Transient Two-Dimensional Heat Conduction Problem With Partial Heating Near Corners

This paper provides a solution for two-dimensional heating over a rectangular region on a homogeneous plate. It has application to verification of numerical conduction codes as well as direct application for heating and cooling of electronic equipment. Additionally, it can be applied as a direct solution for the inverse heat conduction problem, most notably used in thermal protection systems for re-entry vehicles. The solutions used in this work are generated using Green’s functions. Two approaches are used which provide solutions for either semi-infinite plates or finite plates with isothermal conditions which are located a long distance from the heating. The methods are both efficient numerically and have extreme accuracy, which can be used to provide additional solution verification. The solutions have components that are shown to have physical significance. The extremely precise nature of analytical solutions allows them to be used as prime standards for their respective transient conduction cases. This extreme precision also allows an accurate calculation of heat flux by finite differences between two points of very close proximity which would not be possible with numerical solutions. This is particularly useful near heated surfaces and near corners. Similarly, sensitivity coefficients for parameter estimation problems can be calculated with extreme precision using this same technique. Another contribution of these solutions is the insight that they can bring. Important dimensionless groups are identified and their influence can be more readily seen than with numerical results. For linear problems, basic heating elements on plates, for example, can be solved to aid in understanding more complex cases. Furthermore these basic solutions can be superimposed both in time and space to obtain solutions for numerous other problems. This paper provides an analytical two-dimensional, transient solution for heating over a rectangular region on a homogeneous square plate. Several methods are available for the solution of such problems. One of the most common is the separation of variables (SOV) method. In the standard implementation of the SOV method, convergence can be slow and accuracy lacking. Another method of generating a solution to this problem makes use of time-partitioning which can produce accurate results. However, numerical integration may be required in these cases, which, in some ways, negates the advantages offered by the analytical solutions. The method given herein requires no numerical integration; it also exhibits exponential series convergence and can provide excellent accuracy. The procedure involves the derivation of previously-unknown simpler forms for the summations, in some cases by virtue of the use of algebraic components. Also, a mathematical identity given in this paper can be used for a variety of related problems.

LES Simulations of Rotating Two-Pass Ribbed Duct With Coriolis and Centrifugal Buoyancy Forces at Re=100,000

The focus of this research is to predict the flow and heat transfer in a rotating two-pass duct geometry with staggered ribs using Large-Eddy Simulations (LES). The geometry consists of a U-Bend with 17 ribs in each pass. The ribs are staggered with an e/Dh = 0.1 and P/e = 10. LES is performed at a Reynolds number of 100,000, a rotation number of 0.2 and buoyancy parameters (Bo) of 0.5 and 1.0. The effects of Coriolis forces and centrifugal buoyancy are isolated and studied individually. In all cases it is found that increasing Bo from 0.5 to 1.0 at Ro = 0.2 has little impact on heat transfer. It is found that in the first pass, the heat transfer is quite receptive to Coriolis forces which augment and attenuate heat transfer at the trailing and leading walls, respectively. Centrifugal buoyancy, on the other hand has a bigger effect in augmenting heat transfer at the trailing wall than in attenuating heat transfer at the leading wall. On contrary, it aids heat transfer in the second half of the first pass at the leading wall by energizing the flow near the wall. The heat transfer in the second pass is dominated by the highly turbulent flow exiting the bend. Coriolis forces have no impact on the augmentation of heat transfer on the leading wall till the second half of the passage whereas it attenuates heat transfer at the trailing wall as soon as the flow exits the bend. Contrary to phenomenological arguments, inclusion of centrifugal buoyancy augments heat transfer over Coriolis forces alone on both the leading and trailing walls of the second pass.

Using Thermoelectric Cooling With Tourniquets for Nerve Preservation

The use of a tourniquet leads to nerve damage, even if applied for short periods of time. This damage can be minimized if the limb is cooled. Because of the low conductivities of human tissue, core limb cooling is slow unless the surface temperature is very cool. Subzero surface temperatures can lead to skin injury (i.e., frostbite). Ideally one would adjust the limb surface temperatures as a function of time to maximize the cooling rate while avoiding permanent tissue damage. One possible approach is to use a thermoelectric cooler (TEC) in conjunction with a programmable power supply. TEC performance varies strongly with heat absorption rate, a function of limb thermal properties, and hot side temperatures that are strongly affected by the surface conditions on the hot side, i.e., overall heat transfer coefficients and ambient conditions. The paper describes the use of finite element simulation to predict the usefulness of using thermoelectric coolers applied to the surface of a limb when compared to the standard approach of using ice packs. Since the TEC performance is strongly influenced by its warm side thermal conditions, experimental results are presented for different ambient temperatures, free and forced convection, and evaporation of water from a wickable covering.

An Experimental Study of Boiling Heat Transfer During Quenching of Nanofluids With Carbon Nanotubes of Various Sizes

Quenching experiments were performed with hot stainless steel spheres in a pool of water-based nanofluids in the presence of carbon nanotubes (CNTs) of various sizes. In order to explore the size effect, a test matrix was developed by choosing multi-walled CNTs with lengths from 1 μm to 5 μm and outer diameters from 30 nm to 60 nm. The concentration was fixed at 0.5% by mass for all types of CNTs. The initial temperature was 400 °C and the transient temperature variations at the center of the sphere were recorded as quenching curves. By establishing a lumped capacitance model, the transient surface heat flux variations were obtained as boiling curves. The original and boiled surfaces were both subjected to a series of characterizations to determine the changes in morphology, roughness, and wettability to identify the effects of CNT size on the surface properties of the formed deposition layers as well as to elucidate the mechanisms for regulation of the boiling and quenching behaviors. The results suggested that the critical heat flux (CHF) and the Leidenfrost point (LFP) are enhanced to various degrees due to the discrepancy in the size of the CNTs in nanofluids. It was shown that the CNTs deposited on the surfaces create various morphologies depending on their size. The CNTs with a length of 5 μm and a diameter of 60 nm exhibited the most significant effect on the boiling behaviors. In comparison to CNTs with a shorter length of 1 μm, the 5 μm long CNTs were much easier to form porous layers. The results of the contact angle and roughness tests showed that the porous layers tend to affect the surface roughness instead of surface wettability. The increases of the nucleation site density and surface roughness due to the presence of porous layers were identified as the primary cause for the modified boiling behaviors during quenching.

Bubble Behavior at an Uneven Wall

The present study deals with single bubble growth on an uneven wall. A model problem is defined and solved using a three-dimensional numerical simulation. The wall has the shape of a triangular cavity and feature vortices. The equations solved in the present study are based on macro region modelling of the bubble alone and describe its growth from the initial state to detachment from the surface and consequent motion. The model includes a simultaneous solution of conservation equations for the liquid and gaseous phases, in conjunction with three-dimensional interface tracking. The latter is achieved using the level-set method. The numerical modeling includes the multi-grid method. The complete three-dimensional model is discretized using an original in-house numerical code realized in MATLAB. Different cases of bubble growth on the triangular cavity walls are investigated. The main conclusion from the calculations is that the bubble shape and its growth rate strongly depend on its location and on the channel orientation. New features, not possible for flat walls and special for this case, are revealed and discussed. It is demonstrated that under certain conditions, the bubble is obstructed by the surface geometry. It is also shown how a growing bubble affects the flow field inside a cavity, interacting with the vortex structure.

A Computational Study of Thin Film Dynamics on Micro-Structured Surfaces

The present study is motivated by interest in understanding of physical mechanisms that govern the effect of material and micro-structural characteristics of heat surface on boiling heat transfer and burnout at high heat fluxes. The effect was reported and investigated experimentally and analytically over several past decades. Only recently, with the advent of nanotechnology including microscale manufacturing, it becomes possible to perform high heat-flux boiling experiments with control of surface conditions. Of particular importance for practice is the potential for significant enhancement of boiling heat transfer (BHT) and critical heat flux (CHF) in pool and flow boiling on heaters with specially manufactured and controlled micro-structured surfaces. This enhancement is very important to a very wide range of engineering applications, like heat exchanger and cooling system, where maximum flux is needed. Currently, there are many controlled experiments that investigate such effect and they lend themselves a subject for detailed computational analysis. The focus of this study is micro-hydrodynamics of the evaporating thin liquid film at the receding triple contact line, corresponding to formation of dry spot in the footprint of a growing bubble. Parametric investigations are performed to assess the hypotheses that micro-structured surfaces enhance resilience to burnout due to residual liquid in the dry patch after contact line receding. Towards the study objective, a particle-based (mesh-less) method of computational fluid dynamics called Smoothed Particle Hydrodynamics (SPH) is adopted. The SPH method is selected for its capability to handle fluid dynamics in complex geometries and free surface problems without mass loss (characteristic of alternative interface capturing schemes used in mesh-based methods). Both surface tension and surface adhesion (hydrophilicity) are implemented and tested. The solid (heater) surface and manufactured micro-structures are represented by solid-type particles. Heat transfer, phase change (evaporation) and vapor dynamics are not included in the present simulation. The bouncing drop case measures the contact time of water droplet with solid surface. This case is used for “mesh” sensitivity (particle size) study and calibration of boundary conditions and surface tension coefficient. Subsequently, case studies are formulated and performed for contact line dynamics on heater surfaces with the fabricated Micro Pillar Arrays surfaces (MPA) and smooth surface. Variable characteristics include surface tension and pillar density on structured surface (modified by changing distance between pillars). First of all, residual fluid are found in all simulations with structured surface, while fluid are drained for smooth cases. For structured surface, it’s found that after the contact line recedes, fluid with higher surface tension resides in the dry patch more than fluid with lower coefficient, and the relation tends to be non-linear. While for smooth surface, all fluid will be drained after certain time and the relations are non-monotonic; it’s also found that the amount of residual fluid increase as the distance between pillars decreases until a limit. The fluid then starts to decrease with pillars being set further apart. The increase starts from 30 μm and the limit is around 10 μm.

Heat Transfer Characteristics of Aviation Kerosene in Vertical Upward High Flux Tubes at Supercritical Pressure

An experimental investigation on heat transfer peculiarity of kerosene flowing in vertical upward high flux tubes at supercritical pressure is presented. Three inner-sintered steel powder coating tubes (high flux tubes) and one smooth tube are tested under the different super-critical pressure and different mass flux of kerosene in the experiment. Results are found that all three high flux tubes perform much better than smooth tube at the same parameters of the tube and same working conditions. It can be obviously deduced that the outer wall temperature is reduced by the disturbance in the flow field of the sintered metal coating at the inner tube-side, while the reduced mass flux can increase the wall temperature on the contrary. Heat transfer coefficient is found 2.5 times as the smooth tube, yet both too large and too small particle diameters of metal powder sintered on the tube surface can deteriorate heat transfer. Density and viscosity, thermal conductivity of kerosene at different temperatures and pressures under supercritical pressure can be evaluated by using the extended corresponding state principle, which shows good consistency with the experimental results.

Modeling of Steel Slab Reheating Process in a Walking Beam Reheating Furnace

Slab reheating is a very important step in steel product manufacturing. A small improvement in reheating efficiency can translate into big savings to steel mills in terms of fuel consumption and productivity. Computational fluid dynamics (CFD) has been employed in conducting numerical simulations of the slab reheating furnace operation. However, a full industrial scale three-dimensional (3D) simulation of a slab reheating furnace, while comprehensive, is not an efficient way to conduct broad studies of the slab heating process. In this paper, a comprehensive two-dimensional (2D) numerical heat transfer model for slab reheating in a walking beam furnace was developed using the finite difference method. The 2D heat transfer model utilizes the heat transfer coefficients derived from a 3D reheating furnace CFD model which was validated by using mill instrumented slab trials. The 2D heat transfer model is capable of predicting slab temperature evolutions during the reheating processes based on the real time furnace conditions and steel physical properties. The 2D model was validated by using mill instrumented slab trials and production data. Good agreement between the model predictions and production data was obtained.

Numerical Evaluation of Multiple Phase Change Materials for Pulsed Electronics Applications

A simple and easy to implement 1-D heat transfer modeling approach is presented in order to investigate the performance of various phase change materials (PCMs) under fast transient thermal loads. Three metallic (gallium, indium, and Bi/Pb/Sn/In alloy) and two organic (erythritol and n-octadecane) PCMs were used for comparison. A finite-difference method was used to model the transient heat transfer through the system while a heat integration or post-iterative method was used to model the phase change. To improve accuracy, the material properties were adjusted at each iteration depending on the state of matter of the PCM. The model assumed that the PCM was in direct contact with the heat source, located on the top of the chip, without the presence of a thermal conductivity enhancement. Results show that the three metallic PCMs outperform organic PCMs during fast transient pulses in spite of the fact that two of the metallic PCMs (i.e. indium and Bi/Pb/Sn/In) have considerably lower volumetric heats of fusion than erythritol. This is due to the significantly higher thermal conductivity values of metals which allow faster absorption of the heat energy by the PCM, a critical need in high-energy short pulses. The most outstanding case studied in this paper, Bi/Pb/Sn/In having only 52% of erythritol’s heat of fusion, showed a maximum temperature 20°C lower than erythritol during a 32 J and 0.02 second pulse. This study has shown thermal buffering benefits by using a metallic PCM directly in contact with the heat source during short transient heat loads.

Transient Electrohydrodynamic Manipulation of Particles on the Surface of a Drop

In our previous studies we have shown that particles adsorbed on the surface of a drop can be concentrated at its poles or equator by applying a uniform electric field. This happens even when the applied electric field is uniform; the electric field on the surface of the drop is nonuniform, and so particles adsorbed on the surface are subjected to dielectrophoretic (DEP) forces. In this study, we use leaky dielectric model to model the transient behavior of particles at low electric field frequencies. We show that the frequency of the electric field is an important control parameter that under certain conditions can be used to collect particles at the poles or the equator, and to move them from the poles to the equator. The speed with which particles move on the surface depends on the strength of the electrohydrodynamic flow which diminishes with increasing frequency.