bluuebunny/crossref_metadata_2025 huggingface dataset:
Forced-Convection Heat Transfer in a Spherical Annulus Heat Exchanger
Authors: Tuft D. B. , Brandt H.
Published: October 2009

Results are presented of a combined numerical and experimental study of steady, forced-convection heat tranfer in a spherical annulus heat exchanger with 53°C water flowing in an annulus formed by an insulated outer sphere and a 0°C inner sphere. The inner sphere radius is 139.7 mm, the outer sphere radius is 168.3 mm. The transient laminar incompressible axisymmetric Navier-Stokes equations and energy equation in spherical coordinates are solved by an explicit finite-difference solution technique. Turbulence and buoyancy are neglected in the numerical analysis. Steady solutions are obtained by allowing the transient solution to achieve steady state. Numerically obtained temperature and heat-flux rate distributions are presented for gap Reynolds numbers from 41 to 465. Measurements of inner sphere heat-flux rate distribution, flow separation angle, annulus fluid temperatures, and total heat transfer are made for Reynolds numbers from 41 to 1086. The angle of separation along the inner sphere is found to vary as a function of Reynolds number. Measured total Nusselt numbers agree with results reported in the literature to within 2.0 percent at a Reynolds number of 974, and 26.0 percent at a Reynolds number of 66.
Heat Transfer in Laminar Flow With a Phase Change Boundary
Authors: Asgarpour S. , Bayazitoglu Y.
Published: October 2009

Thermal analysis of a shell-and-tube heat exchanger with a phase change material (PCM) on the shell side and a heat transfer fluid flowing through the tube is presented. The phase change material was initially liquid at its solidification temperature. The heat transfer fluid originates from an isothermal reservoir at a temperature which is lower than the temperature of the phase change material. Numerical results of finite difference method are obtained with a ratio of the thermal properties of the phase change material to the fluid to represent n-octadecane, wax-water system. Variations of the temperature distribution for the fluid, and the PCM, and the interface position of the phase change material in the radial and axial directions are presented. The bulk temperature of the fluid is shown to be a function of the Stefan number, the Fourier number and the velocity profile. It is also shown that the Biot number varies in the axial direction and the heat capacity effects of the phase change material, even at low Stefan numbers are significant.
Design and Optimization of Air-Cooled Heat Exchangers
Authors: Hedderich C. P. , Kelleher M. D. , Vanderplaats G. N.
Published: October 2009

A computer code has been developed for analysis of air-cooled heat exchangers and was coupled with a numerical optimization program to produce an automated air-cooled, heat-exchanger design and optimization procedure. A general iteration free approximation method was used for the analysis which calculates the mean overall heat-transfer coefficient and the overall pressure drop for many flow arrangements. The analysis takes into account the variation of the heat-transfer coefficients and the pressure drop with temperature and/or length of flow path. The code is not limited to surfaces found in the literature, but will accommodate any triangular pitch bank of finned tubes in multiple-pass configurations. The numerical optimization code is a general purpose program based on the Method of Feasible Directions and the Augmented Lagrange Multiplier Method. The capability is demonstrated by the design of an air-to-water finned-tube heat exchanger and is shown to be a useful tool for heat exchanger design.
Effect of Blockage-Induced Flow Maldistribution on the Heat Transfer and Pressure Drop in a Tube Bank
Authors: Sparrow E. M. , Ruiz R.
Published: October 2009

Detailed experiments, encompassing per-tube heat-transfer measurements and row-by-row pressure measurements, were performed to investigate the response of a tube bank to maldistribution of the flow at the inlet cross section. The maldistribution was created by a partial blockage of the inlet section. Baseline experiments for uniformly distributed inlet flow were also carried out. The experiments spanned an order of magnitude range in the Reynolds number. On the whole, the inlet-section flow maldistribution tends to enhance the heat transfer at a given Reynolds number, with an accompanying additional pressure drop of about 2 1/2 velocity heads. Enhancements in the 30–40 percent range are encountered in the first several rows in the corridor downstream of the unblocked portion of the inlet section. Reductions (up to 50 percent) are confined to a narrow alley behind the blockage. Ten-percent maldistribution-related effects persist to the seventh row, while effects at the 5 percent level occur at least as far downstream as the twelfth row.
Laminar and Turbulent Boundary Layers on Moving, Nonisothermal Continuous Flat Surfaces
Authors: Moutsoglou A. , Bhattacharya A. K.
Published: October 2009

The heat-transfer characteristics of buoyancy-affected laminar and turbulent boundary layers on nonisothermal continuous flat surfaces that move steadily through a quiescent ambient fluid are studied analytically. Both cooling and heating of the continuous plate which is moving upward or downward in a horizontal, vertical, or inclined direction are considered. A mixing length model for the eddy diffusivities of momentum and heat based on an extension of the Van Driest model is employed in the turbulent boundary layers. Numerical results, such as wall shear stress, surface heat-transfer rate, and surface temperature variation, are presented for various Reynolds and Grashof numbers for fluids with a Prandtl number of 0.7, for both laminar and turbulent boundary layers. A good agreement is found between the analytical and experimental results for friction factor in turbulent boundary layer over an isothermal, continuous moving plate.
Mass Transfer in the Neighborhood of Jets Entering a Crossflow
Authors: Goldstein R. J. , Taylor J. R.
Published: October 2009

The mass-transfer coefficient in the neighborhood of a row of jets entering a cross flow is determined by measuring the local sublimation rate from a naphthalene surface. This mass transfer relates directly to the heat transfer that would occur on a film-cooled wall. The experiments indicate that jets significantly increase the transfer coefficient in the neighborhood of the holes through which the jets emanate—in particular, immediately adjacent to the holes and also some distance downstream of the centerlines of the holes.
Effect of Pressure on Bubble Growth Within Liquid Droplets at the Superheat Limit
Authors: Avedisian C. T.
Published: October 2009

A study of high-pressure bubble growth within liquid droplets heated to their limits of superheat is reported. Droplets of an organic liquid (n-octane) were heated in an immiscible nonvolatile field liquid (glycerine) until they began to boil. High-speed cine photography was used for recording the qualitative aspects of boiling intensity and for obtaining some basic bubble growth data which have not been previously reported. The intensity of droplet boiling was found to be strongly dependent on ambient pressure. At atmospheric pressure the droplets boiled in a comparatively violent manner. At higher pressures photographic evidence revealed a two-phase droplet configuration consisting of an expanding vapor bubble beneath which was suspended a pool of the vaporizing liquid. A qualitative theory for growth of the two-phase droplet was based on assuming that heat for vaporizing the volatile liquid was transferred across a thin thermal boundary layer surrounding the vapor bubble. Measured droplet radii were found to be in relatively good agreement with predicted radii.
A Solution for Dispersed Flow Heat Transfer Using Equilibrium Fluid Conditions
Authors: Yoder G. L. , Rohsenow W. M.
Published: October 2009

A method for predicting steady state dispersed vertical upflow film boiling heat transfer under constant heat flux conditions is presented. Differential transport equations and accepted heat transfer correlations are used to form a solution dependent upon knowledge of conditions at the dryout point only. Thermal nonequilibrium is included in the analysis and the actual flow quality is determined from local equilibrium conditions. A nondimensional grouping is derived which indicates the extent of nonequilibrium present in the flow. Results of this analysis are compared to data of three fluids in tube geometry: Freon 12, nitrogen, and steam. Predictions compare favorably with data from all three fluids.
Natural Convection at the Interface Between a Vertical Porous Layer and an Open Space
Authors: Bejan A. , Anderson R.
Published: October 2009

This paper examines the interaction by natural convection between a fluid-saturated porous medium and a fluid reservoir separated by a vertical impermeable partition. The two fluid systems are maintained at different temperatures. The analysis is simplified by assuming Pr > > 1 in the fluid reservoir. It is shown analytically that the flow and temperature fields in the boundary layer regime consist of two fluid layers in counterflow. The interface temperature is shown to increase monotonically with altitude. The important dimensionless group which governs the fluid mechanics is B = (kRaK1/2) / (k′Ra1/4), where k, k′, RaK and Ra are, respectively, the porous medium conductivity, reservoir fluid conductivity, Darcy-modified Rayleigh number based on partition height, and the reservoir Rayleigh number based on partition height. The effect of parameter, B, on the flow, temperature, and heat transfer is documented in the range 0 < B < ∞.
The Effect of Nonlinear Density Stratification on the Stability of a Vertical Water Layer in the Conduction Regime
Authors: Shaaban A. H. , O¨zis¸ik M. N.
Published: October 2009

The thermal stability of a layer of water between two vertical parallel plates maintained at different temperatures, T1 and T2, is investigated for the conduction regime. Three cases are considered include where: (a) the maximum density layer is within the water region; (b) is at the boundary; and (c) is outside the water region. Cubic polynomials are used to represent the density-temperature relation in the temperature range 0–55°C. The numerical results show that the critical states of stability do not depend on Prandtl number but instead depends on the combinations of T1 and T2. Of the three cases considered, the first case is the most unstable. In all three cases, the instabilities set in as a traveling wave, moving against gravity, for most T1 and T2 combinations. Stationary waves were also found for case (c).
A Correlation Theory for Steady Natural Convective Heat Transport in Horizontal Annuli
Authors: Boyd R. D.
Published: October 2009

A correlation theory for two-dimensional natural convective heat transport data for horizontal annuli of arbitrary cross section has been developed and applied to two configurations: (i) concentric circular cylinders and (ii) annuli formed by an inner hexagonal cylinder and an outer circular cylinder. Also embodied in the theory is the capability to predict local as well as mean heat transfer. Thermal boundary conditions of the form T′xm can be accommodated. Data for the Rayleigh number (RaR) varied from 10 to 107, Prandtl number (Pr) varied from 0.7 to 3100, and the aspect ratio (Δ′/r′, maximum annulus gap/minimum radius of inner annulus) varied from 0.5 to 2.0. Even with these large variations, the present correlation theory collapses all the experimental data for the annular geometries to a signle line. The physical problem appears to be completely specified by a single equation when the following is known: thermal boundary condition (i.e., m), the fluid (i.e., Pr), the aspect ratio, the Rayleigh number, and the geometry. This work demonstrates that the present theory is applicable to annuli of arbitrary cross section, and therefore the theory will be extended to include curvature effects and axisymmetric geometry.
An Experimental Study of Plane Plumes in Cold Water
Authors: Joshi Y. , Gebhart B.
Published: October 2009

The peculiar density variation of water with temperature makes the Boussinesq approximations invalid in the vicinity of density extremum conditions. The buoyancy force reversals which often arise from the density extremum have been studied in many recent investigations. The formulation of an accurate density relation has resulted in a simplified analysis for many convective motions. Two such analyses have dealt with the flow generated above a heated line source in cold water, around the extremum point. We present an experimental investigation of such flow. Temperature measurements have been carried out for ambient temperatures, t∞ ≥ tm, the temperature of density extremum, for pure water at atmospheric pressure. These measurements are in satisfactory agreement with the analyses. As the ambient temperature is successively increased above the density extremum temperature, the transformation of the flow behaviour from non-Boussinesq to Boussinesq is very clearly observed. Velocity measurements have been made at t∞=4°C, the extremum temperature. For t∞<tm, very complex flow patterns exist, due to the bidirectional buoyancy force. These patterns have been visualized. The influence of a bounding impermeable surface below the plume source has also been examined.
The Stratification in Natural Convection in Vertical Enclosures
Authors: Schinkel W. M. M. , Linthorst S. J. M. , Hoogendoorn C. J.
Published: October 2009

This paper presents theoretical results on natural convection in vertical air-filled enclosures with isothermal hot and cold walls. The flow is considered to be two-dimensional, laminar, and stationary. The effect of stratification of the fluid in the core region on the heat transfer and the natural convection flow is discussed. Local heat transfer relations considering this stratification are given. The Rayleigh number varied from 104−106, the aspect ratio from 1–18, and the side walls were both perfectly conducting and adiabatic.
Patterns of Natural Convection Around a Square Cylinder Placed Concentrically in a Horizontal Circular Cylinder
Authors: Chang K. S. , Won Y. H. , Cho C. H.
Published: October 2009

The Galerkin finite element method was used to analyze the natural convection heat transfer in an irregular enclosure made by two isothermal concentric horizontal cylinders: the inner square cylinder and the outer circular cylinder. Two different aspect ratios, A/R = 0.2 and 0.4, are considered for two possible symmetric attitudes of the inner square cylinder. For the case of aspect ratio 0.4, experimental verification has also been made by obtaining field temperature measurement and streamline visualization. It is found that there is no boundary layer separation past the sharp edges of the inner cylinder in the range of Rayleigh numbers less than 105, although this phenomenon plays a negative role in the local and overall heat transfer. Above the upper horizontal surface of the inner square cylinder, a well-defined symmetric plume is found despite its low flow speed and temperature gradient. For the geometry of stand-on-edge position of the inner cylinder, vortex cores exist in the enclosure in quadruple for Ra≤5.0×104 and A/R = 0.4, and in double for other cases including A/R = 0.2.
Radiative Heat Transfer Through a Randomly Packed Bed of Spheres by the Monte Carlo Method
Authors: Yang Y. S. , Howell J. R. , Klein D. E.
Published: October 2009

Radiative heat transfer through evacuated randomly packed beds of uniform-diameter spheres is considered. A Monte Carlo technique is used to simulate the energy bundle traveling through the voids of the bed. The randomly packed bed is assumed to be an absorbing-scattering medium with effective absorption and scattering coefficients. The packing pattern is modeled by a numerical simulation of rigid spheres slowly settling into a randomly packed assemblage. The Monte Carlo simulation of radiant energy transport through the packed beds generates the transmission curve as a function of bed height and sphere emissivity. The effective absorption and scattering coefficients of the randomly packed bed are evaluated by using the solution of the two-flux equations and Monte Carlo transmission results. Results show a strong dependence of the thermal radiative properties on the packing structure and the size and emissivity of constitutent spheres. Qualitative agreement is shown in comparison with other work which used regular cubic packing, and with existing experimental data.
Numerical Study of Transient High Rayleigh Number Convection in an Attic-Shaped Porous Layer
Authors: Poulikakos D. , Bejan A.
Published: October 2009

Scaling arguments and numerical analysis are used to document the transient and steady-state regimes of natural convection in a triangular porous layer cooled from above (along the sloping wall). The numerical simulations are conducted in the high Rayleigh number domain, Ra = 100, 1000, where Ra is the Darcy-modified Rayleigh number based on height, H. The scale analysis predicts the existence of distinct thermal boundary layers if Ra1/2 (H/L) > 1, where H/L is the height/length geometric ratio of the attic-shaped porous layer. The numerical simulations confirm the scaling results, as well as the prediction that the flow consists primarily of an elongated horizontal counterflow driven by the cold wall. In addition, the numerical solutions show the presence of a Be´nard-type instability at high enough Rayleigh numbers. For example, if H/L = 0.2, the instability is present when Ra > 620; this critical Rayleigh number is found to increase as H/L increases.
Analysis of Coolant Entrance Boundary Shape of Porous Region to Control Cooling Along Exit Boundary
Authors: Siegel R. , Snyder A.
Published: October 2009

A cooled porous region has a plane surface exposed to a specified spatially varying heat flux. The coolant leaves the region through this surface, and it is desired to control the flow distribution to maintain a specified uniform surface temperature. This is accomplished by having the coolant entrance surface shaped to provide in the region the necessary variation of path length and, hence, flow resistance. The surface shape at the coolant entrance is found by solving a Cauchy boundary value problem. An exact solution is obtained that will deal with a wide variety of heating distributions for both two- and three-dimensional shapes.
Vortex Instability of Horizontal and Inclined Natural Convection Flows From Simultaneous Thermal and Mass Diffusion
Authors: Chen T. S. , Tzuoo K. L. , Moutsoglou A.
Published: October 2009

An analysis is performed to study the heat/mass transfer and vortex instability characteristics of buoyancy induced flows that result from simultaneous diffusion of heat and mass in laminar boundary layers adjacent to horizontal and inclined surfaces. Numerical results are obtained for a Prandtl number of 0.7 over a range of Schmidt numbers and various angles of inclination from the horizontal, φ. For a given φ, it is found that when the two buoyancy forces from thermal and mass diffusion act in the same direction, both the surface heat and mass transfer rates increase, causing the flow to become more susceptible to the vortex mode of instability. These trends are reversed when the two buoyancy forces act in the opposite directions. On the other hand, as φ is increased, the heat and mass transfer rates are enhanced, but the instability of the flow to the vortex mode of disturbances decreases and eventually vanishes at φ = 90 deg.
Laser-Doppler Measurements of the Velocity Along a Heated Vertical Wall of a Rectangular Enclosure
Authors: Ozoe H. , Ohmuro M. , Mouri A. , Mishima S. , Sayama H. , Churchill S. W.
Published: October 2009

The horizontal and vertical velocity profiles near a heated vertical wall of rectangular enclosure were measured for the laminar regime of natural convection with a laser-Doppler anemometer. The horizontal temperature profiles near the heated wall were measured with a thermocouple. An almost perfect two-dimensional mode of flow was confirmed for the central regime of the box. A minimum in the temperature profile between the hot wall and the thermally stratified central core resulted in a downward flow just outside the boundary layer of upward flow, but the central core was stagnant. Visualization of the flow with a phenolphtalein tracer confirmed the two-dimensionality of the flow along the vertical heated wall and revealed a zone of three-dimensional flow in the form of spiral streaklines along the insulated top plate toward the opposing cooled vertical wall. Measurements such as these provide for the first time the basis for a critical test of the accuracy of numerical solutions.
Mixed Convection Heat Transfer in a Horizontal Open-Channel Flow With Uniform Bottom Heat Flux
Authors: Wang G. S. , Incropera F. P. , Viskanta R.
Published: October 2009

Flow visualization studies and heat transfer measurements have been made for water flow in an open channel which is uniformly heated from below. In addition, a two-dimensional boundary layer model, which includes a buoyancy term in the momentum equation and accounts for the effect of buoyancy on turbulence, has been used to predict the heat transfer measurements. Thermal boundary layer development involves an inlet region for which buoyancy effects are negligible, a transition region characterized by mixed convection, and a downstream region which is dominated by turbulent free convection. The regions are delineated in terms of the mixed convection parameter Grx/Rex3/2, and heat transfer measurements are compared with existing forced, free, and mixed convection correlations.
Turbulent Boundary Layer Heat Transfer Experiments: A Separate Effects Study on a Convexly Curved Wall
Authors: Simon T. W. , Moffat R. J.
Published: October 2009

Measured heat transfer rates through turbulent and transitional boundary layers on an isothermal, convexly curved wall show Stanton numbers 20–50 percent below flat wall values. Recovery is slow on a flat wall downstream of the curve; after 60 cm, Stanton numbers were 15–20 percent below flat wall values. Five secondary effects were studied: (i) initial boundary layer thickness, (ii) free-stream velocity, (iii) free-stream acceleration, (iv) unheated starting length, and (v) transition. Regardless of the initial state, curvature without acceleration eventually forced the boundary layer into an asymptotic condition: StαReΔ2−1. Strong acceleration with curvature brought the exponent on ReΔ2 to −2.
Heat Transfer Coefficient in Ducts With Constant Wall Temperature
Authors: Haji-Sheikh A. , Mashena M. , Haji-Sheikh M. J.
Published: October 2009

An analytical method for the numerical calculation of the heat transfer coefficient in arbitrarily shaped ducts with constant wall temperature at the boundary is presented. The flow is considered to be laminar and fully developed, both thermally and hydrodynamically. The method presented herein makes use of Galerkin-type functions for computation of the Nusselt number. This method is applied to circular pipes and ducts with rectangular, isosceles triangular, and right triangular cross sections. A three-term or even a two-term solution yields accurate solutions for circular ducts. The situation is similar for right triangular ducts with two equal sides. However, for narrower ducts, a larger number of terms must be used.
Study on Properties and Growth Rate of Frost Layers on Cold Surfaces
Authors: Tokura I. , Saito H. , Kishinami K.
Published: October 2009

An experimental study was carried out on the properties and growth rate of the frost layer which developed on a cooled vertical plate in free convective flow. Dimensionless parameters introduced by dimensional analysis were found to be effective in predicting frost densities, its thermal conductivities and growth rates. It was also found that the frost formation process can be divided into two periods if the frost growth data are correlated with the dimensionless parameters presented.
On the Existence of an Oscillatory Approach to Steady Natural Convection in Cavities
Authors: Patterson J. C.
Published: October 2009

The recent paper by Patterson and Imberger [1], which analysed the transient phase of natural convection in low aspect ratio cavities, gave a criterion for the presence of an oscillatory approach to steady state in such flows. However, the experiments of Yewell et al. [3] displayed no evidence of this oscillatory approach, even though the criterion was apparently satisfied. In this paper, it is shown that since the flow regimes are described by a series of critical Rayleigh numbers, the ordering of which changes with changing aspect ratio, a criterion for the existence of transient internal waves, valid for all orderings, may be established. Further, the results of [1] are extended by means of flow descriptions valid for two additional orderings. Consequently, it is shown that the experiments addressed a transient flow regime in which internal wave activity would not be expected and that the experimental results are in support of the scaling analysis of [1].
Natural Convection in a Rectangular Porous Cavity With Constant Heat Flux on One Vertical Wall
Authors: Prasad V. , Kulacki F. A.
Published: October 2009

Numerical solutions for two-dimensional, steady, free convection are presented for a rectangular cavity with constant heat flux on one vertical wall, the other vertical wall being isothermally cooled. The horizontal walls are insulated. Results are presented in terms of streamlines and isotherms, local and average Nusselt numbers at the heated wall, and the local heat flux at the cooled wall. Flow patterns are observed to be quite different from those in the case of a cavity with both vertical walls at constant temperatures. Specifically, symmetry in the flow field is absent and any increase in applied heat flux is not accompanied by linearly proportional increase in the temperature on the heated wall. Also, for low Prandtl number, the heat transfer rate based upon the mean temperature difference is higher as compared to experimental results for the isothermal case. Heat transfer results, further, indicate that the average Nusselt number is correlated by a relation of the form Nu = constant Ra*mAn, where Ra* is the Rayleigh number and A the height-to-width ratio of the cavity.
The Representation of Regenerator Fluid Carryover by Bypass Flows
Authors: Banks P. J.
Published: October 2009

A regenerator transfers sensible heat between two fluid streams by means of a porous matrix through which the streams are passed alternately. The fluid contained in the matrix passages is carried over from one fluid stream to the other, and contributes to the heat transfer process. It has been suggested that this contribution may be predicted by treating the fluid carryover as fluid flows bypassing the matrix. The validity of this representation is explained, and its accuracy is explored in a case for which numerical solutions of the governing equations are available. A published analysis of the representation is discussed and completed.
An Investigation of Steady Wall-Ceiling and Partial Enclosure Fires
Authors: Mao C.-P. , Fernandez-Pello A. C. , Humphrey J. A. C.
Published: October 2009

A numerical model has been developed to: (a) study the buoyancy-driven combusting flows of partial enclosure fires and (b) to help assess the fire hazards of different burning materials. The calculations provide the flow patterns and distributions of velocity, temperature, species concentration, and flame location in the flow. The model assumes steady laminar flow and makes use of the flame sheet approximation to describe the gas-phase chemical reaction. In corresponding experiments, photographic determinations of flame location were made. Two different cases were studied: (i) a fire occurring in a wall-ceiling configuration with variable pyrolyzing length (of PMMA material); and (ii) a partial enclosure fire with variable soffit and pyrolyzing lengths (the latter of PMMA or POM materials). Good agreement was obtained between measurements and calculations of the flame location for the first case. However, a significant discrepancy was found for the second case and is attributed to the neglect of turbulence and radiation transport in the model. Notwithstanding these limitations, it is found that a simple laminar flow model provides a correct qualitative description of the evolution of partial enclosure fires. For example, stratified (layered) motions, recirculation zones and the so-called “firewind” are correctly predicted as a function of pyrolysis and soffit lengths. The present approach, of incorporating physico-chemical parameters and boundary conditions of practical systems into a numerical model for assessing fire hazards, is very attractive due to its relative ease of execution. The accuracy of the numerical prediction approach can be improved by including radiation and turbulent transport.
Finite Difference Analysis of Laminar Separated Forced Convection in Cavities
Authors: Bhatti A. , Aung W.
Published: October 2009

Results are presented for a comprehensive numerical analysis of the two-dimensional heat transfer in cavities of rectangular profiles. The walls of the cavity are held at a uniform temperature and calculations are carried out at various aspect ratios and Reynolds numbers in laminar flow. The numerical technique is based on a hybrid upwind/central differencing of the governing differential equations that are first integrated over control volumes surrounding the node points in a rectilineal, nonuniform grid system. Results indicate that while the average Nusselt number in the cavity is related to the Reynolds number raised to a power, the latter depends on the aspect ratio and varies between the cavity floor and the side walls. The influence of the upstream boundary layer thickness is found to be negligible. The numerical results are found to be well represented by the following equation: Nu¯t=0.0345(Res)0.46(w/s)−0.142
Periodically Converging-Diverging Tubes and Their Turbulent Heat Transfer, Pressure Drop, Fluid Flow, and Enhancement Characteristics
Authors: Souza Mendes P. , Sparrow E. M.
Published: October 2009

A comprehensive experimental study was performed to determine entrance region and fully developed heat transfer coefficients, pressure distributions and friction factors, and patterns of fluid flow in periodically converging and diverging tubes. The investigated tubes consisted of a succession of alternately converging and diverging conical sections (i.e., modules) placed end to end. Systematic variations were made in the Reynolds number, the taper angle of the converging and diverging modules, and the module aspect ratio. Flow visualizations were performed using the oil-lampblack technique. A performance analysis comparing periodic tubes and conventional straight tubes was made using the experimentally determined heat transfer coefficients and friction factors as input. For equal mass flow rate and equal transfer surface area, there are large enhancements of the heat transfer coefficient for periodic tubes, with accompanying large pressure drops. For equal pumping power and equal transfer surface area, enhancements in the 30–60 percent range were encountered. These findings indicate that periodic converging-diverging tubes possess favorable enhancement characteristics.
Role of the Liquid Layer in Ice Accumulation on Flat Surfaces
Authors: Chung P. M. , Bywater R.
Published: October 2009

Ice formation on a flat plate from humid air at above-freezing temperatures is studied. Condensations from both laminar-forced and natural convective boundary layers are considered. The governing equations are hyperbolic. One family of characteristics immediately coalesces to form a mathematical shock. Physically, the shock represents the extent to which the liquid layer has spread. Behind the shock, the thin liquid layer completely transforms the ice layer profile at near the shock speed. Various parameters affecting the shock speed and the condensate profile are discussed.
Heat Transfer From Rough and Finned Horizontal Tubes in a Gas Fluidized Bed
Authors: Goel I. , Saxena S. C. , Dolidovich A. F.
Published: October 2009

Experimental results of the heat transfer coefficient for smooth, rough, and finned tubes of o.d. 12.7 and 50.8 mm immersed in fluidized beds of silica sand particles of average diameters (dp) 145, 167, 488, and 788 μm are reported as a function of fluidizing velocity. The surface roughness is of V-shaped fins with the values of pitch (Pf) as 5.08, 3.18, 1.58, 0.79, 0.40, and 0.24 mm. The qualitative trends of these heat transfer coefficients in regard to their dependence on various systems and operating parameters are discussed on the concept of particle mode of heat transfer, contact geometry of the heat transfer surface, particle residence time, particle size and size range, tube diameter, etc. Results are also analyzed in terms of the fin effectiveness factor (φ) and heat transfer function (β). It is shown that φ and β are only weakly dependent on tube diameter, particle size range, and fluidizing velocity and therefore have been correlated in terms of the dimensionless ratio (Pf/dp). It is also shown that particle residence time on the heat transfer surface controls the value of the heat transfer coefficient rather sensitively.
Flow Reversibility of Heat Exchangers
Authors: Pignotti A.
Published: October 2009

A symmetry property which relates the thermal behavior of a heat exchange process to that of the reverse process, in which the directions of flow of both fluids are reversed, is demonstrated for the ideal case of no change of phase, no heat losses, and temperature-independent heat transfer coefficients and heat capacities. The symmetry is formulated in terms of a relation between the matrices that describe the direct and reverse process, which can be used to obtain one of them if the other is known. The formalism used does not require the inlet and outlet streams to be completely mixed, but when this is the case, both matrices coincide, and therefore, the effectiveness is the same for both processes. The consequences of the symmetry are ilustrated by the discussion of a three-row, two-pass air cooler, and the TEMA G split flow shell-and-tube heat exchanger.
Recirculation of Purged Flow in an Adiabatic Counterflow Rotary Dehumidifier
Authors: Jurinak J. J. , Mitchell J. W.
Published: October 2009

The average process stream outlet humidity ratio of an adiabatic counterflow dehumidifier can be lowered if a portion of the process outlet stream is purged from the bulk flow. The purged stream can be recirculated and introduced at the inlet of the regenerating period. In this paper, the performance of such a purged counterflow dehumidifier is studied. Two purge geometries that result in a spatially nonuniform inlet condition in the regenerating period are considered. Wave diagram solutions for the limiting case of infinite heat and mass transfer coefficients are used to qualitatively predict the behavior of the purged dehumidifier. A finite difference solution is used to verify the general trends of the approximate wave diagram solutions. The effect of the recirculated purge on the process stream outlet states of high performance silica gel dehumidifiers with low and high thermal capacitance matrices operated at nearly optimal rotational speeds is evaluated.
Melting Around a Horizontal Heated Cylinder: Part I—Perturbation and Numerical Solutions for Constant Heat Flux Boundary Condition
Authors: Prusa J. , Yao L. S.
Published: October 2009

The melting of a solid about a heated cylinder presents an irregularly shaped, moving boundary problem. A transformation is used to immobilize this boundary—replacing the problem of variable geometry by one of constant geometry. A constant heat flux boundary condition is used along the cylinder surface. Using perturbation and numerical methods, several solutions for this transient problem are generated for Stefan, Rayleigh, and Prandtl numbers of Stq = 0.374, Ra = 5000, and Pr = 54. Stq is the ratio of heat transfer rate to the thermal energy needed to melt the solid. Ra • B3 is the measure of the magnitude of the natural convection effect, where B is a dimensionless measure of the size of the melt region called the gap function. Ra itself can be thought of as a dimensionless heat flux, since it does not take the size of the melt region into account. The dimensionless groups Stq and Ra (based upon the surface heat flux) are used to determine two parameter expansions of the dependent variables for the regular perturbation method. The first three terms of the series solutions are determined. They provide accurate solutions for short times after the start of melting, for small values of Stefan and Rayleigh numbers. The accuracy of the perturbation method is verified using a numerical method, which is not limited to short initial time intervals or to small values of Stefan and Rayleigh numbers. Detailed predictions of the melt volume, shape, temperature field, global and local heat transfer rates are given for representative cases. Comparisons with earlier experimental results are made.
Selective Freezing of a Dilute Salt Solution on a Cold Ice Surface
Authors: Fang L. J. , Cheung F. B. , Linehan J. H. , Pedersen D. R.
Published: October 2009

The growth of a solid–liquid, two-phase region during selective freezing of a dilute, eutectic-forming, salt solution over a subcooled ice slab is investigated experimentally and theoretically. The morphology of the two-phase region and the kinetics of the solid–liquid interface observed for a NaCl-H2O system are described photographically. The motion of the two-phase, liquidus front, recorded by a telescopic device that amplifies the local phenomena of the two-phase region, is presented along with the measured transient temperature distribution of the system. Based on the assumption that the solution element of the two-phase region is in local thermodynamic equilibrium with the solid phase, a similarity model is developed to predict the dependence of the freezing rate on various controlling parameters of the system. Transient heat conduction in the ice slab is also included in the model to study the effect of the wall. Comparison is made between the analytical and the experimental results and found to be good.
Effect of Inclination on Freezing in a Sealed Cylindrical Capsule
Authors: Larson E. D. , Sparrow E. M.
Published: October 2009

Experiments were performed to study the heat transfer processes that occur during freezing inside of a sealed cylindrical capsule when the inclination of the capsule is varied parametrically from vertical to horizontal. The phase-change medium was 99 percent pure n-eicosane paraffin. It was found that the amount of mass that solidified during a given freezing period was insensitive to the inclination of the capsule, as was the amount of energy extracted from the capsule. Only highly localized quantities such as the local frozen layer thickness reflected the inclination of the cylinder. Parametric variations were also performed for the degree of sub-cooling of the capsule wall below the fusion temperature and for the degree of superheating of the liquid phase at the onset of freezing. These variations facilitated the identification of the relative importance of the latent and sensible energies to the total extracted energy.
Flash Evaporation From Turbulent Water Jets
Authors: Bharathan D. , Penney T.
Published: October 2009

Results of an experimental investigation of flash evaporation from turbulent planar and axisymmetric water jets are reported. In the range of jet thicknesses tested, for planar jets, due to shattering, evaporation is found to be nearly independent of the jet thickness. Evaporation from the planar jets was found to be dependent on the initial level of turbulence in the water supply manifold. An approximate analysis to model the evaporation process based on the physical phenomena and experimental observations is outlined. Comparisons between the experimental data and analytical predictions of the liquid temperature variation along the jet are included. Use of screens in the water jet are shown to be effective for enhancing evaporation.
Analysis of Radiative Equilibrium in a Rectangular Enclosure With Gray Medium
Authors: Yuen W. W. , Wong L. W.
Published: October 2009

Radiative heat transfer and temperature profile in a two-dimensional rectangular enclosure with gray medium are calculated. Successive approximate solutions are generated by a point allocation method in which the temperature profile is expressed as polynomials of successively higher order. The technique is shown to converge rapidly with the third-order results already comparing favorably with available numerical solution. It is also demonstrated to be computationally efficient. Comparing with a solution with the same number of unknowns generated by the Hottel zonal method, the present approach represents a reduction in computational time by at least one order of magnitude. Based on the mathematical behavior of the numerical results, simple empirical closed-form approximate expressions for both the heat transfer and temperature profile in general multidimensional systems at radiative equilibrium are proposed. For a rectangular enclosure, these expressions are demonstrated to be quite accurate over all optical thickness.
A Limiting Approach for the Evaluation of Geometric Mean Transmittance in a Multidimensional Absorbing and Isotropically Scattering Medium
Authors: Yuen W. W.
Published: October 2009

The calculation of the geometric-mean transmittance factor between areas with an intervening absorbing and isotropically scattering medium is considered. While an exact expression for the factor is shown to be quite complicated, the upper and lower limits of the factor can be readily generated from physical consideration. Integral expressions for successively increasing (decreasing) values of the lower (upper) limits are obtained. For two-dimensional systems, these expressions are reduced to integrals involving Sn (x), a class of exponential integral function that has been tabulated in a previous work. Utilizing the kernel substitution technique, these integrals are evaluated analytically in closed form for some selected geometries. For cases with small optical thickness and large scattering albedo, both limits are shown to converge relatively slowly to the actual transmittance factor. But the decreasing difference between the two limits provides accurate estimate of the geometric-mean transmittance factor. Based on these results, some interesting conclusions concerning the effect of scattering on multidimensional radiative transmission are established.
Condensation Heat Transfer on Laminar, Falling Film
Authors: Rao V. D. , Sarma P. K.
Published: October 2009

The process of condensation of vapors on a laminar, falling film of immiscible liquid is formulated within the framework of certain assumptions for a laminar, two-film model. The numerical solutions are presented for a wide range of parameters, and it is observed that the dynamics of the falling film has a profound influence on the condensation heat transfer rates. The condensation heat transfer coefficient is found to be a function of the modified Graetz number, subcooling parameter, and the heat capacity ratio of coolant-to-condensate. Further, shorter liquid film lengths would yield considerably high condensation heat transfer rates in comparison with the Nusselt analysis.
Simplified Analysis of Air-Bubble Plumes in Moderately Stratified Environments
Authors: Hussain N. A. , Narang B. S.
Published: October 2009

This paper is concerned with the behavior of buoyant plumes driven by rising gas bubbles through a moderately stratified liquid environment. A two-phase mathematical model is proposed for calculating the induced turbulent vertical liquid flow and its temperature. Simultaneous numerical solutions of the continuity, momentum, and energy equations are obtained for the two cases of an axisymmetric and a two-dimensional air jet submerged in water. Water pumping rates, liquid velocities, plume radii (widths), and temperatures are obtained as a function of air flow rates, depth of submergence, and the assumed temperature profile of the water in the region far away from the jet. Effects of temperature stratification in the liquid region far away from the jet resulted in increased liquid flow rates as well as increased plume cross-section areas. Comparisons are made with the experimental information available in the literature.
Analysis of Laminar Mixed Convective Plumes Along Vertical Adiabatic Surfaces
Authors: Rao K. V. , Armaly B. F. , Chen T. S.
Published: October 2009

Laminar mixed forced and free convection from a line thermal source imbedded at the leading edge of an adiabatic vertical surface is analytically investigated for the cases of buoyancy assisting and buoyancy opposing flow conditions. Temperature and velocity distributions in the boundary layer adjacent to the adiabatic surface are presented for the entire range of the buoyancy parameter ξ (x) = Grx/Rex5/2 from the pure forced (ξ(x) = 0) to the pure free (ξ(x) = ∞) convection regime for fluids having Prandtl numbers of 0.7 and 7.0. For buoyancy-assisting flow, the velocity overshoot, the temperature, and the wall shear stress increase as the plume’s strength increases. On the other hand, the velocity overshoot, the wall shear stress, and the temperature decrease as the free-stream velocity increases. For buoyancy opposing flow, the velocity and wall shear stress decrease but the temperature increases as the plume’s strength increases.
Jet-Impingement Heat Transfer for a Circular Jet Impinging in Crossflow on a Cylinder
Authors: Sparrow E. M. , Altemani C. A. C. , Chaboki A.
Published: October 2009

Quasi-local heat transfer coefficients were measured on a cylinder on which a circular jet impinged in crossflow. The jet diameter and the distance between the initiation of the jet and the cylinder surface were varied parametrically, as was the jet Reynolds number. The measurements showed that the axial distribution of the heat transfer coefficient peaked at the impingement point. For a fixed jet diameter and Reynolds number, the peak heat transfer coefficient increased as the distance between the initiation of the jet and the cylinder surface decreased. The peak coefficient also increased with decreasing jet diameter at fixed values of the jet initiation distance and the Reynolds number. User-oriented correlations of the peak Nusselt number with the geometrical parameters and with the Reynolds number were derived. The dropoff of the heat transfer coefficient with increasing axial distance from the impingement point was more rapid for smaller jet initiation distances (at a fixed jet diameter and Reynolds number) and for smaller jet diameters (at a fixed initiation distance and Reynolds number). The impingement pattern was examined by flow visualization.
Effects of Wall Conduction on Heat Transfer for Turbulent Flow in a Circular Tube
Authors: Lin Y. K. , Chow L. C.
Published: October 2009

In predicting convective heat transfer for turbulent flow inside a circular tube, the thermal boundary condition at the solid–fluid interface is usually assumed to be known. However, in reality, the thermal boundary condition is normally specified at the outside surface of the tube. The temperature and heat transfer coefficent at the interface are not known a priori. An analytical procedure is used here to obtain the interfacial temperature and the local Nusselt number for turbulent flow with axial and radial wall conduction taken into account. Wall conduction effects are examined by varying four important parameters, namely, the Reynolds number, the Prandtl number, the ratio of thermal conductivity of solid wall to that of fluid, and the nondimensional thickness of the tube wall. Numerical results are obtained to determine their influence on heat transfer.