Showing papers in "Journal of Heat Transfer-transactions of The Asme in 1996"

Nonlocal and Nonequilibrium Heat Conduction in the Vicinity of Nanoparticles

Abstract: Heat transfer around nanometer-scale particles plays an important role in a number of contemporary technologies such as nanofabrication and diagnosis The prevailing method for modeling thermal phenomena involving nanoparticles is based on the Fourier heat conduction theory This work questions the applicability of the Fourier heat conduction theory to these cases and answers the question by solving the Boltzmann transport equation The solution approaches the prediction of the Fourier law when the particle radius is much larger than the heat-carrier mean free path of the host medium In the opposite limit, however, the heat transfer rate from the particle is significantly smaller, and thus the particle temperature rise is much larger than the prediction of the Fourier conduction theory The differences are attributed to the nonlocal and nonequilibrium nature of the heat transfer processes around nanoparticles This work also establishes a criterion to determine the applicability of the Fourier heat conduction theory and constructs a simple approximate expression for calculating the effective thermal conductivity of the host medium around a nanoparticle Possible experimental evidence is discussed

Optimizing and Predicting CHF in Spray Cooling of a Square Surface

Abstract: Spray cooling of a hot surface was investigated to ascertain the effect of nozzle-to-surface distance on critical heat flux (CHF). Full cone sprays of Fluorinert FC-72 and FC-87 were used to cool a 12.7 X 12.7 mm 2 surface. A theoretical model was constructed that accurately predicts the spray's volumetric flux (liquid volume per unit area per unit time) distribution across the heater surface. Several experimental spray sampling techniques were devised to validate this model. The impact of volumetric flux distribution on CHF was investigated experimentally. By measuring CHFfor the same nozzle flow rate at different nozzle-to-surface distances, it was determined CHF can be maximized when the spray is configured such that the spray impact area just inscribes the square surface of the heater. Using this optimum configuration, CHF data were measured over broad ranges of flow rate and subcooling, resulting in a new correlation for spray cooling of small surfaces.

The intertube falling film: Part 1 - Flow characteristics, mode transitions, and hysteresis

Abstract: When a liquid film falls from one horizontal tube to another below it, the flow may take the form of discrete droplets, jets, or a continuous sheet ; the mode plays an important role in the wetting and heat transfer characteristics of the film. Experiments are reported that explore viscous, surface tension, inertial, and gravitational effects on the falling-film mode transitions. New flow classifications, a novel flow regime map, and unambiguous transition criteria for each of the mode transitions are provided. This research is part of an overall study of horizontal-tube, falling-film flow and heat transfer, and the results may have important implications on the design and operation of falling-film heat exchangers.

Nucleate Boiling Heat Transfer in Spray Cooling

Abstract: An experimental study to determine the effect of liquid and secondary gas flow in droplet impingement cooling is presented The nucleate boiling regime in particular is analyzed A correlation to predict the Nusselt number based on the liquid film thickness is derived and compared with the experimental data

Absorption/Scattering Coefficients and Scattering Phase Functions in Reticulated Porous Ceramics

Abstract: Spectral absorption and scattering coefficients and spectral scattering phase functions have been derived for partially stabilized zirconia (PS ZrO 2 ) and oxide-bonded silicon carbide (OB SiC) reticulated porous ceramics (RPCs) across the wavelength range 0.4-5.0 μm. These spectral radiative properties were investigated and quantified for 10 ppi (pores/inch), 20 ppi, and 65 ppi materials. Radiative properties were recovered from spectral hemispherical reflectance and transmittance measurements using inverse analysis techniques based upon discrete ordinates radiative models. Two dual-parameter phase functions were investigated for these materials : one based on the physical structure of reticulated porous ceramics and the other a modified Henyey-Greenstein phase function. The modified Henyey- Greenstein phase function provided the most consistent spectral radiative properties. PS ZrO 2 radiative properties exhibited strongly spectrally dependent behavior across the wavelength range studied. OB SiC radiative properties exhibited radiative behavior that was relatively independent of wavelength across the wavelength spectrum studied. OB SiC also demonstrated consistently higher absorption coefficients than PS ZrO 2 at all wavelengths. Spectral scattering albedos of PS ZrO 2 were discovered to be in the range 0.81-0.999 and increased as ppi rating increased, while those for OB SiC were lower in the range 0.55-0.888 and decreased as ppi rating increased. The average extinction efficiencies for 0.4-5.0 μm were discovered to be 1.45 for PS ZrO 2 and 1.70 for OB SiC. Extinction coefficients were discovered to correlate well with geometric optics theoretical models and electromagnetic wave/fiber interaction models based on independent scattering and absorption mechanisms.

Heater Orientation Effects on Pool Boiling of Micro-Porous-Enhanced Surfaces in Saturated FC-72

Abstract: Experiments are performed to understand the effects of surface orientation on the pool boiling characteristics of a highly wetting fluid from a flush-mounted, micro-porous-enhanced square heater Micro-porous enhancement was achieved by applying copper and aluminum particle coatings to the heater surfaces Effects of heater orientation on CHF and nucleate boiling heat transfer for uncoated and coated surfaces are compared A correlation is developed to predict the heater orientation effect on CHF for those surfaces

A Numerical Study of Thermal Dispersion in Porous Media

Abstract: Thermal dispersion in convective flow in porous media has been numerically investigated using a two-dimensional periodic model of porous structure. A macroscopically uniform flow is assumed to pass through a collection of square rods placed regularly in an infinite space, where a macroscopically linear temperature gradient is imposed perpendicularly to the flow direction. Due to the periodicity of the model, only one structural unit is taken for a calculation domain to resolve an entire domain of porous medium. Continuity, Navier-Stokes and energy equations are solved numerically to describe the microscopic velocity and temperature fields at a pore scale. The numerical results thus obtained are integrated over a unit structure to evaluate the thermal dispersion and the molecular diffusion due to tortuosity. The resulting correlation for a high-Peclet-number range agrees well with available experimental data.

Bubble Behavior and Mean Diameter in Subcooled Flow Boiling

Abstract: Bubble behavior and mean bubble diameter in subcooled upward flow boiling in a vertical annular channel were investigated under low pressure and mass flux conditions. A high-speed video system was used to visualize the subcooled flow boiling phenomenon. The high-speed photographic results indicated that, contrary to the common understanding, bubbles tend to detach from the heating surface upstream of the net vapor generation point. Digital image processing technique was used to measure the mean bubble diameter along the subcooled flow boiling region. Data on the axial area-averaged void fraction distributions were also obtained using a single-beam gamma densitometer. Effects of the liquid subcooling, applied heat flux, and mass flux on the mean bubble size were investigated. A correlation for the mean bubble diameter as a function of the local subcooling, heat flux, and mass flux was obtained.

Theoretical analysis of the maximum heat transport in triangular grooves : A study of idealized micro heat pipes

Abstract: A mathematical model for predicting the minimum meniscus radius and the maximum heat transport in triangular grooves is presented. In this model, a method for determining the theoretical minimum meniscus radius was developed and used to calculate the capillary heat transport limit based on the physical characteristics and geometry of the capillary grooves. A control volume technique was employed to determine the flow characteristics of the micro heat pipe, in an effort to incorporate the size and shape of the grooves and the effects of the frictional liquid-vapor interaction. In order to compare the heat transport and flow characteristics, a hydraulic diameter, which incorporated these effects, was defined and the resulting model was solved numerically. The results indicate that the heat transport capacity of micro heat pipes is strongly dependent on the apex channel angle of the liquid arteries, the contact angle of the liquid flow, the length of the heat pipe, the vapor flow velocity and characteristics, and the tilt angle. The analysis presented here provides a mechanism whereby the groove geometry can be optimized with respect to these parameters in order to obtain the maximum heat transport capacity for micro heat pipes utilizing axial grooves as the capillary structure.

Spectral extinction coefficients of soot aggregates from turbulent diffusion flames

Abstract: The spectral extinction coefficients of soot aggregates were studied in the fuel-lean (overfire) region of buoyant turbulent diffusion flames. Extinction measurements were carried out in the wavelength region of 0.2-5.2 μm for flames fueled with acetylene, propylene, ethylene, and propane, burning in air. The present measurements were combined with earlier measurements of soot morphology and light scattering at 0.514 μm in order to evaluate the spectral soot refractive indices reported by Dalzell and Sarofim (1969), Let and Tien (1981), and Chang and Charalampopoulos (1990). The specific extinction coefficients and emissivities were predicted based on Rayleigh-Debye-Gans theory for polydisperse fractal aggregates, which has been recently found to be the best approximation to treat optical cross sections of soot aggregates. The results indicated that available refractive indices of soot do not predict the spectral trends of present measurements in the ultraviolet and infrared regions. Soot complex refractive index was inferred to be m = 1.54 + 0.48i at 0.514 μm, which is surprisingly in best agreement with the values reported by Dalzell and Sarofim (1969). Additionally, specific extinction coefficients of soot aggregates varied with wavelength as λ -0.83 from the visible to the infrared. Finally, soot refractive indices were found to be relatively independent of fuel type for the visible and infrared spectral regions over the H/C ratio range of 0.08-0.22.

The intertube falling film: Part 2-Mode effects on sensible heat transfer to a falling liquid film

Abstract: When a liquid film falls from one horizontal tube to another below it, the flow may take the form of discrete droplets, jets, or a continuous sheet ; the mode plays an important role in the heat transfer. Experiments are reported that explore the local heat transfer behavior for each of these flow patterns, and the results are related to the important features of the flow. Spatially averaged Nusselt numbers are presented and discussed, and new mode-specific design correlations are provided. This research is part of an overall study of horizontal-tube, falling-film flow and heat transfer.

Combined natural convection-conduction and radiation heat transfer in a discretely heated open cavity

Abstract: Combined natural convection, conduction, and radiation heat transfer in an open-top upright cavity containing a discrete heat source has been modeled numerically. The surface emissivity has been varied and its effects on the flow and thermal fields have been determined for different values of Rayleigh number. The complex interaction of the three modes of heat transfer mechanisms is explored by solving the coupled convection, conduction, and radiation equations. It is noted that the inclusion of radiation has a significant effect on the flow, resulting in the formation of a recirculation zone within the cavity. Comparison of the local heat transfer coefficients for the conjugate analysis and no radiation case reveals that the inclusion of radiation has a negligible effect on the heat transfer performance of the heat source. However, comparison of the numerical results with experimental observations shows that accurate prediction of the flow and thermal fields is strongly dependent on the consideration of radiation heat transfer in the numerical case.

Heat Transfer in Open Cell Foam Insulation

Abstract: Heat transfer in open cell foam insulation occurs by conduction through the solid material and though the gas in the cell interior and by thermal radiation, which propagates through the structure The conductive process within these media is described using a simple parallel-series model Spectral volumetric absorption and scattering coefficients as well as the spectral phase function are predicted using a combination of geometric optics laws and diffraction theory to model the interaction of radiation with the particles forming the foam The particles considered are both struts formed at the juncture of three cells and strut junctures The radiative properties can then be utilized to obtain a weighted extinction coefficient, which can be used in the Rosseland equation to obtain the radiative flux The innovative part of the work lies in the radiative properties predictive model This new model is compared with simpler ones 21 refs, 6 figs, 4 tabs

Elastoplastic Contact Conductance Model for Isotropic Conforming Rough Surfaces and Comparison With Experiments

Abstract: A new thermal elastoplastic contact conductance model for isotropic conforming rough surfaces is proposed. This model is based on surface and thermal models used in the Cooper, Mikic, and Yovanovich plastic model, but it differs in the deformation aspects of the thermal contact conductance model. The model incorporates the recently developed simple elastoplastic model for sphere-flat contacts, and it covers the entire range of material behavior, i.e., elastic, elastoplastic, and fully plastic deformation. Previously data were either compared with the elastic model or the plastic model assuming a type of deformation a priori. The model is used to reduce previously obtained isotropic contact conductance data, which cover a wide range of surface characteristics and material properties. For the first time data can be compared with both the elastic and plastic models on the same plot. This model explains the observed discrepancies noted by previous workers between data and the predictions of the elastic or plastic models.

Local Heat Transfer in Rotating Smooth and Ribbed Two-Pass Square Channels With Three Channel Orientations

Abstract: This paper presents experimental heat transfer results in a two-pass square channel with smooth and ribbed surfaces. The ribs are placed in a staggered half-V fashion with the rotation orthogonal to the channel axis. The channel orientation varies with respect to the rotation plane. A change in the channel orientation about the rotating frame causes a change in the secondary flow structure and associated flow and turbulence distribution. Consequently, the heat transfer coefficient from the individual surfaces of the two-pass square channel changes. The effects of rotation number on local Nusselt number ratio distributions are presented. Heat transfer coefficients with ribbed surfaces show different characteristics in rotation number dependency from those with smooth surfaces. Results show that staggered half-V ribs mostly have higher heat transfer coefficients than those with 90 and 60 deg continuous ribs. 16 refs., 10 figs.

Thickness of the Liquid Film Formed by a Growing Bubble in a Narrow Gap Between Two Horizontal Plates

Abstract: An experiment was performed to measure the thickness of the liquid film formed by a growing flattened bubble in a narrow gap whose width ranged from 0.1 to 0.4 mm. High-speed photographs were also taken to measure the bubble growth velocity in order to validate an investigation into the mechanism of the liquid film formation. From the experimental results, it was clarified that the liquid film thickness was controlled by the viscous boundary layer thickness or the capillary number according to whether the Bond number was greater or smaller than 2. 9 refs., 11 figs., 1 tab.

Experimental Investigation of the Maximum Heat Transport in Triangular Grooves

Abstract: An experimental investigation was conducted and a test facility constructed to measure the capillary heat transport limit in small triangular grooves, similar to those used in micro heat pipes. Using methanol as the working fluid, the maximum heat transport and unit effective area heat transport were experimentally determined for ten grooved plates with varying groove widths, but identical apex angles. The experimental results indicate that there exists an optimum groove configuration, which maximizes the capillary pumping capacity while minimizing the combined effects of the capillary pumping pressure and the liquid viscous pressure losses. When compared with a previously developed analytical model, the experimental results indicate that the model can be used accurately to predict the heat transport capacity and maximum unit area heat transport when given the physical characteristics of the working fluid and the groove geometry, provided the proper heat flux distribution is known. The results of this investigation will assist in the development of micro heat pipes capable of operating at increased power levels with greater reliability.

Numerical and Experimental Investigation of Interface Bonding Via Substrate Remelting of an Impinging Molten Metal Droplet

Abstract: A molten metal droplet landing and bonding to a solid substrate is investigated with combined analytical, numerical, and experimental techniques. This research supports a novel, thermal spray shape deposition process, referred to as microcasting, capable of rapidly manufacturing near netshape, steel objects. Metallurgical bonding between the impacting droplet and the previous deposition layer improves the strength and material property continuity between the layers, producing high-quality metal objects. A thorough understanding of the interface heat transfer process is needed to optimize the microcast object properties by minimizing the impacting droplet temperature necessary for superficial substrate remelting, while controlling substrate and deposit material cooling rates, remelt depths, and residual thermal stresses. A mixed Lagrangian-Eulerian numerical model is developed to calculate substrate remelting and temperature histories for investigating the required deposition temperatures and the effect of operating conditions on remelting. Experimental and analytical approaches are used to determine initial conditions for the numerical simulations, to verify the numerical accuracy, and to identify the resultant microstructures. Numerical results indicate that droplet to substrate conduction is the dominant heat transfer mode during remelting and solidification. Furthermore, a highly time-dependent heat transfer coefficient at the droplet/substrate interface necessitates a combined numerical model of the droplet and substrate for accurate predictions of the substrate remelting. The remelting depth and cooling rate numerical results are also verified by optical metallography, and compare well with both the analytical solution for the initial deposition period and the temperature measurements during droplet solidification.

On the Role of Marangoni Effects on the Critical Heat Flux for Pool Boiling of Binary Mixtures

Abstract: The Marangoni effect on the critical heat flux (CHF) condition in pool boiling of binary mixtures has been identified and its effect has been quantitatively estimated with a modified model derived from hydrodynamics. The physical process of CHF in binary mixtures, and models used to describe it, are examined in the light of recent experimental evidence, accurate mixture properties, and phase equilibrium revealing a correlation to surface tension gradients and volatility. A correlation is developed from a heuristic model including the additional liquid restoring force caused by surface tension gradients. The CHF condition was determined experimentally for saturated methanol/water, 2-propanol/water, and ethylene glycol/water mixtures, over the full range of concentrations, and compared to the model. The evidence in this study demonstrates that in a mixture with large differences in surface tension, there is an additional hydrodynamic restoring force affecting the CHF condition.

Thermal Conduction in Nonhomogeneous CVD Diamond Layers in Electronic Microstructures

Abstract: Chemical-vapor-deposited diamond layers of thickness between 0.1 and 5 {mu}m have the potential to improve conduction cooling in electronic microstructures. However, thermal conduction in these layers is strongly impeded by phonon scattering on defects, whose concentrations can be highly nonhomogeneous, and on layer boundaries. By assuming that defects are concentrated near grain boundaries, this work relates the internal phonon scattering rate to the local characteristic grain dimension and to the dimensionless grain-boundary scattering strength, a parameter defined here that varies little within a given layer. Solutions to the Peierls-Boltzmann phonon transport equation for conduction along and normal to layers account for the nonhomogeneous internal scattering rate. Predictions for conduction along and normal to layers as thin as 0.2 {mu}m agree well with room-temperature data. This research helps optimize diamond layer thicknesses for specific microstructures, such as silicon-on-diamond (SOD) circuits. 28 refs., 7 figs.

The Interline Heat Transfer of Evaporating Thin Films Along a Micro Grooved Surface

Abstract: An analytical investigation of the heat transfer characteristics for evaporating thin liquid films in V-shaped microgrooves with nonuniform input heat flux was conducted. This investigation assumed that the capillary pressure difference caused by the receding of the meniscus is responsible for the axial liquid flow along the groove, and that the disjoining pressure difference along the groove side wall provided the driving force for the flow up the groove wall. The combined heat transfer mechanisms of both liquid conduction and interfacial vaporization were used to describe the local interfacial mass flux in the interline region. Based on this approach, a local heat transfer coefficient was defined. The local and average heat transfer coefficients were both found to be sensitive to the characteristic thermal resistance ratio. In addition, when the film superheat was constant, the primary factor affecting the length of the evaporating interline region was found to be the heat flux supplied to the bottom plate, and for high heat flux conditions, the highest heat transfer coefficient did not necessarily exist at the axial dryout point. The expression developed for the evaporating film profile was shown to assume an exponential form if the heat flux distributed on the active interline region was assumed to be uniform.

Inverse Determination of Boundary Conditions and Sources in Steady Heat Conduction With Heat Generation

Abstract: A Boundary Element Method (BEM) implementation for the solution of inverse or ill-posed two-dimensional Poisson problems of steady heat conduction with heat sources and sinks is proposed. The procedure is noniterative and cost effective, involving only a simple modification to any existing BEM algorithm. Thermal boundary conditions can be prescribed on only part of the boundary of the solid object while the heat sources can be partially or entirely unknown. Overspecified boundary conditions or internal temperature measurements are required in order to compensate for the unknown conditions. The weighted residual statement, inherent in the BEM formulation, replaces the more common iterative least-squares (L2) approach, which is typically used in this type of ill-posed problem. An ill-conditioned matrix results from the BEM formulation, which must be properly inverted to obtain the solution to the ill-posed steady heat conduction problem. A singular value decomposition (SVD) matrix solver was found to be more effective than Tikhonov regularization for inverting the matrix. Accurate results have been obtained for several steady two-dimensional heat conduction problems with arbitrary distributions of heat sources where the analytic solutions were available.

Optimal Spacing Between Pin Fins With Impinging Flow

Abstract: This is an experimental, numerical, and theoretical study of the heat transfer on a pin-finned plate exposed to an impinging air stream. The pin fins are aligned with the air approach velocity. The base plate and the fin cross section are square. It is demonstrated experimentally that the thermal conductance between the plate and the air stream can be maximized by selecting the fin-to-fin spacing S. Next, a simplified numerical model is used to generate a large number of optimal spacing and maximum heat transfer data for various configurations, which differ with respect to fin length (H), fin thickness (D), base plate size (L), fluid type (Pr), and air velocity (Re L ). Finally, the behavior of the optimal spacing data is explained and correlated theoretically based on the intersection of asymptotes method. The recommended correlations for optimal spacing, S opt /L≃0.81 Pr -0.25 Re L -0.32 , and maximum thermal conductance, (q/ΔT) max /k a H ≃ 1.57 Pr 0.45 Re L 0.69 (L/D) 0.31 , cover the range D/L = 0.06 - 0.14, H/L = 0.28-0.56, Pr = 0.72-7, Re D = 10-700, and Re L = 90-6000.

Oscillatory Heat Transfer in a Pipe Subjected to a Laminar Reciprocating Flow

Abstract: An experimental and numerical study has been carried out for laminar forced convection in a long pipe heated by uniform heat flux and subjected to a reciprocating flow of air. Transient fluid temperature variations in the two mixing chambers connected to both ends of the heated section were measured. These measurements were used as the thermal boundary conditions for the numerical simulation of the hydrodynamically and thermally developing reciprocating flow in the heated pipe. The coupled governing equations for time- dependent convective heat transfer in the fluid flow and conduction in the wall of the heated tube were solved numerically. The numerical results for time-resolved centerline fluid temperature, cycle-averaged wall temperature, and the space-cycle averaged Nusselt number are shown to be in good agreement with the experimental data. Based on the experimental data, a correlation equation is obtained for the cycle-space averaged Nusselt number in terms of appropriate dimensionless parameters for a laminar reciprocating flow of air in a long pipe with constant heat flux.

The Conjugate Graetz Problem With Axial Conduction

Abstract: Our study is motivated by recent investigations of heat transfer in microheat exchangers fabricated on silicon wafers. The objective is to assess the importance of axial heat conduction in both the solid and the liquid. To this end, we studied slug and Poiseuille flows between parallel plates and in circular cylinders

Monte Carlo Simulation of Radiation in Gases With a Narrow-Band Model and a Net-Exchange Formulation

Abstract: The Monte Carlo method is used for simulation of radiative heat transfers in nongray gases. The proposed procedure is based on a Net-Exchange Formulation (NEF). Such a formulation provides an efficient way of systematically fulfilling the reciprocity principle, which avoids some of the major problems usually associated with the Monte Carlo method : Numerical efficiency becomes independent of optical thickness, strongly nonuniform grid sizes can be used with no increase in computation time, and configurations with small temperature differences can be addressed with very good accuracy. The Exchange Monte Carlo Method (EMCM) is detailed for a one-dimensional slab with diffusely or specularly reflecting surfaces.

Conjugate Heat Transfer From a Single Surface-Mounted Block to Forced Convective Air Flow in a Channel

Abstract: Conjugate heat transfer from a surface-mounted block (31 x 31 x 7 mm 3 ) to forced convective air flow (1 - 7 m/s) in a parallel-plate channel was studied experimentally and analytically. Particular attention was directed to the heat flow from the block to the floor through the block support, which was eventually transferred to the air flow over the floor. The concepts of adiabatic wall temperature (T ad ) and adiabatic heat transfer coefficient (h ad ) were employed to account for the effect of thermal wake shed from the block on the heat transfer from the floor. The experimental data of T ad and had were used in setting the boundary condition for the numerical analysis of heat conduction in the floor. The accuracy of the numerical predictions of the thermal conductances for different heat flow paths was proven experimentally. The heat conduction analysis code was then used to find the heat transfer capability qf various block-support/floor combinations.

Prediction of Jet Impingement Heat Transfer Using a Hybrid Wall Treatment With Different Turbulent Prandtl Number Functions

Abstract: The local heat transfer coefficient distribution on a square heat source due to a normally impinging, axisymmetric, confined, and submerged liquid jet was computationally investigated. Numerical predictions were made for nozzle diameters of 3.18 and 6.35 mm at several nozzle-to-heat source spacings, with turbulent jet Reynolds numbers ranging from 8500 to 13,000. The commercial finite-volume code FLUENT was used to solve the thermal and flow fields using the standard high-Reynolds number k-e turbulence model. The converged solution obtained from the code was refined using a post-processing program that incorporated several near-wall models. The role of four alternative turbulent Prandtl number functions on the predicted heat transfer coefficients was investigated. The predicted heat transfer coefficients were compared with previously obtained experimental measurements. The predicted stagnation and average heat transfer coefficients agree with experiments to within a maximum deviation of 16 and 20 percent, respectively. Reasons for the differences between the predicted and measured heat transfer coefficients are discussed.

Two-Phase Crossflow and Boiling Heat Transfer in Horizontal Tube Bundles

Abstract: An experimental study has been conducted to determine the void fraction, frictional pressure drop, and heat transfer coefficient for vertical two-phase crossflow of refrigerant R-113 in horizontal tube bundles under saturated flow boiling conditions. The tube bundle contained 5 X 20 tubes in a square in-line array with pitch-to-diameter ratio of 1.3. R-113 mass velocity ranged from 50 to 970 kg/m 2 s and test pressure from 103 to 155 kPa. The void fraction data exhibited strong mass velocity effects and were significantly less than the homogeneous and in-tube flow model predictions. They were found to be well correlated in terms of the dimensionless gas velocity, j 8 * . The two-phase friction multiplier data could be correlated well in terms of the Lockhart-Martinelli parameter. The validity of these correlations was successfully tested by predicting the total pressure drop from independent R-113 boiling experiments. The two-phase heat transfer coefficient data were found to agree well with existing pool boiling correlations, implying that nucleate boiling was the dominant heat transfer mode in the heat flux range tested.

Transport Phenomena During Resistance Spot Welding

Abstract: Unsteady, axisymmetric transport of mass, momentum, energy, species, and magnetic field intensity with a mushy-zone phase change in workpieces and temperature, and magnetic fields in electrodes during resistance spot welding, are systematically investigated. Electromagnetic force, joule heat, heat generation at the electrode–workpiece interface and faying surface between workpieces, different properties between phases, and geometries of electrodes are taken into account. The computed results show consistencies with observed nugget growth, electrical current, and temperature fields. The effects of the face radius and cone angle of the electrode, parameters governing welding current, electrical contact resistance, magnetic Prandtl number, electrical conductivity ratio, and workpiece thickness on transport phenomena are clearly provided.