bluuebunny/crossref_metadata_2025 huggingface dataset:
Liquid Jet Impingement Cooling of a Rotating Disk
Authors: Carper H. J. , Saavedra J. J. , Suwanprateep T.
Published: October 2009

Results are presented from an experimental study conducted to determine the average convective heat transfer coefficient for the side of a rotating disk, with an approximately uniform surface temperature, cooled by a single liquid jet of oil impinging normal to the surface. Tests were conducted over a range of jet flow rates, jet temperatures, jet radial positions, and disk angular velocities with various combinations of three jet nozzle and disk diameters. Correlations are presented that relate the average Nusselt number to rotational Reynolds number, jet Reynolds number, jet Prandtl number, and dimensionless jet radial position.
Experimental Investigation of Natural Convection in Partially Divided Enclosures
Authors: Symons J. G.
Published: October 2009

An experimental study has been performed on natural convective heat transfer in inclined enclosures heated from below, and with partitions running in the up-slope direction (see Fig. 1). The influence of a clearance between the partitions and the lower heated isothermal surface is considered. This problem is of particular importance in solar collector design. Heat transfer rates have been measured for Ra < 107, enclosure inclination of 0, 30, 60, and 90 deg from the horizontal, and partition end clearances ranging from zero up to half the enclosure height. A flow visualization study which covers the same range of inclinations and end clearances is also reported. It is shown that introducing a small partition end clearance has no significant effect on the flow or heat transfer rates. However, a large end clearance allows up-slope rolls to be established in the unpartitioned region of the enclosure, resulting in an increase in the heat transfer rates. The natural convective heat transfer rates are found to be independent of both partition end clearance and enclosure inclination over certain ranges of these parameters. The convective heat transfer characteristics are also shown to be related to the flow.
Interaction Between Film Condensation on One Side of a Vertical Wall and Natural Convection on the Other Side
Authors: Poulikakos D.
Published: October 2009

This paper reports a theoretical study of conjugate film condensation on one side of a vertical wall and boundary layer natural convection on the other side. Each phenomenon is treated separately and the solutions for each side are matched on the wall. The main heat transfer and flow characteristics in the two counterflowing layers, namely, the condensation film and the natural convection boundary layer, are documented for a wide range of the problem parameters. In addition, the wall heat flux and the wall temperature distribution resulting from the interaction of the two heat transfer modes (condensation and natural convection) are determined. Important engineering results regarding the overall heat flux from the condensation side to the natural convection side are summarized at the end of the study.
Heat Transfer During Forced Convection Boiling of R-12 Under Swirl Flow
Authors: Agrawal K. N. , Varma H. K. , Lal S.
Published: October 2009

This work is an experimental investigation of heat transfer augmentation in a horizontal R-12 evaporator, continuing an earlier study [1] by the authors on swirl flow pressure drops. Twisted tapes were used to create swirl motion during the flow boiling inside an evaporator tube of 10 mm i.d. Average heat transfer coefficients have been determined for 60 runs corresponding to three heat fluxes, five mass velocities, and four twist ratios. Swirl flow heat transfer coefficients have been found, in general, to be greater than the corresponding plain flow values, but the degree of enhancement varies depending on the test conditions and the twist ratio of the inserted tape. An empirical correlation which predicts the average swirl flow heat transfer coefficients within ± 30 percent of the experimentally observed values has been successfully developed.
Condensation Effects in a Fibrous Insulation Slab
Authors: Vafai K. , Sarkar S.
Published: October 2009

This paper analyzes the moisture accumulation and the increase in the effective thermal conductivity of a fibrous insulation slab due to moisture migration. The problem is modeled as a transient, multiphase flow, with variable properties, in a porous slab with impermeable, adiabatic horizontal boundaries and permeable vertical boundaries, A detailed investigation of the interaction between condensation rate, temperature, liquid content, and vapor density fields is presented. The influences of different humidity levels at the boundaries of the insulation slab are investigated in detail and the importance of the Peclet and Lewis numbers on the condensation process is demonstrated. The analysis shows that condensation, and the resulting augmentation of heat transfer, is a serious problem at large Peclet numbers (Pe > 1). Furthermore, the increase in the Nusselt number for fibrous insulation due to condensation is found to be minimized by designing an insulation slab which has a low Lewis number.
Natural Convection in a Vertical Enclosure Filled With Water Near 4°C
Authors: Lankford K. E. , Bejan A.
Published: October 2009

The natural circulation of near-4°C water in a vertical cavity heated from the side was studied experimentally in a 0.74-m-tall enclosure. The results of a scale analysis were used in order to correlate the overall wall-to-wall heat transfer rate measured experimentally in the Rayleigh number range 108–1011. An analytical similarity solution was obtained for the slender enclosure limit. In that limit the flow pattern is one of incomplete vertical penetration, with stagnant maximum-density water filling the lower end of the vertical enclosure.
Effect of Solute Concentration Gradients on the Onset of Convection: Uniform and Nonuniform Initial Gradients
Authors: Kaviany M. , Vogel M.
Published: October 2009

The time of the onset of convection in a fluid layer, which is initially stably stratified and then heated from below in a transient manner, is determined experimentally and analytically. The initial stratification is due to the presence of a solute concentration gradient. In addition to initial linear solute concentration distributions two other specific initial solute concentration distributions are considered. In Case 1, a zero gradient layer is located underneath a nonzero and uniform gradient layer. In Case 2, the zero gradient layer is on the top. The linear amplification theory is applied to the prediction of the onset time. Interferometry is used as a means of determining the onset time experimentally. It is shown that since the adverse temperature gradient is concentrated near the bottom, any nonuniformity in the solute concentration gradient in this region reduces the effectiveness of the gradient in delaying the onset. Experimental and predicted results are in good agreement.
Numerical Calculation of Three-Dimensional Turbulent Natural Convection in a Cubical Enclosure Using a Two-Equation Model for Turbulence
Authors: Ozoe H. , Mouri A. , Hiramitsu M. , Churchill S. W. , Lior N.
Published: October 2009

This paper presents a model and numerical results for turbulent natural convection in a cubical enclosure heated from below, cooled on a portion of one vertical side wall and insulated on all other surfaces. Three-dimensional balances were derived for material, energy, and the three components of momentum, as well as for the turbulent kinetic energy k and the rate of dissipation of turbulent kinetic energy ε. The constants used in the model were the same as those used by Fraikin et al. for two-dimensional convection in a channel. Illustrative transient calculations were carried out for Ra = 106 and 107 and Pr = 0.7. Both the dominant component of the vector potential and the Nusselt number were found to converge to a steady state. Isothermal lines and velocity vectors for vertical cross sections normal to the cooled wall indicated three-dimensional effects near the side walls. A top view of the velocity vectors revealed a downward spiral flow near the side walls along the cooled vertical wall. A weak spiral flow was also found along the side walls near the wall opposing the partially cooled one. The highest values of the eddy diffusivity were 2.6 and 5.8 times the molecular kinematic viscosity for Ra = 106 and 107, respectively. A coaxial double spiral movement, similar to that previously reported for laminar natural convection, was found for the time-averaged flow field. This computing scheme is expected to be applicable to other thermal boundary conditions.
Structure of Turbulent Adiabatic Wall Plumes
Authors: Lai M.-C. , Jeng S.-M. , Faeth G. M.
Published: October 2009

Weakly buoyant turbulent wall plumes were studied for surfaces inclined 0–62 deg from the vertical (stable orientation). The source of buoyancy was carbon dioxide/air mixtures in still air, assuring conserved buoyancy flux. Profiles of mean and fluctuating concentrations and streamwise velocities were measured at several stations along the wall. Flow structure was also observed by Mie scattering from a laser light sheet. Tests with inclined walls showed that low levels of ambient stratification caused the wall plumes to entrain fluid in the horizontal direction, rather than normal to the wall. Structure predictions were made for vertical wall plumes, considering Favre-averaged mixing-length and k–ε–g models of turbulence. Both methods yielded encouraging predictions of flow structure, in spite of the presence of large-scale coherent turbulent structures observed in the flow visualization.
Correlations for Laminar Mixed Convection Flows on Vertical, Inclined, and Horizontal Flat Plates
Authors: Chen T. S. , Armaly B. F. , Ramachandran N.
Published: October 2009

Local Nusselt numbers for laminar mixed convection flows along isothermal vertical, inclined, and horizontal flat plates are presented for the entire mixed convection regime for a wide range of Prandtl numbers, 0.1 ≤ Pr ≤ 100. Simple correlation equations for the local and average mixed convection Nusselt numbers are developed, which are found to agree well with the numerically predicted values and available experimental data for both buoyancy assisting and opposing flow conditions. The threshold values of significant buoyancy effects on forced convection and forced flow effects on free convection, as well as the maximum increase in the local mixed convection Nusselt number from the respective pure convection limits, are also presented for all flow configurations. It is found that the buoyancy or forced flow effect can increase the surface heat transfer rate from pure forced or pure free convection by about 20 percent.
Two-Fluid and Single-Fluid Natural Convection Heat Transfer in an Enclosure
Authors: Sparrow E. M. , Azevedo L. F. A. , Prata A. T.
Published: October 2009

Natural convection experiments were performed for an enclosure of square cross section containing either a single fluid or two immiscible fluids in a layered configuration. The two vertical walls of the cross section were respectively heated and cooled, while the two horizontal walls were adiabatic. The single-fluid experiments, performed with distilled water and with n-hexadecane paraffin (Pr = 5 and 39.2, respectively), yielded Nusselt numbers whose Rayleigh and Prandtl number dependences were perfectly correlated by a single dimensionless group. These single-fluid results were used as baseline information for the development of methods to predict the heat transfer in two-fluid layered systems. To test the utility of the predictive methods, experiments were carried out for water–hexadecane systems in which the position of the interface separating the liquids was varied parametrically. It was found that the experimentally determined, two-layer Nusselt numbers were in excellent agreement with the predicted values. The prediction methods are not limited to the particular fluids employed here, nor do they require additional experimental data for their application.
Multiple Solutions for Buoyancy-Induced Flow in Saturated Porous Media for Large Peclet Numbers
Authors: Islam Rafiqul M. , Nandakumar K.
Published: October 2009

The problem of buoyancy-induced secondary flow in fluid-saturated porous media is examined using a numerical model. The natural convection is coupled either with a forced axial flow or uniform internal heat generation. In both cases the model equations are shown to exhibit dual solutions over certain ranges of flow parameter. In the two-parameter space of aspect ratio and Grashof number, the flow transition between the two-vortex and four-vortex pattern can be explained in terms of a tilted cusp.
Horizontal Plain and Low-Finned Condenser Tubes—Effect of Fin Spacing and Drainage Strips on Heat Transfer and Condensate Retention
Authors: Yau K. K. , Cooper J. R. , Rose J. W.
Published: October 2009

The paper reports a continuation of an experimental investigation of the effect of fin pitch on the heat transfer performance of horizontal, integral-fin tubes for condensation of steam at near-atmospheric pressure. The effects of “drainage strips” located along the lower edge of finned and plain tubes have been studied. These gave significant increases in the heat transfer coefficient for finned tubes but had only marginal effect for the plain tube. Condensate retention angles have also been measured for simulated condensation using water, ethylene glycol, and refrigerant-113 for finned tubes with and without drainage strips. In the latter case the data agreed satisfactorily with theory. Drainage strips were found to reduce the extent of holdup significantly.
Experimental, Variable Properties Natural Convection From a Large, Vertical, Flat Surface
Authors: Siebers D. L. , Moffatt R. F. , Schwind R. G.
Published: October 2009

Natural convection heat transfer from a vertical, 3.02 m high by 2.95 m long, electrically heat surface in air was studied. The air was at the ambient temperature and the atmospheric pressure, and the surface temperature was varied from 60 C to 520 C. These conditions resulted in Grashof numbers up to 2 × 1012 and surface-to-ambient temperature ratios up to 2.7. Convective heat transfer coefficients were measured at 105 locations on the surface by an energy balance. Boundary layer mean temperature profiles were measured with a thermocouple. Results show that: (1) the turbulent natural convection heat transfer data are correlated by the expression Nuy=0.098Gry1/3TwT∞−0.14 when all properties are evaluated at T∞; (2) variable properties do not have a significant effect on laminar natural convection heat transfer; (3) the transition Grashof number decreases with increasing temperature; and (4) the boundary layer mean temperaturue profiles for turbulent natural convection can be represented by a “universal” temperature profile.
Variable Property Effects in Laminar Natural Convection in a Square Enclosure
Authors: Zhong Z. Y. , Yang K. T. , Lloyd J. R.
Published: October 2009

A numerical, finite-difference study has been carried out to determine the effects of variable properties on the temperature and velocity fields and the heat transfer rate in a differentially heated, two-dimensional square enclosure. Calculations have been done for a Rayleigh number range up to 106, and temperature difference ratios θ0 = (TH–TC) / TC of 0.2, 0.5, 1.0, and 2.0, where THand TC are the hot and cold wall temperatures, respectively. Specific issues that have been addressed are the limits of validity of the Boussinesq approximation, the proper use of a reference temperature, variable property correlation of the heat transfer rate, and the limits of conduction-dominated regions.
An Instability Analysis of Ventilated Channels
Authors: Taleyarkhan R. , Podowski M. , Lahey R. T.
Published: October 2009

A mathematical model has been developed for the linear stability analyses of a system of ventilated parallel boiling channels. The model accomodates phasic slip, nonuniform power distribution, local losses, heater wall dynamics, channel-to-channel (radial) power skews, discrete or continuous ventilation between the channels, turbulent mixing between the channels, various donor-cell options for the lateral transport of energy and momentum, and a transverse momentum equation. A special matrix reduction algorithm was developed to efficiently solve the system of linearized, Laplace-transformed, nodal equations. A parametric study revealed that phasic slip, axial power distribution, heater wall dynamics, local losses, lateral ventilation, and radial power skew can have a significant effect on the stability characteristics of the system [5]. Comparisons were made with the available experimental data, and good agreement was achieved.
The Application of the Galerkin Method to the Solution of the Symmetric and Balanced Counterflow Regenerator Problem
Authors: Baclic B. S.
Published: October 2009

The Galerkin method is applied to solve the symmetric and balanced counterflow thermal regenerator problem. In this approach, the integral equation, expressing the reversal condition in periodic equilibrium of regenerator matrix, is transformed into a set of algebraic equations for the determination of the expansion coefficients associated with the representation of the matrix temperature distribution at the start of cold period in a power series in the space variable. The method is easy and straightforward to apply and leads to the explict analytical expressions for expansion coefficients. As explicit analytical formula for regenerator effectiveness is derived and the corresponding numerical values are computed. An excellent agreement is found between the present results and those reported in the literature by different numerical methods. The convergence towards the exact results by carrying out the computations to higher order terms, as well as the extension of this method to the more general counterflow regenerator problem is discussed.
Prediction of Heat and Mass Regenerator Performance Using Nonlinear Analogy Method: Part 1—Basis
Authors: Banks P. J.
Published: October 2009

Coupled heat and mass transfer between fluid streams by a regenerator with a sorbent matrix may be predicted by the superposition of two independent regenerators, in each of which transfer is driven by a combined potential, analogous to temperature in a similar regenerator transferring heat alone. An air-conditioning regenerator for energy recovery or dehumidification with convective transfer controlling is considered. The combined potentials and associated specific capacities are examined, and the nature of the analogy explored, in view of the dependence of matrix sorption properties on state. Approximate nonlinear expressions for the combined potentials, applicable to air-conditioning regenerators, are derived and utilized.
Prediction of Heat and Mass Regenerator Performance Using Nonlinear Analogy Method: Part 2—Comparison of Methods
Authors: Banks P. J.
Published: October 2009

The prediction of heat and mass regenerator performance by analogy from that of a similar regenerator transferring heat alone is studied in view of the dependence of matrix sorption properties on state. Air-conditioning regenerators with convective transfer controlling are considered. For an energy recovery regenerator, the previous linear analogy method is shown to be satisfactory, while a nonlinear method is required for a regenerative dehumidifier. A nonlinear method using approximate nonlinear expressions for the combined potentials is described and is compared with the previous nonlinear method that is shown to be partly linear. The sources of error in the methods are explored for a silica gel dehumidifier, and ways of improvement are indicated.
The Temperature Distribution Within a Sphere Placed in a Directed Uniform Heat Flux and Allowed to Radiatively Cool
Authors: Duffy D.
Published: October 2009

The temperature field within a sphere is found when the sphere is heated by a directed heat flux and cooled by blackbody radiation. For small heat fluxes, the analytic solution is obtained by transform methods. For large heat fluxes, the solution is computed numerically.
Thermal Conditions in Irradiated, Slowly Moving Liquid Layers
Authors: Houf W. G. , Incropera F. P. , Viskanta R.
Published: October 2009

Vertical temperature distributions have been measured in slowly moving, horizontal liquid layers that were irradiated from above. Radiation was concentrated in the spectral range from 350 to 5000 nm, and the low wavelength (λ < 1300 nm) values of the liquid and substrate radiative properties were varied. Due to the effects of infrared radiation absorption, thermal conditions within the liquid did not exhibit a strong dependence on radiative properties. Conditions were characterized by a stably stratified upper layer, a core region of nearly uniform temperature, and a thin bottom layer of large, unstable temperature gradient. Satisfactory agreement was obtained between the measurements and predictions based on three-dimensional, laminar flow and one-dimensional, radiative transfer models. A weak secondary flow, which involves longitudinal vortices and/or ascending-descending thermals, was predicted by the model and was responsible for maintaining the nearly isothermal core conditions.
Computation of Forced Laminar Convection in Rotating Cavities
Authors: Chew J. W.
Published: October 2009

Finite difference solutions are presented for forced laminar convection in a rotating cylindrical cavity with radial outflow. This forms a simple model of the cooling flow between two compressor disks in a gas turbine engine. If the fluid enters the cavity from a uniform radial source, it is shown that the local Nusselt number changes from that of a “free disk” near the center of the cavity to that for Ekman layer flow at larger radii. With an axial inlet, the flow, and consequently, the heat transfer, is more complex. If vortex breakdown occurs, then the results are very similar to those for the radial inlet case, but otherwise a wall jet forms on the downstream disk, and the heat transfer from this disk may be several times that for the upstream disk. Variation of mean Nusselt number with rotational speed is qualitatively similar to previously published experimental measurements in turbulent flow. The effect of Prandtl number on heat transfer has also been demonstrated.
Natural Convection in a Stably Heated Corner Filled With Porous Medium
Authors: Kimura S. , Bejan A.
Published: October 2009

This is a study of the single-cell natural convection pattern that occurs in a “stably heated” corner in a fluid-saturated porous medium, i.e., in the corner formed between a cold horizontal wall and a hot vertical wall situated above the horizontal wall, or in the corner between a hot horizontal wall and a cold vertical wall situated below the horizontal wall. Numerical simulations show that this type of corner flow is present in porous media heated from the side when a stabilizing vertical temperature gradient is imposed in order to suppress the side-driven convection. Based on numerical solutions and on scale analysis, it is shown that the single cell corner flow becomes increasingly more localized as the Rayleigh number increases. At the same time, the mass flow rate engaged in natural circulation and the conduction-referenced Nusselt number increase. Numerical results for the flow and temperature fields and for the net heat transfer rate are reported in the Darcy-Rayleigh number range 10–6000.
Local and Average Heat Transfer Characteristics for a Disk Situated Perpendicular to a Uniform Flow
Authors: Sparrow E. M. , Geiger G. T.
Published: October 2009

Wind tunnel experiments were performed to determine both the average heat transfer coefficient and the radial distribution of the local heat transfer coefficient for a circular disk facing a uniform oncoming flow. The experiments covered the range of Reynolds numbers Re from 5000 to 50,000 and were performed using the naphthalene sublimation technique. To complement the experiments, an analysis incorporating both potential flow theory and boundary layer theory was used to predict the stagnation point heat transfer. The measured average Nusselt numbers definitively resolved a deep disparity between information from the literature and yielded the correlation Nu = 1.05 Pr0.36 Re1/2. The radial distributions of the local heat transfer coefficient were found to be congruent when they were normalized by Re1/2. Furthermore, the radial profiles showed that the local coefficient takes on its minimum value at the stagnation point and increases with increasing radial distance from the center of the disk. At the outer edge of the disk, the coefficient is more than twice as large as that at the stagnation point. The theoretical predictions of the stagnation point heat transfer exceeded the experimental values by about 6 percent. This overprediction is similar to that which occurs for cylinders and spheres in crossflow.
Turbulent Convective Heat Transfer in Forced Cooled Underground Electric Transmission Systems
Authors: Ghetzler R. , Chato J. C. , Crowley J. M.
Published: October 2009

Heat transfer and friction factors were experimentally determined in a scale model of high-voltage, pipe-type underground transmission systems for Reynolds numbers to 8000. Dielectric insulating oil (Sun No. 4) with a Prandtl number of 120 was utilized for the coolant. Two ratios of cable to enclosure pipe diameters, corresponding to standard and oversize enclosure pipes, were examined for the three-cable system. Helical wire wrap was included to simulate protective skid wires around the cables. Three configurations of cable positioning were considered—open triangular, close triangular, and cradled. A method of generalizing the heat transfer coefficients was developed and tested for rough pipe cables based on extensions of previous work in the literature. The generalized correlation, without correction factors, was found to be applicable only in two cases with appropriate flow pattens and geometries. Heat transfer to the pipe wall could be correlated by standard methods in the high Reynolds number range.
Convective Heat Transfer in a Circular Annulus With Various Wall Heat Flux Distributions and Heat Generation
Authors: Arnas O. A. , Ebadian M. A.
Published: October 2009

Convective heat transfer for steady laminar flow between two concentric circular pipes with walls heated and/or cooled independently and subjected to uniform heat generation is presented in analytical closed form utilizing the linearized Navier-Stokes and energy equations. The flow field is hydrodynamically and thermally fully developed. The effect of heat generation is depicted in Fig. 1 where the ratio of the Nusselt number with heat generation to without heat generation is plotted against the radius ratio, the core size ω. It is seen that heat generation may have positive as well as negative effect on the Nusselt number.
An Analytical Model to Predict Condensate Retention on Horizontal Integral-Fin Tubes
Authors: Rudy T. M. , Webb R. L.
Published: October 2009

In this paper, the authors develop a general analytical model to predict the amount of surface that is flooded during condensation on a horizontal, integral-fin tube. The model is based on capillary equations that predict the amount of liquid rise on a vertical u-shaped channel. The space between adjacent integral fins forms such a channel. The authors compare the model to test data taken during condensation on three integral-fin tubes (748-to-1378 fpm) and a range of fluid properties. The analytical model predicts the amount of liquid retention on a horizontal, integral-fin tube within ± 10 percent over most of the data. The analysis is performed for the case of negligible vapor shear.
Prediction of the Condensation Coefficient on Horizontal Integral-Fin Tubes
Authors: Webb R. L. , Rudy T. M. , Kedzierski M. A.
Published: October 2009

A theoretical model is developed for prediction of the condensation coefficient on horizontal integral-fin tubes for both high and low surface tension fluids. The model includes the effects of surface tension on film drainage and on condensate retention between the fins. First, the fraction of the tube circumference that is flooded with condensate is calculated. Typically, the condensation coefficient in the flooded region is negligible compared to that of the unflooded region. Then the condensation coefficient on the unflooded portion is calculated, assuming that surface tension force drains the condensate from the fins. The model is used to predict the R-11 condensation coefficient on horizontal, integral-fin tubes having 748, 1024, and 1378 fpm. The predicted values are within ±20 percent of the experimental values.
On Predicting Burnout in the Jet-Disk Configuration
Authors: Sharan A. , Lienhard J. H.
Published: October 2009

The prediction of boiling burnout in the jet-disk configuration by Lienhard and Eichhorn (based on the mechanical energy stability criterion) is used to recorrelate the data of Katto, Monde, and others. This new correlation includes the identification of the ranges of influence of viscosity (of a Reynolds number) and of gravity (of a Froude number.) The correlation brings the data together within a standard deviation of ±8.66 percent in the range in which viscosity and gravity exert no influence.
An Analysis of Wave Propagation in Bubbly Two-Component, Two-Phase Flow
Authors: Cheng L. Y. , Drew D. A. , Lahey R. T.
Published: October 2009

Wave propagation in bubbly two-phase, two-component flow was analyzed to assess the validity of some interfacial transfer laws for two-fluid models of two-phase flow. A dispersion relation was derived from the linearized conservation equations and the Rayleigh equation. The phase velocity and wave attenuation calculated from the dispersion relation, compared well with existing high- and low-frequency data. The virtual mass term was found to have a significant effect on wave dispersion in the bubbly flow regime. Thermal effects were found to be important in determining the resonance phenomenon and wave scattering was a major source of damping at frequencies higher than the resonance frequency.
Mixed Convective Flows Around a Slowly Rotating Isothermal Sphere
Authors: Farouk B.
Published: October 2009

The mixed convective flows generated by a heated rotating sphere have been investigated theoretically. The solutions are obtained by considering the full Navier-Stokes and energy equations along with the Boussinesq approximation. The governing equations are expressed in the R-θ-φ coordinates and due to the nature of the flow field generated, all three velocity components appear in the formulation. Due to the symmetry of the problem studied, ∂ξ/∂φ = 0, where ξ is any dependent variable considered. The R and θ momentum equations are expressed in the stream function-vorticity formulation. The resulting four coupled elliptic equations (for stream function, vorticity, vφ, and temperature) are solved numerically. Results have been obtained over a large range of Grashof and Reynolds (based on the rotational velocity of the sphere surface) numbers. The study reveals interesting flow patterns for the mixed convective problems. The gravitationally induced free convection is significant for the slowly rotating sphere where the Grashof number is of the order of or more than the square of the Reynolds number. The results are compared with previously published experimental observations and theoretical predictions based on the boundary layer theory.
Application of the Total Transmittance Nonhomogeneous Radiation Model to Methane Combustion
Authors: Grosshandler W. L. , Nguyen H. D.
Published: October 2009

The total transmittance nonhomogeneous model (TTNH) is about 500 times faster than narrow-band models, and it is usually within 10 percent of the more accurate computation. The purpose of this article is to extend the TTNH model to include CH4 and CO as well as CO2 and H2O, and to include interaction with a black boundary where previously the model had been limited to transparent boundaries. Several realistic combustion examples are presented in which the radiant intensity from a hot, black wall interacts with a nonisothermal volume containing variable concentrations of CO2, H2O, CH4, CO, and soot. The calculations indicate that the TTNH model can be reliably applied to nonhomogeneous combustion environments containing methane and that the presence of a radiating boundary poses no computational difficulty.
Application of a Viscous-Inviscid Interaction Procedure to Predict Separated Flows With Heat Transfer
Authors: Hall E. J. , Pletcher R. H.
Published: October 2009

A viscous-inviscid interaction procedure is described for predicting heat transfer in separated flows. The separating flow in a rearward-facing step/asymmetric channel expansion is considered. For viscous regions, the boundary layer momentum and continuity equations are solved inversely in a coupled manner by a finite-difference numerical scheme. The streamwise convective term is altered to permit marching the solution through regions of reversed flow. The inviscid flow is computed by numerically solving the Laplace equation for streamfunction in the region bounded by the displacement surfaces used in the inverse boundary layer solution. The viscous and inviscid solutions are repeated iteratively until the edge velocities obtained from both solutions are in agreement. Predictions using this method compare favorably with experimental data and other predictions.
Free Convective Heat Transfer in a Liquid-Filled Vertical Annulus
Authors: Prasad V. , Kulacki F. A.
Published: October 2009

An experimental study of convective heat transfer in liquid-filled vertical annulus of radius ratio κ = 5.338 has been conducted for the height-to-gap width ratio A = 0.5, 1, and 1.5. By using water, heptane, and ethylene glycol as the test fluids, a Rayleigh number range of 8 × 106 < Ra < 3 × 1010, and a Prandtl number range of 4 < Pr < 196 have been covered. Curvature effects on the temperature field are significant and result in a lower effective sink temperature for the boundary layer on the isothermally heated inner wall. The Nusselt number Nu thus increases with radius ratio κ. However, the slope of ln (Nu) versus ln (κ) curve is not a constant, and decreases with an increase in κ. The effect of Prandtl number is weak. In the laminar flow regime, the Nusselt number is weakly dependent on the aspect ratio when Nu and Ra are considered in terms of the annulus height L. The start of laminar flow regime is delayed with an increase in radius ratio. For A = 0.5, κ = 5.338, the critical Grashof number is GrL = 7 × 104, which decreases with an increase in A. Turbulence is initiated when the local Grashof number Grx ≃ 4 × 109.
Experiments and Theory on Natural Convection Heat Transfer From Bodies of Complex Shape
Authors: Chamberlain M. J. , Hollands K. G. T. , Raithby G. D.
Published: October 2009

Measurements of the heat transfer by natural convection from isothermal bodies to air are reported and compared to the predictions of the method proposed by Raithby and Hollands [7, 8]. The bodies tested were the cube in various orientations and a body consisting of two touching spheres (a bisphere). The experimental Rayleigh number range extended from 10 to 107. The experimental method incorporated measuring the heat transfer by the transient method and varying the Rayleigh number by varying the pressure. The predictions agreed with the measurements to within an average error of about 3 percent. The results are correlated by single equations, which can be extended to fluids other than air.
An Analytical Mixing Model for Buoyant Jet Injected Into Pipe Flow
Authors: Kim J. H.
Published: October 2009

An analytical model based on jet trajectory, jet diffusion layer, and flow establishment which predicts mixing of a cold jet injected at an angle into a hot crossflow in a horizontal pipe is presented. The impetus of the present study is to provide a method for calculating fluid temperature when a cold jet is injected into a pipe carrying a hot fluid, without recourse to a sophisticated multidimensional computer program. Such a method is urgently needed to resolve the so-called pressurized thermal shock issue in nuclear industry. The model prediction is compared with representative cases of existing test data, and is shown to predict the temperature distribution reasonably well.
Film Boiling Heat Transfer on an Isothermal Vertical Surface
Authors: Bui T. D. , Dhir V. K.
Published: October 2009

Natural convection film boiling heat transfer of saturated liquids on an isothermal vertical surface is investigated both experimentally and theoretically. Local heat transfer coefficients are obtained at steady-state conditions on a 6.3-cm-wide and 10.3-cm-high heated surface which was machined from a large block of copper. Effectively isothermal surface conditions are achieved even for wall superheats up to 450 K. Experiments conducted with water at 1 atm pressure show that predictions from existing theoretical models are inadequate and a detailed consideration of the liquid-vapor interface behavior is required. Still and motion pictures of the vapor film are taken and data on vapor film thickness, interfacial wave behavior, and bubble detachment characteristics are obtained to build an analytical model for predicting film boiling heat transfer. This time-dependent model based on laminar flow in the film incorporates the effects of both large-scale and small-scale waves. Results from analysis are compared with experimental data.
Freezing in the Presence of Rotation
Authors: Nelson J. S. , Sparrow E. M.
Published: October 2009

Freezing of a phase-change medium in a sealed, rotating cylindrical capsule was studied experimentally. The axis of rotation was either colinear with the axis of the capsule or perpendicular to the axis of the capsule, with corresponding maximum centrifugal forces of about 2g and 4 1/2g. The role of rotation differed depending on whether the capsule was fully or partially filled with liquid at the onest of freezing. For the fully filled capsule, rotation-related effects occurred only when the liquid was initially superheated relative to the fusion temperature. Rotation, acting via the Coriolis force, decreased the heat flow from the superheated liquid to the solid-liquid interface which, in turn, gave rise to a small increase in the rate of solidification and in the energy extracted from the capsule, with the net effect being no larger than 5 percent. In the perpendicular mode, rotation had a significant effect on the spatial distributions of the frozen layer thickness and of the voids. For the case of a partially filled capsule, rotation altered the position and shape of the air space associated with the partial filling and in this way gave rise to substantial increases (up to 17 percent) in the rate of solidification.
Natural Convection Near a Cold Plate Facing Upward in a Porous Medium
Authors: Kimura S. , Bejan A. , Pop I.
Published: October 2009

It is shown that the phenomenon of natural convection driven in a porous medium by a cold plate facing upward or by a warm plate facing downward consists of a finite-length boundary layer flow chopped off by the sharp edges of the plate. The heat and fluid flow features of the boundary layer are determined analytically employing scale analysis and integral analysis. The overall heat transfer rate between porous medium and plate is found to vary as Nu/Ra1/3 = 0(1), where Ra is the Darcy-modified Rayleigh number based on plate half-length. The boundary layer features of the flow and the heat transfer effected by it are confirmed in the Ra range 100–700 by numerical solutions of the complete partial differential equations.
Two-Dimensional Periodic Natural Convection in a Rectangular Enclosure of Aspect Ratio One
Authors: Briggs D. G. , Jones D. N.
Published: October 2009

A two-dimensional rectangular cavity of aspect ratio one is studied experimentally using a laser-doppler velocimeter. The enclosure is air filled and consists of two vertical walls at unequal isothermal temperatures and two connecting horizontal walls with temperatures varying linearly between the two vertical surfaces. This study clearly defines the existence of periodic laminar flow regimes detectable at Ra numbers above 0.3 × 107. These periodic variations in velocity are induced by the upper and lower boundary conditions. The envelopes of vertical and horizontal velocity fluctuations are reported as a function of position for Rayleigh numbers of 0.25 × 107, 0.50 × 107, and 0.85 × 107. In addition, the effect of Ra number on frequency of flow is reported.
Natural Convection in a Confined Fluid-Filled Space Driven by a Single Vertical Wall With Warm and Cold Regions
Authors: Poulikakos D.
Published: October 2009

This paper reports heat and fluid flow results which describe the phenomenon of natural convection in an enclosure heated and cooled along a single vertical wall. In the first part of the paper, the case where the side-heating effect is positioned above the side-cooling effect is considered. Numerical simulations and scale analysis show that the temperature field in this configuration transforms from one of incomplete vertical penetration to one of incomplete horizontal penetration depending on the values of the Rayleigh number based on the enclosure height (Ra) and the height-to-length aspect ratio of the enclosure (H/L). The heat transfer scales differ substantially from one type of penetrative convection to the other in agreement with the numerical findings. The parametric domain of validity of the conclusions of this part of the study is outlined on the H/L-Ra plane. When the heated portion of the driving side wall is positioned below the cooled portion the flow spreads throughout the cavity. This configuration results in an enhancement of the overall heat transfer through the enclosure.
Interaction of Natural Convection Wakes Arising From Thermal Sources on a Vertical Surface
Authors: Jaluria Y.
Published: October 2009

A numerical study of the interacting natural convection flows generated by isolated thermal energy sources, such as electronic components, located on a vertical adiabatic surface is carried out. Of particular interest were the effects of the wake on the heat transfer from and the flow over a downstream heat source and the nature of the wall plume far from the sources. This consideration is related to the positioning of finite-sized electronic components and the relevant heat removal process. A two-dimensional flow is considered, without making the boundary-layer assumptions. The full elliptic equations governing the flow are solved numerically, employing finite-difference methods. The results are compared with the boundary layer solutions, obtained in earlier studies, in order to determine the nonboundary-layer effects. This is an important consideration in several practical circumstances that involve small heat inputs, sources of relatively small heights, and small separation distances between the sources. It is found that the flow downstream rapidly approaches the characteristics of an idealized wall plume due to a line source. A boundary-layer flow arises far from the heat sources and this flow provides the boundary conditions for the elliptic problem. The nature of the velocity and temperature fields is studied in detail for a wide range of governing parameters and the heat transfer coefficients for the heated elements determined. The relevance of the results obtained to practical systems is outlined, particularly for small Grashof numbers which necessitate a solution of the full equations.
A Study of the Relationship Between Free-Stream Turbulence and Stagnation Region Heat Transfer
Authors: VanFossen G. J. , Simoneau R. J.
Published: October 2009

A study has been conducted at the NASA Lewis Research Center to investigate the mechanism that causes free-stream turbulence to increase heat transfer in the stagnation region of turbine vanes and blades. The work was conducted in a wind tunnel at atmospheric conditions to facilitate measurements of turbulence and heat transfer. The model size was scaled up to simulate Reynolds numbers (based on leading edge diameter) that are to be expected on a turbine blade leading edge. Reynolds numbers from 13,000 to 177,000 were run in the present tests. Spanwise averaged heat transfer measurements with high and low turbulence have been made with “rough” and smooth surface stagnation regions. Results of these measurements show that, at the Reynolds numbers tested, the boundary layer remained laminar in character even in the presence of free-stream turbulence. If roughness was added the boundary layer became transitional as evidenced by the heat transfer increase with increasing distance from the stagnation line. Hot-wire measurements near the stagnation region downstream of an array of parallel wires has shown that vorticity in the form of mean velocity gradients is amplified as flow approaches the stagnation region. Finally smoke wire flow visualization and liquid crystal surface heat transfer visualization were combined to show that, in the wake of an array of parallel wires, heat transfer was a minimum in the wire wakes where the fluctuating component of velocity (local turbulence) was the highest. Heat transfer was found to be the highest between pairs of vortices where the induced velocity was toward the cylinder surface.
Three-Dimensional Numerical Calculations of Flow and Plume Spreading Past Cooling Towers
Authors: Demuren A. O. , Rodi W.
Published: October 2009

The paper reports on the application of an existing three-dimensional computer code to the calculation of the flow and temperature field past cooling towers. The code uses a rectangular grid so that the round tower geometry has be approximated by steps. Simulations are presented of various idealized laboratory studies carried out with cylindrical cooling tower models with the ratio of plume exit to cross-wind velocity varying in the range 0.2 to 1.7 and the densimetric Froude number in the range ∞ to 2. By comparison with the experimental results it is shown that the computer model is capable of reproducing the main features of the complex flow and temperature field past cooling towers including the downwash effect at strong cross winds. The quantitative agreement is not always entirely satisfactory, and suggestions are made for improving the computer model.
Free Convective Heat Transfer Over a Nonisothermal Body of Arbitrary Shape Embedded in a Fluid-Saturated Porous Medium
Authors: Nakayama A. , Koyama H.
Published: October 2009

The problem of free convective heat transfer from a nonisothermal two-dimensional or axisymmetric body of arbitrary geometric configuration in a fliud-saturated porous medium was analyzed on the basis of boundary layer approximations. Upon introducing a similarity variable (which also accounts for a possible wall temperature effect on the boundary layer length scale), the governing equations for a nonisothermal body of arbitrary shape can be reduced to an ordinary differential equation which has been previously solved by Cheng and Minkowycz for a vertical flat plate with its wall temperature varying in an exponential manner. Thus, it is found that any two-dimensional or axisymmetric body possesses a corresponding class of surface wall temperature distributions which permit similarity solutions. Furthermore, a more straightforward and yet sufficiently accurate approximate method based on the Ka´rma´n-Pohlhausen integral relation is suggested for a general solution procedure for a Darcian fluid flow over a nonisothermal body of arbitrary shape. For illustrative purposes, computations were carried out on a vertical flat plate, horizontal ellipses, and ellipsoids with different minor-to-major axis ratios.