Nusselt Number Data Research Articles

Study on Advanced Internal Cooling Technologies for the Development of Next-Generation Small-Class Aircraft Engines

An innovative internal cooling structure named multislot cooling has been invented for high-pressure turbine (HPT) nozzles and blades. This cooling structure has been designed to be simple and inexpensive and to exhibit good cooling performance. In order to confirm the cooling performance of this structure, test pieces of dummy turbine nozzles were manufactured. Three geometric parameters (width of slots, overall height of cooling channel, and height of jet impingement) are associated with these test pieces. The cooling performance tests were conducted by using these test pieces for several Reynolds numbers of the mainstream hot gas [2.2×105–3.4×105] and cooling airflow [3×103–1×104]. Infrared images of the heated surfaces of the test pieces were captured for every Reynolds number in the tests, and then the distributions of the cooling effectiveness were obtained. Simultaneously, the pressure losses were measured. This paper describes the hot gas flow tests performed to confirm the effects of the geometric parameters on the cooling performance and pressure loss, and to obtain data of Nusselt number and pressure loss coefficient for the design of turbine nozzles in the future by applying this new cooling structure to next-generation small-class aircraft engines. Additionally a preliminary analysis of airfoil cooling was performed to evaluate both cooling performance of conventional impingement cooling and multislot cooling when applied to a HPT nozzle. As a result it was found that the multislot cooling is well applicable to cooling of HPT airfoils.

Mathematical modeling of the heat transfer and flow field of liquid refrigerants in a hydrofluidization system with a stationary sphere

Hydrofluidization is a method of chilling and freezing of foods that uses a circulating system that pumps the refrigerating liquid upwards through orifices and/or nozzles into a refrigerating vessel, thereby creating submerged agitating jets and increasing heat transfer to foods during freezing. The objective of this work was to develop a model to estimate the fluid flow and heat and mass transfer in a hydrofluidization system. A study case of modeling and validating the heat transfer to a single stationary copper sphere of 20-mm diameter impinged by a single round jet of liquid was carried out using computational fluid dynamics. The simulations were performed using parameters such as: velocity of the liquid at the orifice exit (2.36–7.07 m s −1), temperature of the liquid refrigerant (−5 to −15 °C) and distance between the orifice and the stagnation point of the sphere (1 and 5 cm). In general, the errors of the model were in the order of magnitude of the uncertainty of the experimental data of Nusselt number averaged over the sphere surface. Also, the simulated heat transfer and flow field parameters were comparable with those obtained in literature for similar systems.

Heat transfer from rotating finned heat exchangers with different orientation angles

The local and average heat transfer characteristics of spoke like fins that extend outward from a rotating shaft have been determined experimentally. The experiments encompassed a number of geometrical parameters, including the length and chord of the fins, the number of fins deployed around the circumference of the shaft and the orientation angles of the fin. The experiments cover a wider range of rotational speeds, which varies from 25 up to 2,000 rpm. Three wire heat flux sensors have been used in conjunction with a slip ring apparatus to evaluate the local and average heat transfer coefficients. The output results indicated that, the heat transfer transition on rotating fins occurs at Reynolds number lower than encountered on the stationary rectangular fins in crossflow. In general, with non zero incidence angle, the rotating system acts as a fan and creates axial air motion, which enhance the heat transfer rate. However, the effect of orientation angle reduces with increasing the rotational speed. The Nusselt number data are independent of the number of fins in the circumferential array at high rotational speed and are weakly dependent at low Reynolds numbers. To facilitate the use of the results for design, correlations were developed which represent the fin heat transfer coefficient as a continuous function of the investigated independent parameters.

Heat transfer of a radially rotating furrowed channel with two opposite skewed sinusoidal wavy walls

An experimental study of heat transfer in a radially rotating furrowed channel with two opposite walls enhanced by skewed sinusoidal waves was performed to generate the full-field Nusselt number ( Nu) data over two wavy walls. Although the static wavy channel has been proven as an effective heat transfer enhancement (HTE) measure, no previous study examined its heat transfer performances with rotation. As another first-time attempt for turbine cooling researches, the Nu scans over the entire rotational leading (stable) and trailing (unstable) walls were acquired using the infra-red thermography which proved highly advantageous due to its capability to examine the rotating buoyancy effects in details. A selection of experimental data illustrates the full-field Nu variations responding to the changes of Reynolds ( Re), rotation ( Ro) and buoyancy ( Bu) numbers. Parametric analysis is subsequently followed to disclose the individual and interdependent Re, Ro and Bu effects on Nu in the attempt to derive the heat transfer correlations for the area-averaged Nu over the developed flow region ( N u ¯ FD ) on the rotational leading and trailing wavy walls. Within the parametric ranges tested, the rotational leading and trailing N u ¯ FD values respectively fall between 3.4–4.3 and 4.2–6.4 times of the Dittus–Boelter datum, which grant the potential applicability of wavy channel as a HTE measure for cooling of gas turbine rotor blades.

Application of artificial neural networks for prediction of natural convection from a heated horizontal cylinder

A generalized neural network analysis for natural convection heat transfer from a horizontal cylinder is developed in this paper. Cylinder diameter, cylinder surface temperature and ambient temperature are selected as the input parameters, while the Nusselt number as the output. A three-layer network is used for predicting the Nusselt number. The number of the neurons in the hidden layer was determined by a trial and error process together with cross-validation of the experimental data evaluating the performance of the network and standard sensitivity analysis. The trained network gives the best values over the correlations with less than 2.5% mean relative error. The experimental data of the average Nusselt number over the horizontal cylinders having different diameters of 4.8 mm–9.45 mm are from Atayılmaz and Teke [1]. The results from the trained network were compared with the proposed correlation for the average Nusselt number over the cylinder and it is shown that the results are in satisfactory agreement. The Nusselt numbers obtained from the experimental study were seen to be consistent by ± 20% with the well known correlations for natural convection heat transfer from horizontal cylinder developed by Morgan [2], Fand and Brucker [3], and Churchill and Chu [4]. Moreover it is seen that that results from the trained network show absolute agreement with the experimental data in ± 5% deviation band better than the correlations given by Morgan [2], Fand and Brucker [3], and Churchill and Chu [4].

A CFD study of convection in a double glazed window with an enclosed pleated blind

A numerical study has been conducted of steady free convection in a double glazed window with a between-panes pleated cloth blind. The model geometry is based on a commercial product that is available on the consumer market in North America. The study considers the effects of Rayleigh number, enclosure aspect ratio, and blind geometry on the convective heat transfer. A simplified model of the coupled convective and radiative heat transfer is also presented. Sample results show that the average Nusselt number data from the CFD study can be combined with a one-dimensional model to closely predict the glazing-to-glazing U-value.

Effects of confining walls on heat transfer from a vertical array of isothermal horizontal elliptic cylinders

Steady state two-dimensional natural convection heat transfer from the vertical array of five horizontal isothermal elliptic cylinders with vertical major axis which confined between two adiabatic walls has been studied experimentally. Experiments were carried out using a Mach–Zehnder interferometer. The Rayleigh number based on cylinder major axis was in the range 10 3 ⩽ Ra ⩽ 2.5 × 10 3 , and dimensionless wall spacing 1.5 ⩽ t / b ⩽ 9 and infinity. The effect of wall spacing and Rayleigh number on the heat transfer from the individual cylinder and the array were investigated. Experiments are performed for ratio wall spacing to major diameter t/ b = 1.5, 2, 2.5, 3, 3.5, 4, 5, 6, 7, 8, 9 and infinity. A correlation based on the experimental data for the average Nusselt number of the array as a function of Ra and t/ b is presented in the aforementioned ranges. A relation has been derived for optimum wall spacing at which the Nusselt number of the array attains its maximum value. At optimum wall spacing, approximately 10% increase in the heat transfer from the confined array of elliptic cylinders has been observed as compared to the unconfined case. Also, a heat transfer correlation has been proposed for a single elliptic cylinder with vertical major axis and has been compared with earlier works.

Liquid Single-Phase Flow in an Array of Micro-Pin-Fins—Part I: Heat Transfer Characteristics

This is Paper I of a two-part study concerning thermal and hydrodynamic characteristics of liquid single-phase flow in an array of micro-pin-fins. This paper reports the heat transfer results of the study. An array of 1950 staggered square micro-pin-fins with 200×200 μm2 cross-section by 670 μm height were fabricated into a copper test section. De-ionized water was used as the cooling liquid. Two coolant inlet temperatures of 30°C and 60°C and six maximum mass velocities for each inlet temperature ranging from 183 to 420 kg/m2 s were tested. The corresponding inlet Reynolds number ranged from 45.9 to 179.6. General characteristics of average and local heat transfer were described. Six previous conventional long and intermediate pin-fin correlations and two micro-pin-fin correlations were examined and were found to overpredict the average Nusselt number data. Two new heat transfer correlations were proposed for the average heat transfer based on the present data, in which the average Nusselt number is correlated with the average Reynolds number by power law. Values of the exponent m of the Reynolds number for the two new correlations are fairly close to those for the two previous micro-pin-fin correlations but substantially higher than those for the previous conventional pin-fin correlations, indicating a stronger dependence of the Nusselt number on the Reynolds number in micro-pin-fin arrays. The correlations developed for the average Nusselt number can adequately predict the local Nusselt number data.

Heat transfer in tilted reciprocating anti-gravity open thermosyphon

This experimental study generates a new set of Nusselt number ( Nu) data from two opposite upper and lower edges of a tilted reciprocating anti-gravity open tubular thermosyphon that emulates closely the realistic ‘ shaker-bored’ cooling conditions inside a piston of marine propulsive diesel engine. The impacts of thermosyphon inclination on heat transfer are described by way of comparisons between two sets of Nu data generated from the vertical and tilted reciprocating thermosyphons. Nusselt number differences between two opposite upper ( Nu Upper) and lower ( Nu Lower) edges along the tilted thermosyphon are amplified as the reciprocating force increases; while no appreciable differences between Nu Upper and Nu Lower are observed in the tilted static thermosyphon or in the vertical static and reciprocating thermosyphon. For such tilted reciprocating open thermosyphon, the individual and interactive influences of inertial, reciprocating and buoyancy forces on heat transfer are described for both sub-cooled (single phase) and superheated (two phase) conditions. Due to the synergistic effects of inertial force, reciprocating force and buoyancy interactions for all the experimental conditions tested, the worst heat transfer scenarios in terms of the axially averaged Nu values in the tilted reciprocating open thermosyphon fall to the level of 0.82 times of the static levels. A set of empirical heat transfer correlations which permits the evaluation of axially averaged Nusselt numbers is developed to assist the design activity of such piston cooling system.

The effect of viscous dissipation and rarefaction on rectangular microchannel convective heat transfer

The effect of viscous dissipation and rarefaction on rectangular microchannel convective heat transfer rates, as given by the Nusselt number, is numerically evaluated subject to constant wall heat flux ( H2) and constant wall temperature ( T) thermal boundary conditions. Numerical results are obtained using a continuum based, three-dimensional, compressible, unsteady computational fluid dynamics algorithm with slip velocity and temperature jump boundary conditions applied to the momentum and energy equations, respectively. For the limiting case of parallel plate channels, analytic solutions for the thermally and hydrodynamically fully developed momentum and energy equations are derived, subject to both first- and second-order slip velocity and temperature jump boundary conditions, from which analytic Nusselt number solutions are then obtained. Excellent agreement between the analytical and numerical results verifies the accuracy of the numerical algorithm, which is then employed to obtain three-dimensional rectangular channel and thermally/hydrodynamically developing Nusselt numbers. Nusselt number data are presented as functions of Knudsen number, Brinkman number, Peclet number, momentum and thermal accommodation coefficients, and aspect ratio. Rarefaction and viscous dissipation effects are shown to significantly affect the convective heat transfer rate in the slip flow regime.

Experimental studies on heat transfer and friction factor characteristics of thermosyphon solar water heater system fitted with spacer at the trailing edge of twisted tapes

Experimental investigation of heat transfer and friction factor characteristics of thermosyphon solar water heater system with full- length twist, twist fitted with rod and spacer fitted at the trailing edge for lengths of 100, 200 and 300 mm for twist ratio 3 and 5 has been carried out and compared with plain tube collector for the same operating conditions. The experimental data for Nusselt number and friction factor for plain tube collector is verified with fundamental equations. Empirical correlations are developed for Nusselt number and friction factor for twist ratio 3 and 5. Results conclude that the decrease in Nusselt number for full length helical twist compared to twist fitted with rod is minimum and is quite significant for twist with spacer. But the decrease in friction factor is maximum in twist fitted with spacer compared to twist fitted with rod. The over all performance for twist fitted with rod is found to be better than twist fitted with spacer.

Experimental Study on Oscillatory Natural Convection in a Hele-Shaw Cell due to Unstably Heated Side

The oscillatory motion of natural convection in a porous medium has been investigated experimentally using a Hele-Shaw cell technique. The cell has been heated on the lower half and cooled on the upper half along the same vertical sidewall. Flows have been visualized using the pH indicator method. Photographs of natural convection patterns as well as average Nusselt number data have been presented for different Rayleigh numbers. Oscillatory motion of natural convection has been observed for large enough Rayleigh numbers and the critical Rayleigh number has been estimated to be between 120 and 450. Scaling analysis has been conducted to understand the heat transfer and the oscillating mechanism. According to the scaling analysis, it has been found that the average Nusselt number is proportional to the square root of the Rayleigh number, and that the oscillation frequency is proportional to the Rayleigh number. Obtained experimental data support the scaling analysis.

人力飛行機の換気口がパイロットの冷却と胴体抵抗に与える影響

We studied effect of ventilation ports on aerodynamics of the fuselage of a human-powered airplane and cooling performance of the pilot. An opening made in the fuselage is one of remedies for enhancing the performance of the pilot. On the other hand, the opening influences aerodynamic characteristics of the airplane, in particular the drag of the fuselage. When the ratio of inlet and outlet areas is larger than 3.0, the flux of air taken at the inlet is almost proportional to the area of inlet and depends weakly on the position and area of the outlet. Cooling of the pilot is estimated from the data of Nusselt number around the cylinder in the uniform flow at the Reynolds number defined by a velocity averaged over a cross section. An additive drag due to interaction between the injected flow from the outlets and the ambient flow around the fuselage depends strongly on the location of the outlet; the nearer to the trailing edge the outlet position moves, the less the drag increases.

The prediction of convective heat transfer in floor-heating systems by artificial neural networks

In this study the floor Nusselt and Rayleigh numbers for the floor-heating systems are estimated by the artificial neural networks (ANN). Numerical data for the floor Nusselt and Rayleigh numbers are available in the literature. A piece of the numerical values are used for training the ANN. The values estimated by the ANN are compared with the numerical values and the results of an equation given in the literature. It has been seen that the results of the ANN are very close to the numerical data and the results of the equation.

Experimental investigation on free convection from a horizontal cylinder beneath an adiabatic ceiling

Steady two-dimensional free convection heat transfer from a horizontal, isothermal cylinder located underneath an adiabatic ceiling is studied experimentally using a Mach–Zehnder interferometer. Effects of the ratio of cylinder spacing from the adiabatic ceiling to its diameter ( L/ D) on heat transfer from the cylinder are investigated for various Rayleigh numbers. Experiments are performed for L/ D = 0.1, 0.3, 0.5, 0.7, 1.0, 1.5 and 2.4, and the Rayleigh number ranging from 1000 to 40,000. For each experiment thermal and flow fields are illustrated. Results indicate that the adiabatic ceiling has no influence on free convection heat transfer from the cylinder for L/ D ⩾ 1.5. But by reducing this ratio from 1.5 to 0.5, Nusselt number decreases considerably. For close spacing of ( L/ D < 0.5), average Nusselt number again increases due to the vortex formation at the top of the cylinder where its effect is present as a sharp increase in the magnitude of local Nusselt number around circumferential position 130 ⩽ θ ⩽ 180. Flow visualization by smoke is done to exhibit the existence and the location of the vortices. A correlation based on the experimental data for the average Nusselt number of the cylinder as a function of Ra and L/ D is presented in the aforementioned ranges.

Effects of shape factors on flow and heat transfer in corrugated-undulated channels with sinusoidal waves

Three-dimensional numerical simulations of flow and heat transfer in crosscorrugated-undulated channels with sinusoidal waves under laminar flow conditions are reported. This simulation adopts the multi-channel computational domain. The main aim of this study is to investigate the effects of shape factors of the undulated plate and Reynolds number ( Re) on flow and heat transfer. Data for Nusselt number ( Nu) and friction factor ( f) are presented for air flowrates in the range 100 ≤ Re ≤ 1500. Performance evaluation and analysis of entry effects are made. The results confirm that the effects of both undulation height and Re are significant but that the effect of undulation pitch is much less marked. As the height of the undulated plate increases, f decreases; the effect of the undulation pitch on f has similar characteristics. Minimum f is obtained in the largest height (CP-UH0) and the largest pitch (CP-UP0) channels, respectively. For the heat transfer, the results indicate that the average Nu with increasing height first decreases and then increases at the same Re, and the maximum average Nu is achieved on the CP-UH0 geometry; the average Nu, however, is nearly independent of the pitch. The maximum local Nu ( Nu C or Nu U) is located in the upstream region of the crest of the conjugate channel and near the downstream end of the trailing edge. The minimum local Nu is situated around the four corners where the top plate touches the bottom one. Performance evaluation shows that the channels having the largest undulation height or largest pitch are optimal. The average Nu having the largest undulation height (CP-UH0) geometry is about ten times higher and the concomitant f is 18.52 times higher, when compared with a straight channel having a square cross-section. With the same reference channel, the average Nu having the largest undulation pitch (CP-UP0) geometry is 9.11 times higher at the cost of a 22.12 times higher f.

Heat transfer and turbulent flow friction in a circular tube fitted with conical-nozzle turbulators

The paper deals with an experimental study of the influence of conical-nozzle turbulator inserts on heat transfer and friction characteristics in a circular tube. In the present work, the turbulators are placed in the test tube section with two different types: (1) diverging nozzle arrangement (D-nozzle turbulator) and (2) converging nozzle arrangement (C-nozzle turbulator). The turbulators are thoroughly inserted inside the tube with various pitch ratios, PR=2.0, 4.0, and 7.0. The Reynolds number based on the bulk average properties of the air is in a range of 8000 to 18,000 and the experimental data obtained are compared with those obtained from the plain tube and from the literature. The experimental results reveal that increasing the Reynolds number at a given pitch ratio of the turbulators leads to the significant increase in Nusselt number indicating enhanced heat transfer coefficient due to rising convection as the flow increases. However, the friction factor at a given Reynolds number considerably increases with the reduction of pitch ratio and Reynolds number. The D-nozzle arrangement, creating stronger reverse/turbulence flow, provides higher the heat transfer rate and friction factor than the C-nozzle arrangement. The heat transfer rates obtained from using both nozzle-turbulators, in general, are found to be higher than that from the plain tube at a range of 236 to 344%, depending on Reynolds number and the turbulator arrangements. In addition, proposed correlations from the present experimental data for Nusselt number and friction factor are also presented.

Convective Cooling of a PCB Like Surface With Mixed Heating Conditions in a Vertical Channel

Abstract Printed circuit boards (PCBs) with uniform surface temperature and uniform wall heat flux are ideal to study. However, in reality, the heating conditions existing on the PCB surfaces are much different from the ideal ones. Present attempts have been made to study different combinations of uniform heat flux (UHF) and uniform wall temperature (UWT) heating conditions on a single surface and to develop more realistic relationships between various flow and thermal parameters for evaluating the local and averaged Nusselt number. Both the numerical and experimental investigations were undertaken to study partial and mixed UHF and UWT heating conditions on a buoyancy assisted convection cooling of simulated PCB forming one wall of the vertical channel while, the other wall was kept insulated. The current work considers moderate to high flow Reynolds number (14.1×103≤Re≤2.35×105) in the channel and range of heat fluxes near that occurring in electronic cooling applications using air as a coolant (0.0&amp;lt;q≤5.0W∕cm2). Data for heat flux and Nusselt number occurring at various locations of the plate surface under different heating conditions are presented to analyze variation patterns; and an empirical relation is put forward which is capable of predicting Nu under the heating conditions mentioned. The empirical expression obtained can be used for getting an optimized layout of the PCBs inside the equipment cabinet, thus resulting in better design for more reliable and safe operation under potentially harsh environment and/or maximum load condition.

Air Cooling of Variable Array of Heated Modules in a Vertical Channel

Abstract The effect of array size and substrate thermal conditions upon heat transfer characteristics of an array of heated modules subjected to buoyancy assisted convection cooling in air is investigated. The comparative analysis of numerical and experimental data for multimodular array of heated modules mounted on a printed circuit board (PCB) forming one of the walls of a vertical channel is presented. Numerical investigation involved turbulent flow analysis based on a realizable k−ε model. Experimental efforts involved development of a test rig and use of state-of-the-art data acquisition system for simulating the heat transfer phenomenon from the module surfaces under various test conditions. Moderate to high flow velocities in the channel and the heat flux values near those occurring in electronic cooling applications using air as coolant are considered. Initially, the data for mean Nusselt number occurring at various rows in the array under consideration are presented, and in order to validate the numerical model, variation pattern and deviation between numerical and experimental results are analyzed keeping the substrate (PCB) as the insulated surface. The same numerical model was extended to study the cases of varying substrate thermal conditions. An empirical relation is proposed for evaluating Nu under different substrate thermal conditions for array geometries considered and flow rates within the parametric ranges discussed.

Heat Transfer to Small Horizontal Cylinders Immersed in a Fluidized Bed

Heat transfer to horizontal cylinders immersed in fluidized beds has been extensively studied, but mainly in the context of heat transfer to boiler tubes in coal-fired beds. As a result, most correlations in the literature have been derived for cylinders of 25-50mm diameter in vigorously fluidizing beds. In recent years, fluidized bed heat treating furnaces fired by natural gas have become increasingly popular, particularly in the steel wire manufacturing industry. These fluidized beds typically operate at relatively low fluidizing rates (G∕Gmf&lt;5) and with small diameter wires (1-6mm). Nusselt number correlations developed based on boiler tube studies do not extrapolate down to these small size ranges and low fluidizing rates. In order to obtain reliable Nusselt number data for these size ranges, an experimental investigation has been undertaken using two heat treating fluidized beds; one a pilot-scale industrial unit and the other a lab-scale (300mm diameter) unit. Heat transfer measurements were obtained using resistively heated cylindrical samples ranging from 1.3 to 9.5mm in diameter at fluidizing rates ranging from approximately 0.5×Gmf (packed bed condition) to over 10×Gmf using aluminum oxide sand particles ranging from dp=145-330μm (50–90 grit). It has been found that for all cylinder sizes tested, the Nusselt number reaches a maximum near 2×Gmf, then remains relatively steady (±5-10%) to the maximum fluidizing rate tested, typically 8-12×Gmf. A correlation for maximum Nusselt number is developed.