Shah Correlation Research Articles

Heat transfer characteristics of subcooled water in a hypervapotron under high mass fluxes and high heat fluxes

In order to investigate the heat transfer characteristics of hypervatron in the divertor dome of the International Thermonuclear Experimental Reactor (ITER), the off-center electrically heating method was used simulate the one-side heating condition in the engineering application. The heat transfer experiments of subcooled water were carried out in a vertically upward hypervapotron under the system parameters as follows: system pressure P = 2.7, 3.2, 3.7 MPa, mass flux G = 2000–5000 kg·m−2·s−1, and equivalent one-side radiating heat flux qe = 2–5 MW·m−2. The effects of parameters on heat transfer were discussed in detail. The results show that the heat transfer coefficient h is significantly affected by G in the single phase (SP) region; the h is synthetically influenced by P, G, q in the partially boiling (PB) region; the h is only affected by q in the fully developed boiling (FDB) region. The experimental data were compared with the typical correlations in single phase region and subcooled boiling region, respectively. The results show that the Dittus-Boelter correlation and the modified Shah correlation have good agreement with the experimental data. The typical CHF correlations for smooth tubes were assessed by the CHF data, the results indicate that experimental Bocr are overpredicted by most CHF correlations, so it can be speculated that the hypervapotron can obtain higher CHF values than smooth tubes.

Simulation of working fluid mass distribution in small-scale Organic Rankine Cycle system under sub-critical conditions

Distribution of working fluid mass will significantly impact off-design performance of the Organic Rankine Cycle. In this paper, both the evaporator and the condenser are divided into three different zones, and the impact of heat transfer correlations and void fraction models selection on the working fluid mass calculation results have been discussed. Afterwards, impact of evaporation and condensation temperatures on working fluid mass distribution in each zone calculated by proposed correlations and models have been evaluated. Four common working fluids which feature different physical properties are taken into account. Results indicate that the selection of heat transfer correlations and void fraction models shows great importance for the calculation of working fluid mass in condenser but rarely affects the calculation results in evaporator. Accordingly, condensation correlation of Shah (1979) and void fraction model of Premoli (1971) is proposed for the discussed system. Furthermore, in condenser the working fluid mass monotonically decreases as the condensation temperature increases, while in evaporator the working fluid mass firstly rises and then falls when the evaporation temperature increases. It can be found that the relevant evaporation temperature at which the largest working fluid mass occurs is related to critical temperatures of the employed working fluids.

Experimental investigation of forced convective condensation heat transfer of hydrocarbon refrigerant in a helical tube

In this paper, the characteristics of two-phase heat transfer and frictional pressure drop for hydrocarbon refrigerant propane condensation in a helical tube were experimentally investigated. A new experimental facility was designed to directly measure the wall temperature along a helical tube with the hydraulic diameter of 10 mm. The experimental conditions were set as: mass flux from 200 to 400 kg/(m2·s), heat flux from 1.4 to 9.6 kW/m2 and saturated temperatures from −40 to 27 °C. Also, the effects of mass flux and vapor quality on heat transfer coefficient and frictional pressure drop were studied. Compared with the experimental data, it showed that Shah correlation could well predict heat transfer coefficients within a mean deviation of ±20%, and Friedel correlation and Müller-Steinhagen & Heck correlation both well predicted frictional pressure drop with a mean deviation less than ±20%. These results will provide important instructions for the tube-side design of spiral wound heat exchanger.

Comparative study of convective heat transfer characteristics of nanofluids

The present research is about to draw a comparison between heat transfer characteristics of gold/deionized water (DIW) and silver/DIW based nanofluid under same heat flux for laminar flow. Experiments are performed on both nanofluid by using different concentrations (0.015, 0.045, 0.0667%) of nano-particles (NPs) in DIW as a base fluid. The experimental study concludes that an appreciable intensification in heat transfer coefficient (HTC) of both nanofluid has been attained as compare to base fluid. However, gold/DIW based nanofluid exhibit better convective heat transfer intensification compared with silver/DIW based nanofluid but Shah correlation cannot predict as much augmentation as in experimental work for both nanofluid. It is also noticed that the anomalous enhancement in Nusselt number and HTC is not only due to the accession in thermal properties but also by the formation of thinner thermal boundary layer at the entrance of the tube due to NPs.

Condensation heat transfer of low GWP ORC working fluids in a horizontal smooth tube

The objective of the current study is to conduct an experimental investigation of condensation heat transfer for the ORC (organic Rankine cycle) working fluids R245fa, Novec®649 and HFE-7000 over a wide range of parameters. Quasi-local condensation heat transfer coefficients are measured in a straight horizontal 7.75-mm-ID smooth tube with flow conditions at mass flux G=150–700kg (m2-s)−1, local equilibrium quality x=0.05–0.95, and reduced pressure, Pr=0.05–0.15. Test data reveal that the environmentally friendly fluids have lower condensation heat transfer coefficients when compared to R245fa. The 141 measured condensation heat transfer coefficients are compared to six well-known correlations. Among the six correlations verified with test data, the Shah correlation shows the best predictive performance for the three fluids tested.

Boiling pressure drop and local heat transfer distribution of water in horizontal straight tubes at low pressure

The objective of the present work is to investigate the heat transfer and pressure drop in flow boiling at low pressure with water as the working medium. The effect of pipe diameter, heat flux and mass flux on boiling pressure drop and local heat transfer coefficient is studied. In the present work, the available correlations are revisited for low pressure flow boiling. Comparison of local heat transfer coefficient with the existing correlation is carried out to identify an appropriate correlation which performs well in complete flow boiling range (subcooled regions and saturated regions) for water at low system pressure.Experiments are performed with eight test sections made of thin walled stainless steel (SS 304) tubes having inner diameters from 5.5 mm to 12 mm and length varying from 550 mm to 1000 mm. The system pressure is varying form 1 bar to 3 bar. No change in slope of heat transfer curve is found for subcooled regions. Heat transfer in all the three regions of subcooled boiling namely partial subcooled boiling, fully developed subcooled and net vapour generation are predicted by a single correlation. Tube diameter has no effect on boiling heat transfer distribution. However, tube diameter affects two phase pressure drop. Increase in mass flux increases the convective heat transfer coefficient. However, mass flux has no influence on subcooled and nucleate boiling heat transfer coefficient. Heat flux increases the boiling heat transfer coefficient. Increase in tube diameter and mass flux decreases the two-phase pressure drop. Most of all the correlations in the subcooled region predict heat transfer coefficient with reasonable accuracy. Kandlikar and Shah correlations perform well in the low pressure saturated boiling i.e. nucleate and convective. None of the available two-phase pressure drop correlations are able to predict the pressure drop in a low pressure system. A correlation is developed to predict two-phase pressure drop in low pressure flow boiling system with a reasonably good accuracy.

Experimental evaluation of the in-tube condensation heat transfer of pure n-pentane/R245fa and their non-azeotropic mixture as an ORC working fluid

The existence of temperature gliding in non-azeotropic mixture working fluids provides a promising opportunity for greatly improved resource utilization in organic Rankine cycle (ORC) systems for geothermal applications. The condensation heat transfer degradation associated with working fluid mixtures is an unavoidable penalty that may reduce the utilization and system benefits by necessitating larger heat exchangers. The objective of the current study is an experimental investigation of condensation heat transfer for R245fa, n-pentane, and a composition of their mixture. Quasi-local condensation heat transfer coefficients are measured in a straight horizontal smooth tube with flow conditions at mass flux G=100 and 150kg(m2s)−1, local equilibrium quality x=0.05–0.80, and reduced pressures Pr=0.05–0.15. The reduced condensation heat transfer coefficients from the test are compared with the predictions from already established mixture correction methods in the literature. Pure components R245fa and n-pentane condensation heat transfer data are well predicted by Shah (1979) correlations for all test conditions. However, their non-azeotropic mixture condensation heat transfer data require additional correction parameter to account for the heat transfer degradation. This correction parameter is correlated by the temperature gliding gradient of mixture fluids. Test data with mixture working fluids from current study are reasonably well predicted by the corrected in-tube correlation.

Boiling heat transfer in small rectangular channels at low Reynolds number and mass flux

Boiling heat transfer experiments were performed in a small rectangular channel (hydraulic diameter, De=3.0mm) with water and methanol. The channel size represents the tube configurations in plate-fin heat exchangers, which are commonly used for generating hydrogen from hydrogen-rich liquid fuels. The tested mass flux ranged from 6.59 to 21.97kgm−2s, heat flux from 13.3 to 30.1kWm−2 and inlet temperatures from ambient to 80°C. Tests were carried out at atmospheric pressure. Local heat transfer coefficients were determined experimentally as a function of vapor quantity along the length of the test section. Insights into heat transfer mechanisms in small channels are presented over a range of Reynolds number from 38 to 263. Experimental results and comparisons with state-of-the-art predictive correlations are presented. The Chen correlation was found to be most suitable for predictions of water boiling heat transfer under the recommended application range for minichannels. For methanol, the Shah correlation was more sound over the range with Re larger than 50, while the Gungor–Winterton equation was more accurate when Re was smaller than 50. In addition, flow boiling instability in minichannels was detected when the flow was dominated by subcooled boiling. However, the periodic oscillations of temperature and pressure disappeared when the heat transfer became dominated by saturated boiling.

Characteristics of Two-Phase Flow Heat Transfer of R-22 and R-290 in Horizontal Circular Small Tube

Hydrocarbon refrigerants have been widely used to replace HFCs. As hydrocarbon, R-290 has no ODP (Ozone Depletion Potential) and negligible GWP (Global Warming Potential). This paper presents flow boiling heat transfer in small tube with R-290 and R-22. The test tube has inner diameter of 7.6 mm and length of 1.07 m. In order to determine the heat transfer coefficient, experiments were carried out for heat fluxes ranging from 10 to 25 kW/m2, mass fluxes ranging from 204 to 628 kg/m2s, and saturation temperatures ranging from 1.87 to 11.9o C. The study analyzed the heat transfer through the local heat transfer coefficient along the flow under the variation of these different parameters. In comparison with R-22, R-290 provides higher heat transfer coefficients. In the prediction of the heat transfer coefficients of R-22 and R-290, the correlation of Shah (1982) and Choi et.al. (2009) best fitted the present experimental result, respectively.

A Study of the Heat Transfer Coefficient of a Mini Channel Evaporator with R-134a as Refrigerant

The present study is to evaluate the heat transfer coefficient of the minichannel copper blocks used as evaporator with R-134a as the refrigerant. Experiments were conducted using three evaporator specimens of different channel hydraulic diameters (1.0mm, 2.0mm, 3.0mm). The total length for each channel is 640 mm. The dimension of each is 100mm.x50mm.x20mm. and the outside surfaces were machined to have fins. They were connected to a standard vapour compression refrigeration system. During each run of the experiment, the copper block evaporator was placed inside a small wind tunnel where controlled flow of air from a forced draft fan was introduced for the cooling process. The experimental set-up used data acquisition software and computer-aided simulation software was used to simulate the pressure drop and temperature profiles of the evaporator during the experimental run. The results were then compared with the Shah correlation. The Shah correlation over predicted and under predicted the values as compared with the experimental results for all of the three diameters and high variation for Dh=1.0mm. This indicates that the Shah correlation at small diameters is not the appropriate equation for predicting the heat transfer coefficient. The trend of the heat transfer coefficient is increasing as the size of the diameter increases.

Critical heat flux of cyclohexane in uniformly heated minichannels with high inlet subcooling

The critical heat flux (CHF) for flow boiling of cyclohexane was experimentally investigated in electrically heated minichannels with inside diameters of (1 and 2)mm, and heated lengths of (360 and 710)mm at mass velocities ranging from (318 to 1274)kg/m2s, heat fluxes from (50 to 1000)kW/m2, and pressures of (1.0, 2.0, 3.0)MPa. Cyclohexane entered the test channel at ambient temperature of about 20°C, equivalent to high subcooling of (162.1, 206.4 and 236.3)°C at (1.0, 2.0 and 3.0)MPa respectively. The critical vapor qualities ranged from −1.35 to 0.83. Results indicated that CHF of cyclohexane increased with increasing mass velocity and decreasing heated length. Reducing channel diameter at the same length-to-diameter ratio was proved to have no effects on CHF values of cyclohexane at the evaluated conditions. CHF mildly increased with an increase in pressure at higher mass velocities, but critical vapor quality always decreased with the increasing pressure. Experimental CHF data were compared with the Katto–Ohno (1984) correlation and Shah (1987) correlation. Good agreements were achieved between the experimental data and those predicted with most deviations not exceeding 30%. A corrected Katto–Ohno CHF correlation is developed to fit the current experimental data. Excellent agreement was obtained with all the deviations (whatever of saturation CHF or subcooled CHF) in the range of ±10% with RMS error of 5.35%.

THERMOFLUID CHARACTERISTICS OF HIGH-QUALITY FLOWIN CHIP-SCALE MICROGAP CHANNELS

Two-phase flow in chip-scale microgap channels offers highly potent thermal management capability and is the foundation for the emerging ”embedded cooling” paradigm of electronic cooling. While heat transfer and pressure drop in such flows are intimately tied to distinct forms of vapor-liquid aggregation, insufficient attention has been paid to characterizing the behavior of high-quality, short channel, microgap flow. This paper focuses on the results of simultaneous photographic and infrared visualization of such two-phase flows, under diabatic conditions, in a single 10 mm × 12 mm× 200 μm microgap channel cooled by low mass fluxes of FC-72. Churn flow, displaying pulsatile flow of confined vapor bubbles and slugs, is found to be the dominant flow regime for this short microgap channel configuration, yielding heat transfer coefficients that are an order-of-magnitude higher than all-liquid flow but are relatively insensitive to flow quality and heat flux. With increasing heat flux, local dryout and regions of elevated wall temperature grow and, periodically, expand to cover a majority of the microgap channel area. The average heat transfer coefficient is found to be in approximate agreement with the Shah correlation for low qualities and the Chen correlation for midlevel flow qualities, but both correlations are found to considerably overestimate the heat transfer coefficient at higher qualities, especially when local dryout becomes more frequent.

친수성 표면 처리를 통한 공기 예열 열교환기의 응축 열전달 성능 연구

콘덴싱 보일러에 이용되는 공기 예열 열교환기에서의 열전달을 향상시키기 위해 전열면에 플라즈마 표면처리가 응축열전달에 미치는 영향에 대하여 연구하였다. 연구 결과 표면처리를 한 친수성 평판이 원판보다 약 10%의 열전달 증진을 보여주었다. 원판과 친수처리 평판에서 측정한 응축 열전달 계수를 Shah 상관식과 비교해 본 결과 Shah 상관식이 원판에서 측정한 응축 열전달 계수를 10% 오차 범위로 잘 예측하는 것으로 나타났다. 따라서, 원판을 이용한 공기예열 열교환기를 설계할 때 Shah 상관식이 이용될 수 있음을 본 연구에서 알 수 있었다. To increase the heat transfer rate of the air pre-heating heat exchanger used for the condensing boiler, We investigated condensation heat transfer coefficients through plasma surface treatment. The hydrophilic surface showed about 10% increase in heat transfer rate than original plate. It shows that Shah correlation can be used to predict the condensation heat transfer coefficient on the original surface within 10% error range after the compatison between Shah correlation and the condensation heat transfer coefficients measured on the hydrophilic surface and original surface. Therefore, we have shown that Shah correlation is available when designing the air pre-heating heat exchanger using the original surface in this study.

An experimental comparison of water based alumina and silica nanofluids heat transfer in laminar flow regime

Experimental investigations were carried out to determine the convective heat transfer performance and pressure drop of Al2O3/water and SiO2/water nanofluids flowing through a circular tube. Measurements show that the addition of small amounts of nano-sized Al2O3 particles to the base fluid increases heat transfer coefficients considerably, while the result for the silica nanofluids contradicts with the alumina nanofluids and this leads to some interesting results. In the case of alumina nanofluids, an average increase of 16% in convective heat transfer coefficient is observed with an average penalty of 28% in pressure drop. Moreover, flow resistance increases significantly compared to the base fluid even at very low concentrations of nanofluids. Finally, measured heat transfer coefficients are compared with predicted ones from the correlation of Shah under the same conditions.

An Empirical Correlation for Steam Condensing and Flowing Downward in a 50mm Diameter Inclined Tube

The heat transfer characteristic of steam condensation in a 50mm diameter and 30° inclined tube was experimentally investigated. Based on the experiment and Akhavan-Behabadi correlation, a new correlation has been developed. It is shown that the heat transfer coefficients for the inclined tube are approximately 1.06-2.98 times higher than those for the horizontal tube. The heat transfer coefficients predicted by Shah correlation, Würfel correlation and Akhavan-Behabadi correlation deviate greatly, though Akhavan-Behabadi correlation is better. But by the developed correlation, more accurate heat transfer coefficients are predicted than Shah correlation, Würfel correlation and Akhavan-Behabadi correlation, and the deviation is less than 15%. The developed empirical correlation is a better one to predict heat transfer coefficients for steam condensation in larger diameter inclined tubes.

Analysis of Annular and Stratified Flows for Vapor Condensation Heat Transfer in Horizontal Tubes

The greater part of the horizontal condenser tube is occupied by the stratified and annular flows, which play important roles in condensation heat transfer coefficients. Both a volume of fluid (VOF) interface tracking method and k-ε two equations model was applied to analyze the characteristics of the stratified and annular flows for horizontal tubes, obtaining distribution of velocity, contours of both temperature and local condensation heat transfer coefficients. The computation shows that an annular flow having thinner liquid film attached on the inner surface of tubes appears at the inlet of the horizontal condenser tube because vapor exerts a higher interfacial shear stress on the gas-liquid interface, therefore, there are a higher local condensation heat transfer coefficients there. Next, as vapor quality decreases and condensate gravity increases along the condenser tube length, the condensation flow pattern transforms from the annular flow into the stratified flow in which local condensation heat transfer coefficients decreases and distributes unevenly along the circumference as liquid film at the bottom of the condenser tube become thicker. In addition, in the stratified flow, a wave structure is formed in the middle of the condensate pool at the bottom of the condenser tube because condensate on the top of the condenser tube slides into the bottom of the condenser tube and collapse each other. The heat transfer rate calculated by the present method is compared to those predicted from a Shah correlation, the agreement is found to be good, and both errors is within 7%.

Cooling performance of nanofluids in a small diameter tube

This article reports convective single-phase heat transfer performance in laminar flow for some selected nanofluids (NFs) in an open small diameter test section. A 0.50mm inner diameter, 30cm long stainless steel test section was used for screening single phase laminar convective heat transfer with water and five different water based NFs. Tested NFs were; Al2O3 (two types), TiO2 (two types) and CeO2 (one type), all 9wt.% particle concentration. The effective thermal conductivity of the NFs were measured with Transient Plane Source (TPS) method and viscosity were measured with a rotating coaxial cylindrical viscometer. The obtained experimental results for thermal conductivity were in good agreement with the predicted values from Maxwell equation. The local Shah correlation, which is conventionally used for predicting convective heat transfer in laminar flow in Newtonian fluids with constant heat flux boundary condition, was shown to be valid for NFs. Moreover, the Darcy correlation was used to predict the friction factor for the NFs as well as for water. Enhancement in heat transfer for NFs was observed, when compared at equal Reynolds number, as a result of higher velocity or mass flow rate of the NFs at any given Reynolds number due to higher viscosity for NFs. However, when compared at equal pumping power no or only minor enhancement was observed.

납작관의 종횡비가 R-410A 증발열전달 및 압력손실에 미치는 영향

In this study, R-410A evaporation heat transfer tests were conducted in flattened tubes made from 5-mm round tubes. The test range covered a saturation temperature of , heat flux of , and mass flux of . The results showed that both the condensation heat transfer coefficient and the pressure drop increased as the aspect ratio increased, with a pronounced increase for an aspect ratio of 4. A comparison of the flattened tube data with existing correlations revealed that the heat transfer coefficients were reasonably predicted by the Shah correlation, and the pressure drops were reasonably predicted by the Jung and Radermacher correlation.

A theoretical analysis about the effect of aspect ratio on single-phase laminar flow in rectangular ducts

Effects of the aspect ratio on single-phase laminar flow resistance in rectangular duct are theoretically studied by way of analyzing the wall shear stress. And the transition Reynolds number with different aspect ratios is also investigated by energy gradient method. The results show that the Poiseuille number increases as the aspect ratio decreases. And the contribution of the skin friction due to the wide side to the total frictional resistance is increased evidently with the decreasing of the aspect ratio. Although the aspect ratio has limited influences on shear stress occurs on narrow side, the decrease of the aspect ratio leads the distribution of local shear stress on wide side transforms from parabola to trapezia gradually and the mean shear stress increases significantly, if the hydraulic diameter is constant. A simplified expression for Poiseuille number is acquired by approximately displacing the infinite series, showing good agreement with the experiments for mini/micro ducts and the correlation of Shah & London. In addition, an approximate correlation is also given for narrow rectangular duct with the aspect ratio less than 0.2. Finally, a polynomial correlation for transition Reynolds number is achieved by energy gradient method, which is consistent with the previous work and experimental data.

Condensation heat transfer and pressure drop in flattened smooth tubes having different aspect ratios

In this study, condensation heat transfer coefficients of R-410A are obtained in flattened stainless tubes made from 5.0 mm inner diameter round tubes. The test range covers saturation temperature 45°C, heat flux 10 kW/m2, mass flux 100∼400 kg/m2s and quality 0.2∼0.8. Results showed that the effect of aspect ratio on condensation heat transfer coefficient appears to be dependent on the flow pattern. For annular flow, the heat transfer coefficient increases as the aspect ratio increases. For stratified flow, however, reverse is true. The pressure drop always increases as aspect ratio increases. Round tube heat transfer correlations were not successful in predicting the flat tube heat transfer data. Modified Shah correlation is proposed, which predicts the data with 18% RMS error. The pressure drop is reasonably predicted by Muller-Steinhagen and Heck or Friedel correlation (22% and 27% RMS error respectively).