Showing papers in "International Journal of Heat and Mass Transfer in 2000"

Conceptions for heat transfer correlation of nanofluids

Abstract: The nanofluid is a solid–liquid mixture in which metallic or nonmetallic nanoparticles are suspended. The suspended ultrafine particles change transport properties and heat transfer performance of the nanofluid, which exhibits a great potential in enhancing heat transfer. The mechanism of heat transfer enhancement of the nanofluid is investigated. Based on the assumption that the nanofluid behaves more like a fluid rather than a conventional solid–fluid mixture, this article proposes two different approaches for deriving heat transfer correlation of the nanofluid. The effects of transport properties of the nanofluid and thermal dispersion are included.

Three-dimensional conjugate heat transfer in the microchannel heat sink for electronic packaging

Abstract: A three-dimensional model is developed to investigate flow and conjugate heat transfer in the microchannel-based heat sink for electronic packaging applications. The incompressible laminar Navier–Stokes equations of motion are employed as the governing conservation equations which are numerically solved using the generalized single-equation framework for solving conjugate problems. The theoretical model developed is validated by comparing the predictions of the thermal resistance and the friction coefficient with available experimental data for a wide range of Reynolds numbers. The detailed temperature and heat flux distributions as well as the average heat transfer characteristics are reported and discussed. The analysis provides a unique fundamental insight into the complex heat flow pattern established in the channel due to combined convection–conduction effects in the three-dimensional setting. Important practical recommendations are also provided regarding the cooling efficiency of the microchannel heat sinks as well as a possible failure due to the thermal stresses induced by the extremely large temperature gradient at the entrance of the channels.

Heat transfer and friction characteristics of plain fin-and-tube heat exchangers, part II: Correlation

Abstract: A correlation for fin-and-tube heat exchanger having plain fin geometry is proposed in this study. A total of 74 samples were used to develop the correlation. For practical considerations, the proposed heat transfer correlation had absorbed the contact conductance in the development of correlation. The proposed heat transfer correlation can describe 88.6% of the database within ±15%, while the proposed friction correlation can correlate 85.1% of the database within ±15%. The mean deviation of the heat transfer correlation is 7.51%, while that for the proposed friction correlation is 8.31%.

Impact, recoil and splashing of molten metal droplets

Abstract: We studied the impact and solidification of molten tin droplets on a stainless steel surface. Droplet impact velocity was varied from 1.0 to 4.0 m/s and substrate temperature from 25 to 240°C (above the melting point of tin, 232°C). We photographed droplet impact and measured splat diameter and liquid–solid contact angle from these photographs. Substrate temperature under an impacting droplet was measured using a fast response thermocouple. Thermal contact resistance at the droplet–substrate interface was calculated by matching measured surface temperature variation with an analytical solution. A simple energy conservation model was used to predict the maximum spread of droplets during impact. Predictions agreed well with measured values. Instabilities were observed on the periphery of the droplet, which led to the formation of fingers. A model based on the Rayleigh–Taylor instability was used to predict the number of fingers around the periphery of the droplet.

Heat transfer for water flow in trapezoidal silicon microchannels

Abstract: Experiments were conducted to investigate heat transfer characteristics of water flowing through trapezoidal silicon microchannels with a hydraulic diameter ranging from 62 to 169 μm. A numerical analysis was also carried out by solving a conjugate heat transfer problem involving simultaneous determination of the temperature field in both the solid and the fluid regions. The experimental results were compared with the numerical predictions and a significant difference was found. The comparison results indicated that the experimentally determined Nusselt number is much lower than that given by the numerical analysis. The measured lower Nusselt numbers may be due to the effects of surface roughness of the microchannel walls. Based on a roughness-viscosity model established in our previous work, a modified relation which accounts for the roughness-viscosity effects was proposed to interpret the experimental results.

Pressure-driven water flows in trapezoidal silicon microchannels

Abstract: Experiments were conducted to investigate flow characteristics of water through trapezoidal silicon microchannels with a hydraulic diameter ranging from 51 to 169 μm. In the experiments, the flow rate and pressure drop across the microchannels were measured at steady states. The experimental results were compared with the predictions from the conventional laminar flow theory. A significant difference between the experimental data and the theoretical predictions was found. Experimental results indicate that pressure gradient and flow friction in microchannels are higher than those given by the conventional laminar flow theory. The measured higher pressure gradient and flow friction maybe be due to the effect of surface roughness of the microchannels. A roughness–viscosity model is proposed to interpret the experimental data.

Heat transfer in a liquid film on an unsteady stretching surface

Abstract: The momentum and heat transfer in a laminar liquid film on a horizontal stretching sheet is analysed. The governing time-dependent boundary layer equations are reduced to a set of ordinary differential equations by means of an exact similarity transformation. The resulting two-parameter problem is solved numerically for some representative values of the unsteadiness parameter S for Prandtl numbers from 0.001 to 1000. The temperature is observed to increase monotonically from the elastic sheet towards the free surface except in the high diffusivity limit Pr→0 where the surface temperature approaches that of the sheet. A low stretching rate, i.e. high values of S, tends to reduce the surface temperature for all Prandtl numbers. The heat flux from the liquid to the elastic sheet decreases with S for Pr≲0.1 and increases with increased unsteadiness for Pr≳1.

Flow boiling heat transfer of Freon R11 and HCFC123 in narrow passages

Abstract: Flow boiling heat transfer coefficients for Freon R11 and HCFC123 in a smooth copper tube with an inner diameter of 1.95 mm have been experimentally investigated. The parameter ranges examined are: heat fluxes from 5 to 200 kW m−2; mass fluxes from 50 to 1800 kg m−2 s−1; vapour quality from 0 to 0.9; system pressures from 200 to 500 kPa; and experimental heat transfer coefficients from 1 to 18 kW m−2 K−1. It was found that the heat transfer coefficients are a strong function of the heat flux and the system pressure, while the effects of mass flux and vapour quality are very small in the range examined. This suggests that the heat transfer is mainly via nucleate boiling. The present experimental data were compared with some existing correlations and recommendations on their use is made.

Development of the Miniaturized Four-sensor Conductivity Probe and the Signal Processing Scheme

Abstract: The objective of the present study is to develop a miniaturized four-sensor conductivity probe, applicable to a wide range of two-phase flows to obtain the time-averaged local two-phase flow parameters of various types of bubbles. Experimental data acquired by the probe are categorized into two groups in view of two-group interfacial area transport: namely spherical/distorted bubbles as Group 1 and cap/Taylor bubbles as Group 2. Benchmark experiment employing the image analysis method is performed. The results from the benchmark experiment assess both the measurement principle and signal processing scheme of the newly developed four-sensor conductivity probe method.

Entropy generation for natural convection in an inclined porous cavity

Abstract: The issue of entropy generation in a tilted saturated porous cavity for laminar natural convection heat transfer is analysed by solving numerically the mass, momentum and energy balance equations, using Darcy’s law and Boussinesq-incompressible approximation. As boundary conditions of cavity, two opposite walls are kept at constant but different temperatures and the other two are thermally insulated. The parameters considered are the angle of inclination and the Darcy–Rayleigh number. When available, present solutions are compared with known results from the previous researches. Excellent agreement was obtained between results that validate the used computer code. The results show that the calculation of local entropy generation maps are feasible and can supply useful information for the selection of a suitable angle of inclination.

Mass transfer within the gas-phase of porous media

Abstract: The laws of various transport modes—viscous flow, diffusion and Knudsen flow—can be caused by the gradients of concentration, total and partial pressure. Their combined transports are derived and proved by selected experiments in the continuum as well as in the Knudsen region. The combination of these transport modes leads to phenomena like pressure diffusion, slip flow and diffusive slip. The three transport coefficients—the permeability, the binary diffusion coefficient and the Knudsen coefficient—can be determined by steady-state permeability and diffusion measurements. Nonsteady-state measurements deliver additional information about the pore structure of the porous medium. The presented measurements were carried out at cylindrical samples of rock salt with low porosity. Hydrogen and nitrogen were used as nonadsorbing gases. The binary diffusion experiments confirm Graham’s law with good accuracy.

Rationalisation of second law analysis of heat exchangers

Abstract: The purpose of this paper is to review the various approaches to second law analysis and to present a rational method which satisfies the physical requirements. It is not the intention to review all previous work, but to present an approach that resolves some perceived inconsistencies and paradoxes. Some new relationships are derived, particularly for the local rate generation process, and for the nearly-balanced counterflow arrangement with a ‘long’ duty. It is also shown that the basic entropy generation relationship for gas flows is controlled by the flow Mach number, which is consistent with an extension of Shapiro’s classical one-dimensional flow analysis of a compressible gas with friction and heat addition.

Heat transfer and friction characteristics of plain fin-and-tube heat exchangers, part I: New experimental data

Abstract: This study presents the airside performance of fin-and-tube heat exchangers with plain fin configurations. A total of 18 samples were tested. The effect of the number of tube rows, fin pitch and tube diameter on the thermal-hydraulic characteristics was examined. Depending on the number of tube rows, it was found that the heat transfer characteristics were strongly related to the fin pitch. For N=1 or 2 , the heat transfer performance increased with decrease of fin pitch. For N≥4 and ReDc>2000, the effect of fin pitch on heat transfer performance was negligible. For the same fin pitch, the effect of the number of tube rows on the friction performance was very small. The effect of tube diameter on heat transfer performance is related to fin pitch as well. Pressure drops for D c =10.23 mm exceed those of D c =8.51 mm by approximately 10–15%.

One-group interfacial area transport of bubbly flows in vertical round tubes

Abstract: In relation to the development of the interfacial area transport equation, the sink and source terms in an adiabatic bubbly flow system were modeled based on the mechanisms of bubble–bubble and bubble–turbulent eddy random collisions, respectively. The interfacial area transport mechanism was discussed based on the derived model. One-dimensional interfacial area transport equation with the derived sink and source terms was evaluated by using the area averaged flow parameters of adiabatic air–water bubbly flows measured in 25.4 mm and 50.8 mm diameter tubes. The flow conditions of the data set covered most of the bubbly flow regime, including finely dispersed bubbly flow (inlet superficial gas velocity: 0.0414–3.90 m/s, superficial liquid velocity: 0.262–5.00 m/s, void fraction: 1.27–46.8%). Excellent agreement was obtained between modeled and measured interfacial area concentrations within the average relative deviation of 11.6%. It was recognized that the present model would be promising for the interfacial area transport of the examined bubbly flows.

A first incursion into the 3d structure of natural convection of air in a differentially heated cubic cavity, from accurate numerical solutions

Abstract: Accurate solutions to the equations governing the natural convection of air in a cubic cavity, thermally driven on two vertically opposite faces, are given for Rayleigh number values up to 10 7 . These solutions are obtained with a pseudo-spectral Chebyshev algorithm based on the projection‐diAusion method [1,2] with a spatial resolution supplied by polynomial expansions, which go up to 111 111 111. The solutions are believed to be accurate— better than (0.03, 0.05)% in relative global error for the corresponding Rayleigh number (Ra) range (10 3 ,1 0 7 ). This clearly indicates a non monotonic evolution of the flow structure as Ra increases. 7 2000 Elsevier Science Ltd. All rights reserved.

Low turbulence natural convection in an air filled square cavity: Part I: the thermal and fluid flow fields

Abstract: An experimental study of low level turbulence natural convection in an air filled vertical square cavity was conducted. The dimensions of cavity were 0.75 m × 0.75 m × 1.5 m giving two-dimensional flow. The hot and cold walls of the cavity were isothermal at 50 and 10°C, respectively, giving a Rayleigh number of 1.58 × 109. The temperature and velocity distribution was systematically measured at different locations in the cavity, and was nearly anti-symmetrical. An experimentally obtained contour plot of the thermal field and a vector plot of the air flow in the cavity are reported for low turbulence natural convection in such cavities for the first time. The wall shear stress and the local and average Nusselt numbers are also presented. The Nusselt number compares well with previous results; the agreement on the velocity and temperature profiles at mid-height near the vertical walls is fair. Differences were found at mid-width and in the rate of velocity and temperature changes near the walls. The experiments were conducted with high accuracy. Therefore, the results can form experimental benchmark data and will be useful for CFD code validation.

Influence of design parameters on the heat transfer and flow friction characteristics of the heat exchanger with slit fins

Abstract: This study systematically analyzes the effect of various design parameters on the heat transfer and pressure drop characteristics of the heat exchanger with a slit fin. The Taguchi method, known to be a very reasonable tool in a parametric study, is employed in the present work. Only seven cases of experimental factors are considered because of the difficulty in producing samples and the manufacturing cost. Eighteen kinds of scaled-up models are made by compounding levels on each factor, and the heat transfer and flow characteristics of each model are analyzed. The results allow us to quantitatively estimate the various parameters affecting heat exchanger performance, and the main factors for optimum design of a heat exchanger are selected. The optimum design value of each parameter is presented and the reproducibility of the results is discussed.

Thermal characteristics of paraffin in a spherical capsule during freezing and melting processes

Abstract: The objective of the present study was to investigate the thermal characteristics of paraffin in a spherical capsule during freezing and melting processes. Experiments were performed with paraffin, i.e., n-tetradecane, and a mixture of n-tetradecane (40%) and n-hexadecane (60%) and water. The parameters were the Reynolds number and the inlet temperature during the freezing process and initial temperature during the melting process for a PCM-thermal-storage system. The phase-change period for the capsule at the edge of a storage tank was shorter than that at the center of the storage tank due to smaller porosity at the center than the edge of the storage tank. Water showed a bigger of subcooling than paraffin. It took longer for water to reach the dimensionless thermal-storage capacity of 1 during the freezing process, and shorter during the melting process than that for paraffin. The average heat-transfer coefficients were affected by the inlet or initial temperature and Reynolds number more during the melting process than during the freezing process due to a natural-convention effect during the melting process. The average heat-transfer coefficients for paraffin were larger by a maximum of 40% than those for water during the freezing and melting processes.

Heat and moisture transfer with sorption and condensation in porous clothing assemblies and numerical simulation

Abstract: A dynamic model of heat and moisture transfer with sorption and condensation in porous clothing assemblies is presented in this paper. The model considers for the first time the effect of water content in the porous fibrous batting on the effective thermal conductivity as well as radiative heat transfer, which is a very important mode of heat transfer when there is a great difference in the boundary temperatures. The distributions of temperature, moisture concentration and liquid water content in the porous media for different material parameters and boundary conditions were numerically computed and compared. The presented numerical results showed that the condensation zone expends towards its boundaries with time.

Constructal T-shaped fins

Abstract: This paper reports the geometric (constructal) optimization of T-shaped fin assemblies, where the objective is to maximize the global thermal conductance of the assembly, subject to total volume and fin-material constraints. Assemblies of plate fins and cylindrical fins are considered. It is shown that every geometric feature of the assembly is delivered by the optimization principle and the constraints. These optimal features are reported in dimensionless terms for this entire class of fin assemblies. Corresponding results are developed for more evolved versions of the T-shaped assembly, namely, the tau-shaped assembly where the free ends of the thinner fins are bent, the tau-shaped assembly that is narrower than the space allocated to it, and the umbrella-shaped construct containing cylindrical fins. The results show that some of the optimized geometrical features are relatively robust, i.e., insensitive to changes in some of the design parameters.

The effect of free-floating dendrites and convection on macrosegregation in direct chill cast aluminum alloys. Part II : predictions for Al-Cu and Al-Mg alloys

Abstract: In Part I, a binary mixture model of the DC casting process was proposed, that accounts for fluid flow in the melt and mushy zone, as well as in a slurry zone characterized by the transport of solute-depleted, free-floating dendrites. In this paper, the model is applied to the DC casting of Al–4.5 wt% Cu and Al–6.0 wt% Mg billets, and the predicted surface-to-centerline distribution of macrosegregation is consistent with trends observed in DC cast ingots. These trends include the development of negative segregation at the centerline, subsurface solute enriched and depleted regions, and positive segregation at the billet surface. Negative segregation at the centerline increased with an increase in the packing fraction at which free-floating dendrites are presumed to coalesce into a rigid dendritic structure. Likewise, negative segregation at the centerline and positive segregation in the enriched region increased with an increase in the characteristic diameter of the free-floating dendrites.

Transient heat conduction in one-dimensional composite slab. A ‘natural’ analytic approach

Abstract: The transient response of one-dimensional multilayered composite conducting slabs to sudden variations of the temperature of the surrounding fluid is analysed. The solution is obtained applying the method of separation of variables to the heat conduction partial differential equation. In separating the variables, the thermal diffusivity is retained on the side of the modified heat conduction equation where the time-dependent function is collected. This choice is the essence of composite medium analysis itself. In fact, it ‘naturally’ gives the relationship between the eigenvalues for the different regions and then yields a transcendental equation for the determination of the eigenvalues in a less complex form than the ones resulting from the application of traditional techniques. A new type of orthogonality relationship is developed by the author and used to obtain the final complete series solution. The errors, which develop when the higher terms in the series solution are neglected, are also investigated. Some calculated results of a numerical example are shown in a graphical form, by using dimensionless groups, and therefore discussed.

Critical heat flux (CHF) for water flow in tubes—II.: Subcooled CHF correlations

Abstract: The proliferation of critical heat flux (CHF) prediction methods typifies the lack of understanding of the CHF phenomenon and makes it difficult to choose a suitable correlation, look-up table, or model. In fact, an exhaustive literature search by the authors of this study identified over 100 CHF correlations applicable to subcooled water flow in a uniformly heated round tube. The accuracy of the latest versions of these correlations was ascertained using the PU-BTPFL CHF database from Part I of the present study. This database contains the largest volume of subcooled CHF data (5544 data points) of any database available in the literature. In response to the many inaccurate and inordinately complex correlations, two nondimensional, subcooled CHF correlations were formulated, containing only five adjustable constants and whose unique functional forms were determined without using a statistical analysis but rather using the parametric trends observed in less than 10% of the subcooled CHF data. The correlation based on inlet conditions (diameter, heated length, mass velocity, pressure, inlet quality) was by far the most accurate correlation, having mean absolute and root-mean-square errors of 10.3% and 14.3%, respectively, and is recommended for water flow in a tube having a uniform axial heat flux. The outlet (local) conditions correlation was the most accurate correlation based on local CHF conditions (diameter, mass velocity, pressure, outlet quality) and may be applied to water flow in a tube having a nonuniform axial heat flux. Both correlations proved more accurate than a recent CHF look-up table commonly employed in nuclear reactor thermal hydraulic computer codes. The parametric range for the inlet conditions correlation ( 0.25×10 −3 ≤D≤15×10 −3 m, 2≤L/D≤200 , 300≤G≤30,000 kg m−2 s−1, 1×10 5 ≤P≤200×10 5 N m−2, −2.0≤x i ≤0.0 , −1.0≤x o ≤0.0 ) was chosen so as to include those regions where data were most abundant, containing approximately 85% of the subcooled CHF database. Superiority of the correlations was attributed to the systematic development of the functional forms of the correlations from the CHF parametric effects; thus, re-optimization of the constants, when additional subcooled CHF data become available, is not expected to produce an appreciable increase in accuracy.

Experimental verification of the role of Brinkman number in microchannels using local parameters

Abstract: Experiments were performed using water flow in microchannel specimens, with thermocouples mounted axially along the flow for local wall temperature measurement. The processed experimental data obtained locally in the laminar regime exhibited the unusual behaviour of the local Nusselt number decreasing with increasing local Reynolds number along the flow. Though the variation of Nusselt number with Reynolds number has been observed before, it was for averaged parameters, obtained using a different approach in experimentation for calculating these parameters over the entire microchannel specimen. The present experimental data in the laminar regime were also found to correlate well with the Brinkman number for the individual sets and much better globally, by combining all the data sets. The correlation with the Brinkman number in spite of its relatively low values is physically interpreted.

Effect of surface roughness on pool boiling heat transfer

Abstract: In order to clarify the effect of surface roughness on pool boiling heat transfer, the experiments were carried out for the saturated pool boiling of water at atmospheric pressure. The experimental results show that increased surface roughness enhances heat transfer and its effect is magnified as the orientation of a tube changes from the horizontal to the vertical. In addition, it is identified that the increase in the ratio of a tube length to its diameter magnifies the effect of surface roughness on pool boiling heat transfer.

Transient, three-dimensional heat transfer model for the laser assisted machining of silicon nitride: I. Comparison of predictions with measured surface temperature histories

Abstract: Laser assisted machining (LAM), in which the material is locally heated by an intense laser source prior to material removal, provides an alternative machining process with the potential to yield higher material removal rates, as well as improved control of workpiece properties and geometry, for difficult-to-machine materials such as structural ceramics. To assess the feasibility of the LAM process and to obtain an improved understanding of governing physical phenomena, experiments have been performed to determine the thermal response of a rotating silicon nitride workpiece undergoing heating by a translating CO 2 laser and material removal by a cutting tool. Using a focused laser pyrometer, surface temperature histories were measured to determine the effect of the rotational and translational speeds, the depth of cut, the laser-tool lead distance, and the laser beam diameter and power on thermal conditions. The measurements are in excellent agreement with predictions based on a transient, three-dimensional numerical solution of the heating and material removal processes. The temperature distribution within the unmachined workpiece is most strongly influenced by the laser power and laser-tool lead distance, as well as by the laser/tool translational velocity. A minimum allowable operating temperature in the material removal region corresponds to the YSiAlON glass transition temperature, below which tool fracture may occur. In a companion paper [1] , the numerical model is used to further elucidate thermal conditions associated with laser assisted machining.

A numerical study on the transient heat transfer from a sphere at high Reynolds and Peclet numbers

Abstract: The transient heat transfer rate from a particle depends on the flow field as well as the temperature field developed around the particle. The parameters that determine these two fields are the Reynolds number and the Peclet number. A numerical study has been performed in order to determine the transient heat transfer from a spherical particle in terms of both of these parameters. The governing equations of the problem are made dimensionless and are solved by using the stream function-vorticity formulation. The solution of the equations is achieved by using a stretched coordinate system and a tri-diagonal matrix algorithm. Good agreement of the numerical results was observed with previous studies on drag coefficients as well as with analytical and asymptotic expressions derived in the past. The results show a strong dependence of the rate of heat transfer on the Reynolds number, when the Peclet and Reynolds numbers are higher than one.

Thermal management of high power electronics with phase change cooling

Abstract: A study on the prospect of designing high power electronic packages with phase change cooling is presented, with special emphasis on minimising the rising of junction temperatures due to thermal transient effects. The one-dimensional thermal model consists of a finite slab suddenly exposed to a uniform heat flux at the top surface and cooled by convective air at the bottom. The phase change problem is divided into sub-problems and solved progressively. Before the slab starts to melt, both exact and approximate solutions are presented for the distribution of temperature in the slab as functions of time and Biot number Bi . The necessity of partitioning the time domain into two regimes, separated by the time t 0 needed for the thermal front to traverse across the whole slab, is emphasised. After the slab melts, quasi-steady state solutions are obtained both for the melt depth and the evolution of surface temperature as functions of time and Biot number when t m > t 0 , with t m denoting the time needed for melting to commence at the top surface of the slab. The quasi-steady state solutions are compared with those obtained by using the method of finite elements. Approximate but simple analytical solutions are also constructed for the t m t 0 case which, again, are compared with the finite element results. Finally, these solutions are analysed to guide the design of advanced packages with optimised phase change cooling strategies.

Slip-flow heat transfer in circular tubes

Abstract: The influence of rarefaction on heat transfer in circular tubes is studied. A spatial rescaling factor rs, which is a measure of rarefaction through its dependence on the Knudsen number, is introduced to identify similarities with the classical Graetz problem. It is found that heat transfer depends both on the degree of rarefaction and on the surface accommodation coeAcients. The temperature jump at the wall, ignored in recent investigations, is found to be of essential importance in the heat transfer analysis. A novel uniform asymptotic approximation to high-order eigenfunctions is derived that allows an eAcient and accurate determination of the region close to the entrance. 7 2000 Elsevier Science Ltd. All rights reserved.