Numerical Simulation of Buoyancy-Induced Turbulent Flow Between Two Concentric Isothermal Spheres

Buoyancy-induced turbulent flow and natural convection heat transfer between two differentially heated concentric isothermal spheres is studied numerically. The low-Reynolds-number k–ω model is used for turbulence modeling. The two-dimensional governing equations are discretized using control volume method and solved by employing the alternating direction implicit scheme. Results are presented in the form of streamline and temperature patterns, and local and average Nusselt numbers, over the heated and cooled boundaries for a wide range of Rayleigh numbers (10²–10¹⁰), extending the previous studies to the turbulent flow regime and for the radius ratio of 2. The results of the flow pattern and average Nusselt numbers were compared with the previously published experimental and numerical investigations and very good agreements were observed. For low values of Rayleigh numbers, regions with conduction-dominated flow pattern accompanied with low values of Nusselt numbers were observed, while for higher Rayleigh numbers, the flow pattern was changed to the convection dominated boundary layer type flow, resulting in an increase in the rate of heat transfer and flow velocities adjacent to both inner and outer boundaries. The average Nusselt numbers were correlated against Rayleigh number and a 1/4 power dependence of Ra in both laminar and turbulent regimes is obtained.     

Heat transfer study in a discoidal system: The influence of rotation and space between disks

This article presents an experimental study of the local heat transfer on the rotor surface in a discoidal rotor–stator system air-gap in which an air jet comes through the stator and impinges the rotor. To determine the surface temperatures, measurements were taken on the rotor, using an experimental technique based on infrared thermography. A thermal balance was used to identify the local convective heat transfer coefficient. The influence of the dimensionless spacing interval G between the disks and of the rotational Reynolds number Re was measured and compared with the data available in bibliography. Local convective heat transfer coefficients were obtained for an axial Reynolds number Re_j = 41.6 × 10³, a rotational Reynolds number Re between 0.2 × 10⁵ and 5.16 × 10⁵, and a dimensionless spacing interval G ranging from 0.01 to 0.16.     

Heat transfer study in a rotor–stator system air-gap with an axial inflow

Discoidal rotor–stator systems are nowadays sometimes used in electrical wind generator. The cooling of such a system is a major problem due to the fact that high electrical losses are dissipated for relatively low rotational speed, responsible of the cooling. A new cooling solution is then investigated in this paper. So, this paper presents an experimental study of the local heat transfers on the rotor surface in the air-gap of a discoidal rotor–stator system, in which an air jet comes through the stator and impinges the rotor. To determine the surface temperatures, measurements were taken on the rotor, using an experimental technique based on infrared thermography. A thermal balance equation was used to identify the local convective heat transfer coefficient. The influence of the axial Reynolds number Re_j and the rotational Reynolds number Re was measured and compared with the data available in the literature. Local convective heat transfer coefficients were obtained for an inter-disk dimensionless spacing interval G ranging from 0.01 to 0.16 for Re_j between 0 and 41,666 and for Re between 20,000 and 516,000. The rotating disk can thus be divided into zones: one dominated by the air jet near the center of the rotor and one affected by both the air jet and rotation. Even though these two zones are not located in the same place on the disk, the heat transfers with non-zero impinging jets appear to be continuously improved compared to those with no jets. Critical radii over the rotor surface are identified and correlations are given.     

Experimental study of forced and free convective heat transfer in the thermal entry region of horizontal concentric annuli

Forced and free convective heat transfer for thermally developing and thermally fully developed laminar air flow inside horizontal concentric annuli in the thermal entrance length has been experimentally investigated. The experimental setup consists of a stainless steel annulus having a radius ratio of 2 and an inner tube with a heated length of 900 mm subjected to a constant wall heat flux boundary condition and an adiabatic outer annulus. The investigation covers Reynolds number range from 200 to 1000, the Grashof number was ranged from 6.2 × 10⁵ to 1.2 × 10⁷. The entrance sections used were long tube with length of 2520 mm (L/D_h = 63) and short tube with length of 504 mm (L/D_h = 12.6). The surface temperature distribution along the inner tube surface, and the local Nusselt number distribution versus dimensionless axial distance Z_t were presented and discussed. It is inferred that the free convection effects tended to decrease the heat transfer at low Re number while to increase the heat transfer for high Re number. This investigation reveals that the Nusselt number values were considerably greater than the corresponding values for fully developed combined convection over a significant portion of the annulus. The average heat transfer results were correlated in terms of the relevant dimensionless variables with an empirical correlation. The local Nusselt number results were compared with available literature and show similar trend and satisfactory agreement.     

Experimental Investigation on Flow Boiling Heat Transfer and Pressure Drop of HFC-134a inside a Vertical Helically Coiled Tube

An investigation on flow boiling heat transfer and pressure drop of HFC-134a inside a vertical helically coiled concentric tube-in-tube heat exchanger has been experimentally carried out. The test section is a six-turn helically coiled tube with 5.786-m length, in which refrigerant HFC-134a flowing inside the inner tube is heated by the water flowing in the annulus. The diameter and the pitch of the coil are 305 mm and 45 mm, respectively. The outer diameter of the inner tube and its thickness are respectively 9.52 and 0.62 mm. The inner diameter of the outer tube is 29 mm. The average vapor qualities in test section were varied from 0.1 to 0.8. The tests were conducted with three different mass velocities of 112, 132, and 152 kg/m²-s. Analysis of obtained data showed that increasing of both the vapor qualities and the mass fluxes leads to higher heat transfer coefficients and pressure drops. Also, it was observed that the heat transfer coefficient is enhanced and also the pressure drop is increased when a helically coiled tube is used instead of a straight tube. Based on the present experimental results, a correlation was developed to predict the flow boiling heat transfer coefficient in vertical helically coiled tubes.     

An experimental study of heat transfer to turbulent separation fluid flow in an annular passage

The effect of step height on heat transfer to a radially outward expanded air flow stream in a concentric annular passage was studied experimentally. Separation, subsequent reattachment and developed air flow occurred in the test section at a constant heat flux boundary condition. The experimental investigation was focused on the effect of separation flow on the local and average convection heat transfer. The experimental set-up consists of concentric tubes to form annular passage with a sudden reduction in passage cross-section created by the variations of outer tube diameter at the annular entrance section (D). The outer tube of test section was made of aluminium having 83 mm inside diameter and 600 mm heated length, which was subjected to a constant wall heat flux boundary condition. The investigation was performed in a Re range of 17050-44545, heat flux varied from 719 W/m² to 2098 W/m² and the enhancement of step heights were, s = 0 (without step), 6 mm, 14.5 mm and 18.5 mm, which refer to d/D = 1, 1.16, 1.53 and 1.80, respectively.For all cases, an increase in the local heat transfer coefficient was obtained against enhanced heat flux and or Re. The effect of step variation is prominent in heat transfer at the separation region which increases with the rise of step height and it shows a little effect in the redevelopment region. In the separation region, the local heat transfer coefficient increases up to the maximum value at the reattachment point and then decreases gradually in the redevelopment region. The results have been correlated and compared with forced convection heat transfer in annular passage and show a maximum enhancement of 18% (S_max = 18.5 mm) within the range of step height. The present results show good agreement with previous works and have followed similar trends.     

Experimental and numerical investigation of convection heat transfer of CO2 at supercritical pressures in a vertical mini-tube

Convection heat transfer of CO₂ at supercritical pressures in a 0.27 mm diameter vertical mini-tube was investigated experimentally and numerically for inlet Reynolds numbers exceeding 4.0 × 10³. The tests investigated the effects of heat flux, flow direction, buoyancy and flow acceleration on the convection heat transfer. The experimental results indicate that the flow direction, buoyancy and flow acceleration have little influence on the local wall temperature, with no deterioration of the convection heat transfer observed in either flow direction for the studied conditions. The heat transfer coefficient initially increases with increasing heat flux and then decreases with further increases in the heat flux for both upward and downward flows. These phenomena are due to the variation of the thermophysical properties, especially c_p. The numerical results correspond well with the experimental data using several turbulence models, especially the Realizable k–ε turbulence model.     

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

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

Experimental study on saturated flow boiling heat transfer of R290/R152a binary mixtures in a horizontal tube

An experimental study on the saturated flow boiling heat transfer for a binary mixture of R290/R152a at various compositions is conducted at pressures ranging from 0.2 to 0.4 MPa. The heat transfer coefficients are experimentally measured over mass fluxes ranging from 74.1 to 146.5 kg/(m²·s) and heat fluxes ranging from 13.1 to 65.5 kW/m². The influences of different parameters such as quality, saturation pressure, heat flux, and mass flux on the local heat transfer coefficient are discussed. Existing correlations are analyzed. The Gungor-Winterton correlation shows the best fit among experimental data for the two pure refrigerants. A modified correlation for the binary mixture is proposed based on the authors’ previous work on pool boiling heat transfer and the database obtained from this study. The result shows that the total mean deviation is 10.41% for R290/R152a mixtures, with 97.6% of the predictions falling within ±30%.     

Three-dimensional natural convection in an enclosure with a sphere at different vertical locations

Numerical calculations are carried out for the three-dimensional natural convection induced by a temperature difference between a cold outer cubic enclosure and a hot inner sphere. The immersed-boundary method (IBM) to model a sphere based on the finite volume method is used to study a three-dimensional natural convection for different Rayleigh numbers varying in the range of 10³–10⁶. This study investigates the effect of the inner sphere location on the heat transfer and fluid flow. The flow and thermal fields eventually reach the steady state for all Rayleigh numbers regardless of the sphere location. For Rayleigh numbers of 10⁵ and 10⁶, the variation of local Nusselt number of the sphere along the circumferential direction is large, showing the strong three dimensionality of the natural convection in the enclosure unlike to the cases of lower Rayleigh numbers of 10³ and 10⁴. For the highest Rayleigh number, the local peaks of the Nusselt number on the top wall of the enclosure shows the sinusoidal distribution along the circumferential direction. The flow and thermal fields, and the local and surface-averaged Nusselt numbers on the sphere and the enclosure are highlighted in detail.     

Condensation heat transfer and flow characteristics of R-134a flowing through corrugated tubes

This article presents the condensation heat transfer and flow characteristics of R-134a flowing through corrugated tubes experimentally. The test section is a horizontal counter-flow concentric tube-in-tube heat exchanger 2000 mm in length. A smooth copper tube and corrugated copper tubes having inner diameters of 8.7 mm are used as an inner tube. The outer tube is made from smooth copper tube having an inner diameter of 21.2 mm. The corrugation pitches used in this study are 5.08, 6.35, and 8.46 mm. Similarly, the corrugation depths are 1, 1.25, and 1.5 mm, respectively. The test conditions are performed at saturation temperatures of 40–50 °C, heat fluxes of 5–10 kW/m², mass fluxes of 200–700 kg/m² s, and equivalent Reynolds numbers of 30000–120000. The Nusselt number and two-phase friction factor obtained from the corrugated tubes are significantly higher than those obtained from the smooth tube. Finally, new correlations are developed based on the present experimental data for predicting the Nusselt number and two-phase friction factor for corrugated tubes.     

Experimental study of thermal behaviors in a rectangular channel with baffle of pores

This experimental study attempts to explore the local heat transfer in rectangular channel with baffles, and analyzes the experimental results of baffles with different heights and pores in the event of five Reynolds numbers and three heating quantities. Apart from increasing the perturbation of flow field, the channel's flow field with baffles, which is similar to a backward-facing step flow field, is very helpful to heat transfer. To obtain an optimized baffle and increase the perturbation of flow field, this experiment employed baffles with five heights (H = 10–50 mm) and different numbers of pores (N = 1–3), as well as heat flux: Q = 40–100 l/min, Reynolds number: 702–1752, and heating quantity: q_in = 90–750 W/m². In addition to measurement of overall temperature distribution, emphasis is also placed on analysis of local heat transfer coefficient. Furthermore, heat transfer distribution of channel can be applied to explain how the baffles of pores have an influence upon backward-facing step flow field, shear layer, recirculation region, reattachment region and redeveloped boundary layer. Finally, some empirical formulas derived form experimental results may provide a reference for future design.     

Flow boiling heat transfer coefficient of R-134a/R-290/R-600a mixture in smooth horizontal tubes using varied heat flux method

An experimental study on in-tube flow boiling heat transfer of R-134a/R-290/R-600a refrigerant mixture has been carried out under varied heat flux test conditions. The heat transfer coefficients are experimentally measured at temperatures between ?8 and 5 °C for mass flow rates of 3–5 g s^?1. Acetone is used as a hot fluid which flows in the outer tube of diameter 28.57 mm while the refrigerant mixture flows in the inner tube of diameters 9.52 and 12.7 mm. By regulating the acetone flow conditions, the heat flux is maintained between 2 and 8 kW/m² and the pressure of the refrigerant is maintained between 3.2 and 5 bar. The comparison of experimental results with the familiar correlations shows that the correlations over predict the heat transfer coefficients for this mixture when stratified and stratified-wavy flow prevail. Multiple regression technique is used to evolve and modify existing correlations to predict the heat transfer coefficient of the refrigerant mixture. It is found that the modified version of Lavin–Young correlation (1965) predicts the heat transfer coefficient of the considered mixture within an average deviation of ±20.5 %.     

Pressure Drop,Boiling Heat Transfer and Flow Patterns during Flow Boiling in a Single Microchannel

The boiling heat transfer and two-phase pressure drop of water in a microscale channel were experimentally investigated. The tested horizontal rectangular microchannel had a hydraulic diameter of 100 μ m and length of 40 mm. A series of microheaters provided heat energy to the working fluid, which made it possible to control and measure the local thermal conditions in the direction of the flow. Both the microchannel and microheaters were fabricated using a micro-electro-mechanical systems (MEMS) technique. Flow patterns were obtained from real-time flow visualizations made during the flow boiling experiments. Tests were performed for mass fluxes of 90, 169, and 267 kg/m²s and heat fluxes from 200 to 500 kW/m². The effects of the mass flux and vapor quality on the local flow boiling heat transfer coefficient and two-phase frictional pressure gradient were studied. The evaluated experimental data were compared with existing correlations. The experimental heat transfer coefficients were nearly independent of the mass flux and vapor quality. Most of the existing correlations did not provide reliable heat transfer coefficient predictions for different vapor quality values, nor could they predict the two-phase frictional pressure gradient except under some limited conditions.     

Experimental Study of Parameters Affecting the Nusselt Number of Generator Rotor and Stator

In this research, the parameters affecting the Nusselt number of a generator rotor and stator under varying heat transfer rate are experimentally studied. In spite of the stator having no grooves, the rotor has four large triangular grooves. The temperature and then heat transfer rate of the rotor and stator are experimentally measured in three longitudinal and two angular positions. First, the effect of axial Reynolds number and rotor rotational speed on the rotor and stator Nusselt number with constant heat transfer rate ratio is studied. The range of the axial Reynolds number and rotational speed used is from 4000 to 30,000 and from 300 to 1500 rpm, respectively. Next, the effect of stator to rotor heat transfer rate ratio on the Nusselt number at constant axial Reynolds number and rotational speed is investigated. Three experiments were conducted at three heat transfer rate ratios (3, 5, and 8), defined as the ratio of heat transfer rate of the stator to the rotor. The results show that the higher the heat transfer rate ratio, the lower is the stator mean Nusselt number and the higher the rotor mean Nusselt number.     

Nonlinear flow and heat transfer dynamics of a slot jet impinging on a slightly curved concave surface

The nonlinear flow and heat transfer characteristics for a slot jet impinging on a slightly curved concave surface are experimentally studied here. The effects of jet Reynolds number on the jet velocity distribution and circumferential Nusselt numbers are examined. The nozzle geometry is a rectangular slot and the dimensionless nozzle-to-surface distance equals to L^⁎ = 8. The constant heat fluxes are accordingly applied to the surface to obtain an impingement cooling by the air jet at ambient temperature. The measurements are made for the jet Reynolds numbers of 8617, 13 350 and 15 415. New correlations for local, stagnation point, and average Nusselt numbers as a function of jet Reynolds number and dimensionless circumferential distance are reported.     

A numerical study of laminar free convection heat transfer between inner sphere and outer vertical cylinder

The effects of height and radius ratio with a Newtonian fluid have been investigated numerically to determine heat transfer by natural convection between the sphere and vertical cylinder with isothermal boundary conditions. The inner sphere and outer vertical cylinder were heated and cooled in a steady change of temperature. Calculations were carried out systematically for a range of the Rayleigh numbers to determine the average Nusslet numbers which are affected by the geometric ratio parameters (HR and RR) on the flow and temperature fields. The governing equations, in terms of vorticity, stream function and temperature are expressed in a spherical polar coordinate system. Results of the parametric study conducted further reveal that the heat and flow fields are primarily dependent on the Rayleigh number and height and radius ratio, for a Prandtl number of 0.7, with the Rayleigh number ranging from 10³ to 10⁶, and the height and radius ratio varying from 1.2 to 5.0. Above all, the specification of different convective configurations has a significant effect on the average heat transfer rate across the composite annulus gap.     

Heat transfer and performance characteristics of axial cooling fans with downstream guide vanes

This study examines experimentally the effect of stators on the performance and heat transfer characteristics of small axial cooling fans. A single fan impeller, followed by nine stator blades in the case of a complete stage, was used for all the experimental configurations. Performance measurements were carried out in a constant speed stage performance test rig while the transient liquid crystal technique was used for the heat transfer measurements. Full surface heat transfer coefficient distributions were obtained by recording the temperature history of liquid crystals on a target plate. The experimental data indicated that the results are highly affected by the flow conditions at the fan outlet. Stators can be beneficial in terms of pressure drop and efficiency, and thus more economical operation, as well as, in the local heat transfer distribution at the wake of the stator blades if the fan is installed very close to the cooling object. However, as the separation distance increases, enhanced heat transfer rate in the order of 25% is observed in the case of the fan impeller.     

Transient and steady-state natural convection heat transfer from a heated horizontal concrete cylinder

In refrigeration systems, it is possible to reduce energy consumption (compressor power) and increase COP by decreasing the condensation temperature. Decreasing the condensation temperature can be achieved either by increasing the overall heat transfer coefficient or heat transfer surface area of the condenser. Usually, the radiuses of condenser tubes of domestic refrigerators are quite smaller than the critical radius. Thus, the radius can be increased up to the critical radius by coating the bare condenser tube to increase heat transfer. On the other hand, refrigerators operate discontinuously depending on the ambient temperatures. Coating material stores some of the heat during the working period and continues heat transfer during the off period so that the condenser continues transferring heat while the compressor is not working. Storage effect depends on the specific heat and density of the coating material. Transient and steady-state natural convection heat transfer from a heated horizontal cylinder covered with concrete layer by molding is studied experimentally and numerically to determine the effects of the parameters considered above. The copper and the concrete test cylinders used in the experimental study have a length of 1 m and outer diameter of 9.45 mm and 68.5 mm respectively. The ambient and copper cylinder surface temperatures varied between 20 °C÷30 °C and 30 °C÷50 °C respectively. Constant heat flux was applied to bare and concrete cylinders. Transient heat transfer experiments were performed when bare, and concrete cylinders were reached to steady state condition. Heat transfer rates under transient conditions from bare and concrete horizontal cylinders were compared and heat transfer enhancement was determined. Based on the experimental data average Nusselt numbers were calculated and compared with the well known correlations. Also temperature distributions obtained from numerical simulations were very close to the experimental data. The effect of the decrease in the temperature of the inner copper cylinder surface (condensation temperature) on COP was investigated considering an ideal Carnot refrigeration cycle. It is found that the enhancement in COP of a Carnot refrigeration cycle is 35.7% under transient condition.