Steady-state Heat Transfer Coefficient Research Articles

ANALYSIS AND OPTIMIZATION OF ACTIVATED CARBON COATED HEAT SINKS

With the enhancements in nanotechnology, electronic devices shrank in size which led to a necessity to develop efficient thermal management strategies. These small electronic devices could be thermally managed through passive systems provided that effective materials are developed. Here, we use a layer of activated carbon on top of anodized aluminum heat sinks to utilize the sorption cycle of atmospheric water to create a desorption induced evaporative cooling effect. The material properties of the activated carbon lead to enhanced cooling by radiation and desorption, while the geometry of the heat sinks ensure surface area maximization. We develop a numerical simulation platform to determine the optimum geometry and the optimal activated carbon coating mass. Our results show that as the fin diameter and spacing shrink, and as the activated carbon mass increases within the considered range (0-100 mg), effective cooling of the chip could be achieved. We further employ our simulations to decouple the effects of desorption, radiation, and convection. Our analyses reveal that desorption only plays a vital role during the initial periods of operation, while cooling due to radiation and convection leads to an ≈20% increase in the overall steady-state heat transfer coefficient. This study goes beyond introducing a passive thermal management strategy for small electronic chips by providing a link between mass diffusion and thermal processes for effective transient operation of thermal devices.

Numerical investigation on the effects of spatial angle on oscillating flow and heat transfer characteristics of piston cooling galleries

• The SOCR and SHTC of gallery are affected by the inlet/outlet position. • The ICOR and IHTC in groups A and B are different at the same crank angle. • The spatial angle has a non-negligible influence on the piston cooling performance. • The results provide reference for piston improvement design of multi-cylinder diesel. The oscillating cooling method is currently one of the most efficient cooling solutions for highly reinforced pistons. Previous studies only focused on the piston galleries with the reciprocating motion along a specified direction relative to the direction of the gravity force, e.g., the vertical direction in inline multi-cylinder engines. There are strong needs to study the cooling performance of the pistons that are designed to have reciprocating motions with different directions relative to gravity. In this paper, a concept of spatial angle is introduced to describe the design angle between the direction of the piston reciprocating motion and the direction of the gravity force in a coordinate system. When the spatial angle is changed, the gravity components of the piston are changed along the direction of the piston axial motion and its perpendicular direction. Moreover, with a given spatial angle, different piston designs can be achieved to obtain different relative positions of the cooling oil inlet and outlet passages, being higher or lower relative to each other. Because both the spatial angle and the relative positions of the oil passages affect flow and cooling performance, several simulation models are established to cover five spatial angles including −90°, −45°, 0°, 45°, and 90° as well as two groups of relative positions, i.e., groups A and B. The CFD simulation is validated by experimental testing. The results show that the flow and heat transfer performance of group B is more stable than that of group A because the inlet and outlet of the cooling passages of group B are at the same height. It is found that the steady-state oil charge ratio and steady-state heat transfer coefficient of group A gradually decrease with the increase of the spatial angle. The fluctuation patterns of the instantaneous oil charge ratios and heat transfer coefficients of groups A and B are very similar, but their spatial distribution values are different at the same crank angle (CA). The maximum difference in the instantaneous heat transfer coefficients between A1 and A3 reaches 23.27% at 303° CA. Moreover, it is found that when the piston moves between 150° CA and 300° CA, a phenomenon of liquid plug attenuates with the increase of the spatial angle. These findings can support the cooling performance analysis and optimization design of the piston galleries of the V-type, W-type, and horizontal opposed-piston diesel engines.

Heat Transfer of Hydrocarbon Fuel Under Steady States and Pressure-Transient States

The heat transfer of a hydrocarbon fuel was investigated experimentally under steady states and pressure-transient states with respect to engineering applications for the scramjet regenerative cooling system. The experiments were carried out in a uniformly heated horizontal minitube with an inner diameter of 1.0 mm. The main objective of this study was to compare the heat transfer coefficients under steady states with those under pressure-transient states as well as to investigate the effect of the pressure-transient rate on heat transfer. The results show that the steady-state heat transfer coefficients are higher than the transient-state heat transfer coefficients, especially in the vicinity of the critical point. Accordingly, the thermal margin for a regenerative cooling system could be further increased by approximately 25% to ensure the reliability of the safety analysis under abnormal pressure-transient conditions.

Numerical analysis of natural convection in sodium plenum below the grid plate of a fast reactor during a severe accident

Heat transfer characteristics of liquid sodium are quite different from that of normal liquids because of its very low Prandtl number. Empirical correlations for convective heat transfer in sodium are rather limited because of inherent difficulties in performing sodium experiments. In this paper, transient and steady natural convection developing inside a cylindrical enclosure heated from the top and cooled along the vertical side wall is studied by a numerical analysis. This problem is of relevance to the safety analysis of sodium cooled pool type fast reactor. The focus of the present investigation is to determine the effect of plate thickness on the natural convection heat transfer characteristics. For the case of a thick top plate, in the transient regime, heat transfer is conduction dominated and Nusselt number is found to be inversely proportional to square root of time as in the case of a thin plate. But the steady state heat transfer coefficient between the lower surface of thick hot plate and liquid sodium is less by about 25% than for a thin plate at the same temperature as the lower surface. The reason for this behaviour is traced to the weaker convective current developed in the case of a thick plate. Based on detailed parametric studies, a correlation for Nusselt number is derived with a correlation coefficient of 0.99, for use in the reactor safety analysis. The Nusselt number is found to be a function of Boussinesq number, thermal conductivity ratio between the wall material and liquid sodium and non-dimensional thickness of the plate. The validity of the correlation is further checked by applying it to different data sets not used for the derivation of the correlation.

Measurement of heat flux in dense air-mist cooling: Part II – The influence of mist characteristics on steady-state heat transfer

The boiling convection heat flux, −q, taking place during the impingement of a water air-mist upon the surface of a Pt-disk, held at steady-state surface temperatures Tw ranging between 550 and 1200°C, has been measured under different conditions of water impact density, w, droplet velocity, u, and droplet size, dd. The new steady-state measurement method controls induction heating to balance the heat extracted from the sample, as described in detail in Part I. Local mist characteristics were determined at room temperature in free non-impinging mists using a patternator for w and a particle/droplet image analyzer (PDIA) for dd and u at positions equivalent to those of the Pt-disk. Three different air-mist nozzles of fan discharge type are characterized over their full range of water flow rates and air inlet pressures and using different positions of the hot surface with respect to the nozzle, to cover the following ranges of local spray characteristics: w from 2 to 106L/m2s; normal volume weighted mean velocities, uz,v, from 9.3 to 45.8m/s and volume mean diameters, d30, from 19 to 119μm. Increasing the air nozzle pressure at constant water flow rate generates mists with finer and faster drops that lead to a higher frequency of drops with large impinging Weber numbers, suggesting a higher probability of wet contact with the surface and an enhanced heat extraction. Heat fluxes as large as ∼12 and ∼10MW/m2 were found in the transition and stable film boiling regimes, respectively. The boiling convection heat flux in the range of 750–1200°C, which corresponded to stable film boiling, was found to correlate very well with the mist characteristics and temperature. The order of importance of the four parameters influencing −q was: d30≪Tw<w≈uz,v. For given local water flux and surface temperature, the correlation indicates that spray cooling becomes more intense as the velocity of the drops increases; the droplet size plays a very minor role. Compared with previous results using a transient method, the steady-state heat transfer coefficients increase faster with w in the range of 5–20L/m2s, reaching much higher values. This suggests that within this range, the steady-state heat flux is controlled by the local water flux, while the transient heat flux must be controlled by the supply of heat conducted to the surface.

Casing Convective Heat Transfer Coefficient and Reference Freestream Temperature Determination Near an Axial Flow Turbine Rotor

The present study explains a steady-state method of measuring convective heat transfer coefficient on the casing of an axial flow turbine. The goal is to develop an accurate steady-state heat transfer method for the comparison of various casing surface and tip designs used for turbine performance improvements. The freestream reference temperature, especially in the tip gap region of the casing, varies monotonically from the rotor inlet to rotor exit due to work extraction in the stage. In a heat transfer problem of this nature, the definition of the freestream temperature is not as straightforward as constant freestream temperature type problems. The accurate determination of the convective heat transfer coefficient depends on the magnitude of the local freestream reference temperature varying in axial direction, from the rotor inlet to exit. The current study explains a strategy for the simultaneous determination of the steady-state heat transfer coefficient and freestream reference temperature on the smooth casing of a single stage rotating turbine facility. The heat transfer approach is also applicable to casing surfaces that have surface treatments for tip leakage control. The overall uncertainty of the method developed is between 5% and 8% of the convective heat transfer coefficient.

An experimental study of closed loop intermittent spray cooling of ICs

Abstract Spray cooling is one of the most prominent high heat flux removal schemes, for various applications including electronics cooling. In the past there has been extensive study conducted on the various factors (nozzle type, location, fluid, heat flux, surface conditions, pressure and mass flow rate) affecting the cooling performance. However, all study has been limited to steady state conditions, and the steady state heat transfer coefficient alone has been investigated. In most of the systems, the heat flux varies temporally and the object to be cooled needs to be maintained at the same temperature. One way of achieving it is by intermittent spray cooling (ISC), in which the spray mechanism is activated only when the temperature starts rising above a set limit. Transient temperature fluctuations, transient heat transfer coefficients and frequency of the process were recorded for pressures of 2, 4 and 6 bar for heat fluxes of 11, 22, and 33 Watt/cm2 at 5, 10 and 15 °C above the steady state temperature (under continuous spray). This paper attempts to understand the various physical mechanisms involved in such a system and discusses a demonstration of ISC to a simulated, variable heat flux-cooling problem. It is also shown that the ISC is energetically more efficient than steady continuous spray.

2217 高速炉における高サイクル熱疲労に関する研究(3) 温度変動に関する Na と水の比較

A quantitative evaluation on thermal striping is of importance for structural integrity and also reactor safety. Thermal conductivity of sodium used in a fast reactor is approximately 100 times larger than that of water. We performed sodium and water experiments with the same geometry in order to evaluate temperature fluctuation characteristics in fluid near the structural surface. In the case of sodium, temperature fluctuation intensity decreased near the structural surface in comparison with water. And also, we investigated transfer characteristics of temperature fluctuation from fluid to structure. It was shown that the transfer characteristics of temperature fluctuation could be predicted using a steady state heat transfer coefficient and one-dimensional heat conduction theory in the structure.

FORCED-CONVECTION AUGMENTATION OF TURBULENT FLOW IN A TRIANGULAR DUCT WITH ARTIFICIALLY ROUGHENED INTERNAL SURFACES

Use of artificially roughened internal surfaces to enhance the steady-state forced convection in an air-cooled horizontal equilateral triangular duct (apex angle of 60°) has been investigated experimentally under a hydrodynamic fully developed turbulent flow condition with hydraulic diameter-based Reynolds numbers ranging from 4,300 to 15,000. The test duralumin triangular ducts were fabricated with the same axial length of 2.4 m and hydraulic diameter of 0.44 m, but four kinds of internal surface finishing. In addition to a smooth surface with an average surface roughness of less than 1 w m, the internal surfaces of the triangular ducts were roughened artificially either by milling/shaping processes, by cutting V-grooves, or by fixing square ribs with a uniform spacing along their axial length. The artificial surface roughness was fabricated in parallel and essentially in the orthogonal direction to the mean flow. By comparing the thermal performance of triangular ducts with the same geometry but different kinds of surface finishing, it was found that forced-convection augmentation could be achieved by the internally roughened surfaces. A much greater enhanced forced convection was obtained by cutting V-grooves or fixing square ribs at uniform spacing, rather than fabricating random roughness on the internal surfaces by machining processes. In addition, the best thermal performance was achieved with the ribbed surface. Nondimensional expressions for the determination of the steady-state heat transfer coefficient of the equilateral triangular ducts, which were internally fabricated with various kinds of artificial surface roughness under consideration, have also been developed.

Forced convection and friction in triangular duct with uniformly spaced square ribs on inner surfaces

Experimental investigation had been conducted to study the steady-state forced convection heat transfer and pressure drop characteristics of the hydrodynamic fully-developed turbulent flow in the air-cooled horizontal equilateral triangular ducts, which were fabricated with the same length and hydraulic diameter. Inner surfaces of the ducts were fixed with square ribs with different side lengths of 6.35, 9.525 and 12.7 mm, respectively, and the uniform separation between the centre lines of two adjacent ribs was kept constant at 57.15 mm. Both the triangular ducts and the ribs were fabricated with duralumin. The experiments were performed with the hydraulic diameter based Reynolds number ranged from 3100 to 11300. The entire inner wall of the duct was heated uniformly, while the outer surface was thermally insulated. It was found that the Darcy friction factor of the duct was increasing rather linearly with the rib size, and forced convection could be enhanced by an internally ribbed surface. However, the heat transfer enhancement was not proportional to the rib size but a maximum forced convection heat transfer augmentation was obtained at the smallest rib of 6.35 mm. Non-dimensional expressions for the determination of the steady-state heat transfer coefficient and Darcy friction factor of the equilateral triangular ducts, which were internally fabricated with uniformly spaced square ribs of different sizes, were also developed.

Inverse determination of steady-state heat transfer coefficient

An experimental setup for the inverse determination of steady-state heat transfer coefficient in a two-dimensional system is proposed. This setup requires temperatures mmeasurements at accessible and non-intrusive locations, but does not require heat flux measurement. The mathematical model of the system is solved numerically by using the boundary element method. It is shown that, as a result of uncertainty in temperature measurement, the estimated heat transfer coefficient will contain uncertainty. This uncertainty can be reduced by varying experimental parameters, some of which are discussed.

Forced convection and pressure drop in a horizontal triangular-sectional duct with V-grooved (i.e. orthogonal to the mean flow) inner surfaces

An experimental investigation has been performed to study the forced convection and pressure-drop characteristics fully-developed steady turbulent flows in air-cooled, horizontal, equilateral-triangular ducts. These ducts were constructed of duralumin, each of the same axial length and hydraulic diameter. The inner surfaces of each duct were either plane or machined with uniformly-spaced parallel, identical V-grooves. For each tested duct, these grooves had a depth of 1 mm, but were all of the same apex angle, θ, where 0⩽θ<150°. The uniform separation between the centre lines of two adjacent V-grooves was kept constant at 34 mm. The measurements were performed with the hydraulic diameter-based Reynolds number for the steady-state air flow, ranging from 2800 to 9500. The entire inner wall of the duct was heated uniformly, while its outer surface was thermally insulated. The forced convection was enhanced by the presence of the V-grooves; the greatest forced-convection augmentation being achieved with V-grooves of apex angle θ≈17.5°. Non-dimensional expressions for the determination of the steady-state heat transfer coefficient and the Darcy friction-factor for the equilateral triangular ducts, which were fabricated with uniformly-spaced identical V-grooves in their inner surfaces, have been deduced.

Visualization of transient natural convection heat transfer from a vertical rectangular fin

Experiments on thermal visualization of transient natural convection from short vertical rectangular fins were conducted using the technique of laser holographic interferometry. A sequence of infinite-fringe interferograms recorded for the heating regime of an aluminum fin demonstrates the effect of fin base heating on local convection coefficients and reveals alternating and oscillatory buoyancy-driven flows similar to those over the top surface of heated horizontal plates. The effect of fin base heating results in greater uniformity of the local heat transfer coefficient along the fin. It also significantly reduces the steady-state heat transfer coefficients of short vertical fins compared to their transient values. Hence, the use of steady-state solutions for the design of short vertical fins operating in transient conditions may not introduce as much error as was previously thought.

Heat Transfer and Surface Renewal Dynamics in Gas-Fluidized Beds

Local instantaneous heat transfer between a submerged horizontal cylinder and a gas-fluidized bed operating in the bubble-flow regime was measured and the resulting signals analyzed. Unique to this investigation is the division of particle convective heat transfer into transient and steady-state contact dynamics through analysis of instantaneous heat transfer signals. Transient particle convection results from stationary particles in contact with the heat transfer surface and yields a heat transfer rate that decays exponentially in time. Steady-state particle convection results from active particle mixing at the heat transfer surface and results in a relatively constant heat transfer rate during emulsion phase contact. The average time of contact for each phase is assessed in this study. Signals were acquired using a constant-temperature platinum film heat flux sensor. Instantaneous heat transfer signals were obtained for various particle sizes by varying the angular position of the heat transfer probe and the fluidization velocity. Individual occurrences of emulsion phase heat transfer that are steady-state in nature are characterized by contact times significantly higher than both the mean transient and mean emulsion phase contact times under the same operating conditions. Transient and steady-state contact times are found to vary with angular position, particle size, and fluidizing velocity. Due to the extremely short transient contact times observed under these fluidization conditions, mean transient heat transfer coefficients are approximately equal to the mean steady-state heat transfer coefficients.

Heat Transfer and Turbulence in a Turbulated Blade Cooling Circuit

The aerothermal performance of a typical turbine blade three-pass turbulated cooling circuit geometry was investigated in a 10X plexiglass test model. The model closely duplicated the blade’s leading edge, midchord, and trailing edge cooling passage geometries. Steady-state heat transfer coefficient distributions along the blade pressure side wall (convex surface) of the cooling circuit passages were measured with a thin-foil heater and a liquid crystal temperature sensor assembly. The heat transfer experiments were conducted on rib-roughened channels with staggered turbulators along the convex and concave surfaces of the cooling passages. Midchannel axial velocity and turbulence intensity measurements were taken by hot-wire anemometry at each passage end of the three-pass cooling circuit to characterize and relate the local thermal performance to the turbulence intensity levels. The near-atmospheric experimental data are compared with results of a Computational Fluid Dynamics (CFD) analysis at the operating internal environment for a 1X rotating model of the blade cooling circuit and other turbulator channel geometry heat transfer data investigations. The comparison between the measurements and analysis is encouraging. Differences with other heat transfer data appear reasonably understood and explainable.

Numerical Simulation of the Stability in Long Cable-in-Conduit Conductors for Fusion Magnets

The stability phenomenon is investigated numerically for a quench initiating in a cable-in-conduit conductor (CICC) at a significant distance from the ends. The thermo-hydraulic computer program, CICC, was used. The geometry chosen for this study is a toroidal field (TF) coil for the conceptual design activity (CDA) of the International Thermonuclear Experimental Reactor (ITER). Previous studies of short conductors have shown that convective helium flows, induced by the initiating heat pulse, control the stability of the conductor. The present study of a long conductor exhibits reduced energy margins and the absence of a transition region between the well-cooled and ill-cooled stability regions because the initiating heat pulse has difficulty sustaining a convective flow. The effect of heat-pulse duration and heated length were considered. For short, high-energy heat pulses, high convective and conductive heat-transfer coefficients can only be maintained for 10 ms. If the heat-pulse energy is spread over 100 ms, the steady-state heat-transfer coefficient is sufficient to stabilize the conductor. Pulse durations between 10 and 100 ms cause a decrease in energy margin. On the other hand, the conductor length heated was found to have only a small effect on stability.

A generalised analysis of a local heat flux probe

A systematic study of the effects of heat flux probe design on its thermal characteristics and response is reported. The probe considered consists of a metallic film sensor deposited onto a substrate and covered by a thin protective coating. This study considers the case of a constant temperature sensor mounted in an isothermal wall with the sensor maintained at the wall temperature. A two-dimensional, transient numerical analysis for a dynamic heat flux probe was formulated and results reported. Asymptotic response limits were studied by considering idealised probe models and are presented. A non-dimensional relationship between steady-state heat transfer coefficient and sensor power was determined for a range of material properties for the substrate and coating. The steady-state effective probe area was found to remain essentially constant for a broad range of heat flux provided that the probe materials are chosen properly. Probe sensitivity was found to be dependent on probe design and material properties. The transient analysis demonstrated the effect of probe design on probe response and sensitivity.

Heat transfer in mechanically mixed CSTR for gas phase reactions

A simple experimental technique has been developed for evaluating the steady state heat transfer coefficient of spherical mechanically stirred continuous tank reactors for gas phase reactions. Results of heat transfer experiments have been used to establish a Nusselt-type correlation, the Reynolds number being based on stirrer speed and diameter. By adjusting stirrer speed and gas composition the Reynolds number has been varied in the range 2000–60,000 and the Prandtl number has been varied in the range 0.46–0.80. The correlation obtained, Nu = 0.39 Re 0.57 Pr 1 3 , compares well with those available in recent literature for liquid phase CSTR.

Heat transfer coefficients of steam condensation on containment vessel wall during blowdown.

Heat transfer coefficients of steam condensation on the containment vessel wall at a LOCA are studied. As to the steady state heat transfer coefficients, though Sagawa's data are a little smaller than Uchida's data, they are very close to the analytical solutions by Mori-Hijikata. Transient heat transfer coefficients are represented by the steady state heat transfer coefficients multiplied by a factor. The factor expresses the agitation effect weakening with time during blowdown. Values of parameters in the factor are determined so as the heat transfer coefficients to fit Sagawa's data. These heat transfer coefficients are applied to the analyses of the experiment with the simulation apparatus of an integrated type marine water reactor. Values of the parameters are also determined so that the temperature transients on the containment vessel wall by analyses fit them of experiment. The differences of the values of parameters by the analyses and by Sagawa's data are discussed.

A design guide for calculating liquid-metal turbulent forced convection heat transfer with non-uniform heat fluxes and transients

Calculation of turbulent forced convection heat transfer in ducts during non-uniform wall heat fluxes and transients is of interest to the national liquid-metal fast breeder nuclear reactor program. This paper presents an improved method whereby such heat transfer can be determined during analysis and design. Since the method involves the use of fully developed, steady-state heat transfer coefficients, several dimensionless coefficients and selected physical properties, tables, graphs, or equations are included for the convenience of the designer. Application of the improved method is specialized to four geometries of interest: circular tube, parallel-plate channel, annular space, and approximation of pin or rod bundle.