforated helical twisted-tapes (P-HTTs) on the heat transfer, friction loss and thermal performance characteristics under a uniform heat flux condition is reported. The P-HTTs were obtained by perforating typical helical twisted-tapes (HTTs) with a prospect to reduce the friction loss of fluid flow. The experiments were conducted using P-HTTs' three different diameter ratios (d/w) of 0.2, 0.4 and 0.6, and three different perforation pitch ratios (s/w) of 1, 1.5 and 2. The helical pitch ratio and twist ratio were fixed at P/D=2 and y/w=3. Tests were performed for Reynolds number between 6000 and 20,000. The experiments using the plain tube and the tubes with HTTs were also carried out for assessment. The experimental results reveal that the use of P-HTTs leads to the reduction of friction loss as compare to that of HTT. Heat transfer, friction loss and thermal performance factor increase as d/w decreases and s/w increases. For the present range, the maximum thermal performance factor of 1.28 is obtained by using the P-HTT with d/w=0.2 and s/w=2.0 at the Reynolds number of 6000. In addition, the empirical correlations for Nusselt number, friction factor and thermal performance factor give accurate predictions within ±4%, ±6% and ±3%, respectively.

Heat transfer enhancement by helically twisted tapes inducing co- and counter-swirl flows

An experimental investigation has been conducted for determining heat transfer enhancement by inserting helically twisted tapes, to induce co- and counter-swirl flows, (the tapes are symbolized as co-HTT and C-HTT, respectively). Tape pitch ratio (p/D) was varied between 1.0 and 2.0, while tape width ratio (w/D) and twist ratio (y/w) were fixed at 0.2 and 3.0, respectively. The experiments were performed for fully developed turbulent flow with Reynolds number range (Re) between 6000 and 20,000, under uniform wall heat flux condition. At similar conditions, the use of Co-HTT results in lower Nusselt number and friction factor but higher thermal performance factor than that of C-HTT. Nusselt number and friction factor increase with decreasing pitch ratio, while thermal performance factor possesses opposite trend. In addition, the empirical correlations for Nusselt number, friction factor and thermal performance factor as functions of the Reynolds number (Re), Prandtl number (Pr) and tape pitch (p/D), were developed through a multi-variant linear normal regression.

Heat transfer and friction factor characteristics in turbulent flow through a tube fitted with perforated twisted tape inserts

This work deals with the experimental investigation on Nusselt number, friction factor and thermal performance factor in a circular tube equipped with perforated twisted tape inserts with four different porosities of Rp=1.6, 4.5, 8.9 and 14.7%. The experiments were conducted in a turbulent flow regime with Reynolds number ranging from 7200 to 49,800 using air as the working fluid under uniform wall heat flux boundary condition. The experimental results revealed that both heat transfer rate and friction factor of the tube fitted with perforated twisted tapes were significantly higher than those of the plain tube. Over the range investigated, Nusselt number, friction factor and thermal performance factor in the tube with perforated twisted tape inserts was found to be 110 –340, 110 –360 and 28–59% higher than those of the plain tube values, respectively. In addition, the empirical correlations of Nusselt number, friction factor and thermal performance factor were formulated from the experimental results of tape inserts.

Heat transfer enhancement in tube by inserting uniform/non-uniform twisted-tapes with alternate axes: Effect of rotated-axis length

Heat transfer enhancement in a tube using twisted tapes with alternate axes at different alternate lengths (in term of alternate length to twist length ratio, l/y = 0.5, 1.0, 1.5 and 2.0) has been investigated in the present work. The twisted tapes with both uniform and non-uniform alternate lengths (TAs and N-TAs) as well as a typical twisted tape (TT) were comparatively tested for Reynolds number between 5000 and 21,500. The experimental results revealed that all the TAs and N-TAs yielded higher Nusselt number and friction factor than the TT and the Nusselt number and friction factor obtained were considerably increased with decreasing the alternate length (l). Heat transfer and friction factor by the N-TAs were found to be directly dependent of alternate length rather than the variation of the length. In the present study, the optimum tradeoff between the enhanced heat transfer and increased friction was found by using the TA at l/y = 0.5, giving the highest heat transfer rate as well as the maximum thermal performance factor. In addition, empirical correlations for Nusselt number, friction factor and performance evaluation criteria to assess the real benefits in using the TAs/N-TAs of the enhanced tube were also determined.

Heat and mass transfer studies on compact generator of R134a/DMF vapour absorption refrigeration system

Experimental investigation on the performance of compact generator of R134a/DMF vapour absorption refrigeration system is presented. The system uses brazed plate heat exchangers as generator, condenser, absorber, evaporator and solution heat exchanger and has a rated cooling capacity of 1 kW. The influence of driving temperature ratio, driving pressure ratio, R134a mass fraction and solution two phase Reynolds number is studied. This kind of system can be operated with low grade thermal energy such as solar energy, waste heat, etc. The generator temperature is chosen accordingly between 353 K and 368 K. Desorption ratio and Sherwood number increase as the solution Reynolds number, solution initial mass fraction, and driving temperature ratio increase whereas they decrease as the driving pressure ratio increases. The performance of the compact generator at different operating conditions is presented. Based on the present data, empirical correlations for Nusselt number and Sherwood number are proposed.

Heat transfer and thermal performance characteristics of heat exchanger tube fitted with perforated twisted-tapes

Twisted tape insert was applied as a swirling flow generator for the passive heat transfer enhancement in the present work. The influences of the perforated twisted tapes (PTs) on the heat transfer, pressure loss and thermal performance characteristics were investigated experimentally. The experiments were performed under uniform wall heat flux condition by using PTs with y/W = 3, 4 and 5, d/W = 0.11, 0.14 and 0.17 and s/W = 0.4, 0.6 and 0.8 where y is a twist length, d is a perforation hole diameter, s is a spacing between holes (pitch) and W is a tape width. The experimental results reveal that Nusselt number increased with decreasing s/W and y/W and increasing d/W. For the present range, the maximum heat transfer was obtained by utilizing the tape with s/W = 0.4, d/W = 0.17 and y/W = 3, which is higher than those obtained from the plain tube with and without typical twisted tape by around 27.4 and 86.7%, respectively. In addition, the empirical correlations for Nusselt number, friction factor and thermal performance are also proposed in the present paper.

Friction and heat transfer characteristics of laminar swirl flow through the round tubes inserted with alternate clockwise and counter-clockwise twisted-tapes

The thermohydraulic characteristics of the circular tubes equipped with alternate clockwise and counter-clockwise twisted-tapes (TA) for the Reynolds number ranging from 830 to 1990, are reported. In the experiments, the twisted tapes with three different twist ratios (y/W = 3, 4 and 5) were inserted individually into the uniform wall heat flux tubes where water was utilized as the working fluid. The plain tube and the tube inserted with twisted tape (TT) were also tested, for comparison. The obtained results reveal that, Nusselt number, friction factor and thermal performance factor associated by TA are higher than those associated by TT. Among the tapes examined, the one with the smallest twist ratio of y/W = 3 is found to be the most efficient for heat transfer enhancement. For the range studied, the applications of both TT and TA for heat transfer enhancement are found to be promising since the thermal performance factors determined under the same pumping power are all above unity. In addition, the empirical correlations for Nusselt number, friction factor and thermal performance factor have also been developed. The consequential results obtained from the correlations are found to be in good agreement with the experimental results within ± 8% variation for Nusselt number (Nu), ± 8% for thermal performance factor (η) and ± 5% for friction factor (f).

Heat Transfer and Friction Factor Studies in a Circular Tube Fitted with Twisted Tape Consisting of Wire-nails

This paper deals with the experimental investigation on Nusselt number, friction factor and thermal enhancement factor of a double pipe heat exchanger equipped with twisted tape consisting wire nails (WN-TT) and plain twisted tapes (P-TT) with three different twist ratios of y = 2.0, 4.4 and 6.0. Test runs are conducted using the water as the working fluid with Reynolds number range between 2000 and 12000 for WN-TT and P-TT. It is found that Nusselt number, friction factor and thermal enhancement factor in the tube equipped with WN-TT appreciably higher than those in the tube fitted with P-TT and plain tube. Over the range considered Nusselt number, friction factor and thermal enhancement factor in a tube with WN-TT are respectively, 1.08 to 1.31, 1.1 to 1.75 and 1.05 to 1.13 times of those in tube with P-TT. The better performance of WN-TT is due to combined effects of the following factors: (1) common swirling flow generated by P-TT, (2) additional turbulence offered by the wire nails. Empirical correlations for Nusselt number, friction factor and thermal enhancement factor are also formulated from the experimental results of WN-TT and P-TT.

Studies on heat transfer and friction factor characteristics of turbulent flow through a micro-finned tube fitted with left–right inserts

Experimental investigation on heat transfer and friction factor characteristics of micro-finned tube fitted with full-length twisted tape and left–right twisted tape inserts of twist ratio 7.44, 8.27 and 11.17 has been presented. The experimental data obtained were compared with those obtained from plain tube published data. The heat transfer coefficient enhancement for left–right twisted inserts is higher than that for full-length twisted tape inserts for a given twist ratio. The empirical correlation for Nusselt number, friction relating Reynolds number and twist ratio was formed for both twisted tape inserts and left–right inserts and found to fit the experimental data within ±3.6% and ±2.5% for Nusselt number and ±7% and ±8.5% friction factor, respectively. Performance evaluation analysis was made and the maximum performance ratio was obtained for left–right twisted tape inserts.