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Stability of an inviscid axisymmetric jet of uniform surface tension and flexural rigidity is investigated. It is shown that for large enough values of flexural rigidity the capillary instabilities are suppressed. The result corroborates the observed stabilization and possible non-breakup of solder jets in the presence of atmospheric oxygen, which causes the appearance of a layer of oxides on the interface. The work is timely because of its direct relevance to a host of emerging technologies exemplified by solder jetting in the manufacturing of microelectronic components. [S0021-8936(00)01203-4]

This paper reports a theoretical study of film condensation on the outside of a vertical pipe containing a cold fluid and imbedded in a porous medium. Two distinct cases are considered. In the first case the collant in the pipe and the falling film of condensate are in parallel flow. In the second case the two forthmentioned fluid streams are in counterflow. The flow in the porous medium is modeled by using both the Brinkman-Darcy model and the Darcy model. The main results of the problem document the effect of the condensation phenomenon on the heat gain in the pipe for a host of the problem parameters.

This paper describes the heat transfer and fluid flow through a confined porous layer heated and cooled along one of the vertical side walls. In the first part of the study, consideration is given to the case when the side-heating effect is positioned above the side-cooling effect. Numerical experiments and scale analysis show that the natural circulation in this first configuration is either one of incomplete vertical penetration, or one of incomplete horizontal penetration. Scale analysis shows that the heat transfer and fluid flow scales differ substantially from one type of penetrative convection to the other, in agreement with the trends revealed by numerical simulations. When the heated portion of the side wall is located below the cooled portion, the flow spreads throughout the porous medium. Scale analysis shows that if the Rayleigh number is sufficiently high, the two mirror-image cells of this flow make contact with the vertical side wall and with each other via slender boundary layer regions. The parametric domain in which the conclusions of this study are valid is outlined on the H/L-RaH plane, where H/L is the height/length ratio and RaH is the Darcy-modified Rayleigh number based on porous system height.

This paper presents a series of numerical simulations which aim to document the problem of forced convection in a channel filled with a fluid-saturated porous medium. In modeling the flow in the channel, the effects of flow inertia, variable porosity and Brinkman friction are taken into account. Two channel configurations are investigated: parallel plates and circular pipe. In both cases, the channel wall is maintained at constant temperature. It is found that the general flow model predicts an overall enhancement in heat transfer between the fluid/porous matrix composite and the walls, compared to the predictions of the widely used Darcy flow model. This enhancement is reflected in the increase of the value of the Nusselt number. Important results documenting the dependence of the temperature and flow fields in the channel as well as the dependence of the thermal entry length on the problem parameters are also reported in the course of the study.

This paper presents a study of the fluid dynamics and heat transfer phenomena occurring during the impingement of a picoliter size liquid solder droplet upon a multilayer, composite substrate. The theoretical model, based on the Lagrangian formulation, is solved numerically with the finite element method. A deforming mesh is utilized to accurately simulate the large deformations, as well as the domain nonuniformities characteristic of the spreading process. The occurrences of droplet recoiling and mass accumulation around the deposit periphery are features of the numerical simulations and yield a nonmonotonic dependence of the maximum radius on time. The results also document the transient temperature fields developing in both the solder droplet and the substrate during the impingement process. Convection effects on the temperature field development in a deforming droplet are found to be important for the entire history of spreading. The work is directly applicable to the miniature solder droplet dispension technology for the mounting of microscopic electronic components on various substrates under development at MicroFab Inc. The results of the numerical simulations are used to explain the shape of solidified microscopic solder bumps.

Low temperature micro-solid oxide fuel cell (micro-SOFC) systems are an attractive alternative power source for small-size portable electronic devices due to their high energy efficiency and density. Here, we report on a thermally self-sustainable reformer micro-SOFC assembly. The device consists of a micro-reformer bonded to a silicon chip containing 30 micro-SOFC membranes and a functional glass carrier with gas channels and screen-printed heaters for start-up. Thermal independence of the device from the externally powered heater is achieved by exothermic reforming reactions above 470 °C. The reforming reaction and the fuel gas flow rate of the n-butane/air gas mixture controls the operation temperature and gas composition on the micro-SOFC membrane. In the temperature range between 505 °C and 570 °C, the gas composition after the micro-reformer consists of 12 vol.% to 28 vol.% H2. An open-circuit voltage of 1.0 V and maximum power density of 47 mW cm−2 at 565 °C is achieved with the on-chip produced hydrogen at the micro-SOFC membranes.

This paper presents a numerical study on the growth of a solid from a line heat sink immersed in a binary alloy. The numerical model takes into account macroscopically the existence of a mushy zone separating the solid region from the liquid region. This zone consists of a mixture of liquid and dendrites. Interesting results shed light on the dependence of the thickness and the temperature of the mushy zone on several important dimensionless groups representing the physical parameters of the problem. It is found that the effect of some of these groups on the solidification process is significant and difficult to predict a priori. The mushy zone disappears when the values of the problem parameters are outside certain ranges.

In situ assembly of high thermal conductivity materials in severely confined spaces is an important problem bringing with it scientific challenges but also significant application relevance. Here we present a simple, affordable, and reproducible methodology for synthesizing such materials, composed of hierarchical diamond micro/nanoparticle scaffolds and an ethylenediamine coating. An important feature of the assembly process is the utilization of ethylenediamine as an immobilizing agent to secure the integrity of the microparticle scaffolds during and after each processing step. After other liquid components employed in the scaffolds assembly dry out, the immobilization agent solidifies forming a stable coated particle scaffold structure. Nanoparticles tend to concentrate in the shell and neck regions between adjacent microparticles. The interface between core and shell, along with the concentrated neck regions of nanoparticles, significantly enhance the thermal conductivity, making such materials an excellent candidate as thermal underfills in the electronics industry, where efficient heat removal is a major stumbling block toward increasing packing density. We show that the presented structures exhibit nearly 1 order of magnitude improvement in thermal conductivity, enhanced temperature uniformity, and reduced processing time compared to commercially available products for electronics cooling, which underpins their potential utility.

This paper reports a series of numerical simulations and a scale analysis of the penetrative convection occurring along the unevenly heated horizontal wall of a semi-infinite porous medium. Modeling the problem as two-dimensional, and assuming that the horizontal wall temperature varies between alternating hot and cold spots, it is found that the natural circulation consists of a row of counter-rotating cells situated near the wall. Each cell penetrates vertically into the porous medium to a distance approximately equal to λ Ra 1 2 λ , where λ is the distance between a hot spot and the adjacent cold spot, and Ragl is the Darcymodified Rayleigh number based on λ and on the temperature difference between each spot and the porous medium situated far enough from the wall. The ability of each cell to convect heat between two adjacent spots increases with the Rayleigh number. The results of numerical simulations in the Raλ range 1–100 are found to support a number of scaling laws derived based on pure scaling arguments.

A predominantly theoretical study is presented of the impact and solidification of molten solder droplets on a multi-layer substrate. This problem is of central importance to the novel micromanufacturing process called solder jetting, in which picoliter-size solder droplets are dispensed for the attachment of microelectronic components. The theoretical model is based on a Lagrangian formulation, and accounts for a host of thermal-fluid phenomena, including surface tension and heat transfer with solidification. Deforming finite elements with integrated automatic mesh generation are utilized to accommodate the large deformations which develop during the computations. An experimental investigation is also presented in which deposits produced by a prototype solder jetting apparatus are analysed using scanning electron microscopy. Results of simulations are presented in which variations of the initial droplet temperature, impact velocity, thermal contact resistance and initial substrate temperature are studied to demonstrate their impact on droplet spreading, on final deposit shapes and on the times to initiate and complete freezing. In many cases, non-intuitive results are observed, such as the non-monotonic dependence of the solidification time on variations of many of the parameters considered. Detailed study of the final solidified shapes, as well as the droplet configuration and flow filed at the onset of phase change, indicate strong coupling between the droplet dynamics and the freezing behavior.

In film-boiling heat transfer, the most important modeling assumption may be that the liquid and vapor phases are separated by a sharp boundary without intervening two-phase region. An effort is presently made to extend the results of Cheng et al. (1982) by using a model for a porous medium's effective conductivity which can account for the structure of the porous matrix used, which in this case is a bed of spherical glass beads. Theory and experiment are found to be in good agreement. 8 refs.

In this paper the main results are reported of a numerical investigation of transient double-diffusive convection in a fluid layer underlying a permeable solid region. Initially, the system is isothermal and possesses a linear distribution of salt in the permeable (porous) region. The system is cooled through its top boundary. The evolution of the transient flow, temperature, and species concentration fields is obtained numerically. In the course of this study the dependence of these fields is determined on the main problem parameters, exemplified by the thermal Rayleigh number, the species Rayleigh number, the Darcy number, the ratio of the height of the porous region to the height of the liquid layer, and the ratio of liquid to solid thermal conductivity. In addition, the above mentioned parameters are investigated in terms of their effect on the heat transfer rate at the top (cold) wall of the system as veil as on the heat and mass transfer rates at the porous-liquid interface.

Scaling arguments and numerical analysis are used to document the transient and steady-state regimes of natural convection in a triangular porous layer cooled from above (along the sloping wall). The numerical simulations are conducted in the high Rayleigh number domain, Ra = 100, 1000, where Ra is the Darcy-modified Rayleigh number based on height, H. The scale analysis predicts the existence of distinct thermal boundary layers if Ra1/2 (H/L) > 1, where H/L is the height/length geometric ratio of the attic-shaped porous layer. The numerical simulations confirm the scaling results, as well as the prediction that the flow consists primarily of an elongated horizontal counterflow driven by the cold wall. In addition, the numerical solutions show the presence of a Be´nard-type instability at high enough Rayleigh numbers. For example, if H/L = 0.2, the instability is present when Ra > 620; this critical Rayleigh number is found to increase as H/L increases.

In this paper a theoretical investigation is reported on the effect of surface roughness on the phenomenon of Leidenfrost-levitation of droplets above a hot surface. The problem is solved first approximately using a macroscopic approach in which the roughness is replaced by a semi-empirical slip condition of the Beavers-Joseph type. Next, a microscopic model which determines the vapor flow in the close vicinity of the rough surface is solved numerically. Three basic periodic roughnesses are examined: triangular, rectangular and semi-cylindrical. The effect of the relative size of the droplet and the roughness elements on the vapor flow is investigated in the course of the study.

The effect of nonuniform permeability and thermal diffusivity on natural convection through a porous system heated from the side is investigated numerically. The first part of the study, in Section 2, focuses on systems composed of vertical sublayers. It is shown that the heat transfer rate is influenced substantially by the thickness and permeability of the peripheral sublayers adjacent to the heated vertical walls. The heat transfer results are correlated by using the ratio of peripheral sublayer thickness divided by the boundary layer thickness based on peripheral sublayer properties. The second part of the study, in Section 3, deals with porous systems composed of horizontal sublayers with different permeabilities. It is shown that due to the lack of homogeneity the vertical walls of the system are lined by boundary layers whose thicknesses vary from one sublayer to the next. A general heat transfer scaling law for horizontally layered systems is reported.

Combined forced and natural convection from a rotating horizontal heated cylinder placed in a low-speed wind tunnel is investigated through numerous experiments set in the counterflow arrangement, i.e., with the free-stream velocity directed parallel to the gravity vector and opposite to the natural convection flow. The main goal of this work is to determine the dependence of the overall heat flux from the rotating cylinder, represented by the Nusselt number, on the free-stream Reynolds number, the rotational Reynolds number, and the Rayleigh number. Several correlations documenting this dependence were obtained and are presented in this paper. Good agreement with former investigations for several limiting cases is found and discussed. Scaling analysis, accurate in an order of magnitude sense, is also applied to define approximately the regions of dominance of the three heat transfer mechanisms involved in the problem: natural convection, free-stream forced convection, and rotational forced convection.

This paper presents an experimental investigation of boundary-layer forced convective heat transfer from a flat isothermal plate in a packed bed of spheres. Extensive experimental results are reported for the thermal boundary-layer thickness, the temperature field, and the local wall heat flux (represented by the local Nusselt number). Theoretical findings of previous investigations using the Darcy flow model as well as a general model for the momentum equation accounting for flow inertia and macroscopic shear with and without variable porosity are used to evaluate the theoretical models. Several trends are revealed regarding the conditions of validity of these flow models. Overall, the general flow model including variable porosity appears to perform better, even though the need for serious improvements in modeling becomes apparent.

Micro-scale solid oxide fuel cell is a promising power generation technology for portable devices such as laptop, medical devices and personal electronics. One of the key goals in design of μ-SOFC systems is to use common hydrocarbon fuels such as propane/butane, which requires an additional micro-scale gas-processing unit (GPU) to reform the fuel, avoiding the coking on the μ-SOFC membranes. However, no integrated micro-fabricated testing platform has been reported for evaluating the stability, thermal management and efficiency of GPU devices as far. Therefore we present such a GPU testing platform, which features integrated heating function and temperature control as well as convenient and reliable fluidic and mechanical interconnects.

An experimental study of natural convection in a parallelepipedal enclosure induced by a single vertical wall is described. The upper half of this wall was warm and the lower half cold. The other enclosure walls were insulated. The temperature and flow measurements were performed in the high Rayleigh number regime (10 10 Ra 10 ) by using water as the working fluid. The Rayleigh number was based on the enclosure height and the temperature difference between the warm and the cold part of the driving wall. The flow field featured two flat cells, one filled with warm fluid along the top horizontal wall, and the other filled with cold fluid along the bottom horizontal wall. Each of these cells was surrounded by an additional cell as tall as half the enclosure height. The above flow structure prohibited extensive thermal contact between warm and cold fluid, thus limiting the role of convection on the heat transfer process in the cavity. The findings of this study differ significantly from the findings of previous studies based on the ‘classical’ enclosure model possessing two isothermal vertical walls, the one warm and the other cold, and support the view that the use of ‘more realistic‘ temperature boundary conditions in enclosure natural convection needs careful examination.

This paper reports a fundamental study of the fluid dynamics inside a triangular (attic-shaped) enclosure with cold upper wall and warm horizontal bottom wall. The study was undertaken in three distinct parts. In the first part, the flow and temperature fields in the cavity are determined theoretically on the basis of an asymptotic analysis valid for shallow spaces (H/L → 0, where H and L are the attic height and length). It is shown that in the H/L → 0 limit the circulation consists of a single elongated cell driven by the cold upper wall. The net heat transfer in this limit is dominated by pure conduction. In the second part of the study, the transient behaviour of the attic fluid is examined, based on a scaling analysis. The transient phenomenon begins with the sudden cooling of the upper sloped wall. It is shown that both walls develop thermal and viscous layers whose thicknesses increase towards steady-state values. The criterion for the existence of distinct thermal layers in the steady state is (H/L)½RaH¼ > 1, where RaH is the Rayleigh number based on attic height. The corresponding criterion for distinct viscous wall jets is (H/L)½RaH¼ Pr−½ > 1, where Pr is the Prandtl number. The third phase of this study focused on a complete sequence of transient numerical simulations covering the ranges H/L = 0.2, 0.4, 1; RaH/Pr = 10, 103, 105; Pr = 0.72, 6. The numerical experiments verify the flow features described theoretically in the first two parts of the study. The effect of thermal convection on the net heat transfer between the bottom and top walls is illustrated numerically. Finally, the transient numerical experiments show that in the present parametric domain the single-cell circulation pattern is stable with respect to the Benard instability expected in fluid layers heated from below.

A numerical study of two‐dimensional natural convection in a horizontal water layer heated from below is reported. The density maximum associated with water at 3.98 °C and atmospheric pressure occurs inside the layer, as the top surface is maintained at 0 °C while the bottom surface temperature varies in the range 4 °C–10 °C. Three separate series of numerical simulations document the effect of Rayleigh number, bottom wall temperature and layer horizontal length on the flow pattern and on the net heat transfer rate vertically through the layer. These effects are documented numerically and graphically in the domain104

This Brief Communication is concerned with establishing the effect of the presence of a third diffusing component on the onset of convection in a horizontal fluid‐saturated porous layer. The linear stability analysis procedures used in double diffusion are extended to take into account a third diffusing constituent. As a result, general expressions for the various stability boundaries are obtained. The presence of a third diffusing component with small diffusivity can seriously alter the nature of the convective instabilities in the system. For the most part, the findings of the present study for a porous layer exhibit similar behavior to the results reported by Griffiths [J. Fluid Mech. 92, 659 (1979)] for triple diffusion in a layer of classical fluid. However, when heat is one of the three diffusing components, the porosity of the porous medium has a considerable effect on the marginal stability boundary for oscillatory convection.

Soft substrates enhance droplet nucleation during water vapor condensation because their deformability inherently reduces the energetic threshold for heterogeneous nucleation relative to rigid substrates. However, this enhancement is counteracted later in the condensation cycle, when substrate viscoelastic dissipation inhibits condensate droplet shedding. Here a polydimethylsiloxane (PDMS) based organogel is designed to overcome this limitation. It is shown that merely 5% bulk lubricant infusion in PDMS reduces viscoelastic dissipation in the substrate by nearly 28 times while doubling the droplet nucleation density. Parameters for water condensation on this organogel are correlated with material properties controlled by design, i.e., fraction and composition of uncrosslinked chains and shear modulus. It is demonstrated that the increase in nucleation density and reduction in precoalescence droplet growth rate is rather insensitive to the lubricant percentage in PDMS within the broad range investigated. These results indicate the presence of a lubricant layer on the substrate surface that cloaks the growing condensate droplets. This cloaking effect is visualized, and it is shown that cloaking occurs significantly faster on PDMS if it is infused with bulk lubricant. Overall, bulk lubricant infusion in PDMS enhances condensation and leads to a more than 40% higher dewing on the substrate., Advanced Functional Materials, 32 (17), ISSN:1616-3028, ISSN:1616-301X