Showing papers in "International Journal of Heat and Mass Transfer in 1975"

Abstract: A simple expression is developed for the space-mean Nu (or Sh ) for all Ra and Pr (or Sc) in terms of the model of Churchill and Usagi. The development utilizes experimental values for Ra approaching zero and infinity, and the theoretical solutions obtained from laminar boundary-layer theory. The expression is applicable to uniform heating as well as to uniform wall temperature and for mass transfer and simultaneous heat and mass transfer. The correlation provides a basis for estimating transfer rates for non-Newtonian fluids and for inclined plates. Even simpler expressions are developed for restricted ranges of conditions. The general and restricted expressions are compared with representative experimental data. The structure of the correlating equation shows why the common power-law-type equations cannot be successful over an extended range of Ra and Pr .

Abstract: A simple empirical expression for the mean value of Nu over the cylinder for all Ra and all Pr is developed in terms of the model of Churchill and Usagi. This expression is applicable for uniform heating as well as for uniform wall temperature and for mass transfer and simultaneous heat and mass transfer. Even simpler expressions are obtained for restricted conditions. These expressions improve upon prior graphical and empirical correlations in both accuracy and convenience.

Abstract: The paper contains a short retrospective review of the works mainly performed by Soviet authors in the field of mathematical description of heat- and mass-transfer phenomena in capillary-porous bodies. The aim of the present work is not only to establish the priority of the scientists working in this field but also to outline the ways of development of the analytical methods for transport phenomena. Presentation is given of the methods to describe transport phenomena with different transfer potentials, of the relationship between the transfer coefficients and thermodynamic characteristics of capillary-porous bodies. The limit transitions to the classical Fourier and Fick equations are described. The basic relationships of the extreme cases are illustrated by experimental data. A short description is given of the recent works on turbulent heat and mass transfer in capillary-porous bodies as well as of the methods for transport problems with moving boundaries when the Dirac delta-function and the single Heaviside function are used.

Abstract: A numerical study of the effects of transients and variable properties on single droplet evaporation into an infinite stagnant gas is presented. Sample calculations are reported for octane droplets, initially at 300°K with Ro = 0·1, 0·5, 2·5 × 10−4m, evaporating into air at temperatures and pressures in the ranges 600–2000°K and 1–10 atm, respectively. It is found that initial size Ro is eliminated from the problem on scaling time with respect to R20 and that the evaporative process becomes quasi-steady with ( R R 0 ) 2 = ( R∗ 0 R 0 ) 2 − βt R 2 0 , as suggested by experiment. Comparisons of solutions using various reference property schemes with those for variable properties show that best agreement obtains using a simple 1 3 rule wherein properties are evaluated at T r = T s + (T e −T s ) 3 and m 1,r = m 1,s + (m 1,e − m 1,s ) 3 . The effects of temporal storage of mass species, energy, etc. and radial pressure variations in the vapor phase prove to be negligible, the early transient behavior being solely due to sensible heat effects within the droplet and related variations in vapor-side driving forces.

Abstract: Values of local flow properties, obtained by solving appropriate conservation equations in finite-difference form and with boundary conditions corresponding to four furnace arrangements, are presented and compared with measurements. The calculation procedure employs, a two-equation turbulence model, so that calculations can be compared with measurements of turbulence energy as well as mean-velocity components. Calculations were performed with three combustion models, characterised by instant reaction, instant reaction with scalar fluctuations and Arrhenius reaction or eddy-break up with scalar fluctuations: comparisons with measurements obtained in the Delft, Harwell, Ijmuiden and Karlsruhe furnaces indicate that the last two lead to reasonably correct results.

Abstract: This paper examines more than thirty ways of predicting the relationship between turbulent transfers of momentum and a passive contaminant such as heat or dissolved matter. The models are divided into seven classes, on the basis of method of derivation or field of application. Three classes comprise modifications of the simplest mixing-length model to allow for diffusion during the lateral motion of the fluid element which is conceived to carry the transferred entities. The other four classes are more heterogeneous: formal analyses based on Reynolds equations; results derived from various expressions for the eddy diffusivities; several kinds of model applicable to wall layers in particular; and purely empirical formulae representing limited data. An attempt has been made to assess the utility and potential for development of these models, both from the practical point of view, that of devising accurate heat- and mass-transfer formulae, and from the fundamental point of view, that of gaining an understanding of the actual transferring mechanisms. There is a plethora of formulae that can, with suitable choices of empirical constants, represent the gross features of experimental data. However, only the formal analyses account in a consistent way for the pressure interactions which influence momentum transfer. At present, formal results are available only for the degenerate case of weak, decaying turbulence, although they do prove useful in suggesting the limiting behaviour to be expected in more general flows.

Abstract: A least-squares-matching technique is presented to analyze fully developed laminar fluid flow and heat transfer in ducts of arbitrary cross-section. Forced convection heat transfer is considered under constant axial heat-transfer rate with arbitrary peripheral thermal boundary conditions. As an application of the method, flow and heat-transfer results are presented for the duct geometries of isosceles triangular, rounded corner equilateral triangular, sine, rhombic and trapezoidal cross-sections. These numerical results are discussed from a heat exchanger designer's viewpoint.

Abstract: A recent equation for calculating heat-transfer coefficients to constant property fluids in pipes is modified to correlate variable property data. The correlating equation is of convenient form, applies to both liquids and gases, correlates constant property results within 10 per cent for 0·1 4 with 10 4 6 , and correlates variable property data within 20 per cent for 0·7 with 10 000 . The equation is compared with the Sieder-Tate equation for liquids and the two equations of Petukhov for gases and liquids. Equations for heat transfer to variable property liquid metals are suggested.

Abstract: New experimental measurements are reported on the natural convective heat transport through a horizontal layer of air, covering the Rayleigh number range from sub-critical to 4 × 106. When these data are combined with Goldstein and Chu's data for air, the full set of data points are demonstrated to bear a Nusselt number dependence which is asymptotic to a 1 3 power on the Rayleigh number as the Rayleigh number approaches infinity. The asymptotic coefficient of proportionality is consistent with that predicted by a simple “conduction layer model” which is described. Knowledge of the asymptote has permitted a simple but accurate correlation equation to be obtained, valid for the full range of Rayleigh number. By extension, a similar correlation equation is also obtained for water.

Abstract: Data were obtained on the effect of free-stream turbulence on heat transfer from heated cylinders placed normal to an air stream. Tests were conducted for a Reynolds number range from 109 000 to 302 000 at values of turbulence intensity from 0·40 to 14·20 per cent. The diameters of the test cylinders used were 4·5 and 7·6 in respectively and the ratio of cylinder diameter to test section width were 0·075 and 0·127. The ratio of turbulence scale to cylinder diameter ranged from 0·015 to 0·095. The scale of turbulence varied from 0·113 to 0·426 in during the study. The structure of the free-stream is characterized and the effects of the artificially induced turbulence on both the local and overall heat transfer are determined. The data are discussed and compared with results of previous studies where appropriate. The results are explained in part by available theory and also indicate areas that require further investigation. A correlation equation is presented that enables the stagnation point heat transfer as a function of turbulence intensity to be determined. The augmentation of heat transfer through the laminar boundary layer as a function of turbulence intensity is also determined. Attempts to determine the effect of turbulence intensity on the overall or average heat transfer were partially successful. A correlation equation for predicting the overall heat transfer as a function of turbulence intensity over a narrow range of correlation parameters is presented.

Abstract: Buoyancy-driven convection in a differentially heated vertical porous layer is studied theoretically by the method developed by Gill [;5];. The model is of finite extent, and the temperature difference between the vertical walls is assumed to be large. Satisfactory agreement with experiment has been obtained for the interior temperature distribution and the Nusselt number. The applied method is also extended to include some effects of a variable viscosity. This is shown to introduce asymmetry into the solutions.

Abstract: Rates of heat transfer were measured for laminar natural convection in silicone oil and air in a long rectangular channel. The aspect ratio (width/height) of the cross-section of the channel was varied over 1, 2, 3, 4·2, 8·4 and 15·5, and the Rayleigh number from 3 × 103 to 105. The channel was heated from below and cooled from above while the other two sides were insulated. The channel was then rotated about the long axis in steps through 180 degrees. The effect of inclination and of the aspect ratio on the rate of heat transfer was measured experimentally. A minimum and a maximum rate of heat transfer occurred as the angle of inclination was increased from 0 to 180 degrees. The angle of inclination at these critical conditions was found to be a strong function of the aspect ratio and a weak function of the Rayleigh number. A transition in the mode of circulation occurred at the angle corresponding to the minimum rate of heat transfer.

Abstract: The total and local heat transfer from a smooth circular cylinder to the cross flow of air has been measured over the Reynolds number range 3 × 104

Abstract: The transfer coefficients resulting from the impingement of a slot jet on a plane surface have been measured by the naphthalene sublimation technique. The experiments were performed with jets that are laminar at the exit of the duct from which the jet issues. In addition, the velocity profiles at the duct exit were fully developed. Distributions of the local mass-transfer coefficient on the impingement surface were determined for five Reynolds numbers and at five separation distances between the duct and the surface. The mass-transfer results can be converted to heat-transfer results by using the heat-mass transfer analogy. It was found that the transfer coefficients generally tended to decrease with increasing separation distance, but there was evidence of non-monotonic behavior owing to the opposite influences of mixing-induced turbulence and diminished jet velocity. Increases in Reynolds number tended to increase the transfer coefficients, and the stagnation point values were correlated with a 0·6-power dependence. The surface distributions of the transfer coefficient were bell-shaped, with the largest value at the stagnation point. Comparisons with available literature suggested that the shape of the initial velocity profile has a significant effect on the transfer characteristics of the impingement surface.

Abstract: Pohlhausen's equation has been used to determine the initial thickness of the evaporating microlayer beneath a hemispherical vapour bubble on a superheated horizontal wall. Microlayer thickness is proportional to the square root of the distance to the nucleation site during early bubble growth, while a linear relationship exists during advanced growth. A (heat and mass) diffusion-type solution is derived for advanced bubble growth, which accounts for the interaction of the mutually dependent contributions due to the relaxation microlayer (around the bubble dome) and the evaporation microlayer. The entire bubble behaviour during adherence is determined by a combination of this asymptotic solution and the Rayleigh solution, which governs early growth. Also, expressions are derived for both the radius of the dry area and the radius of the maximum contact area between bubble and wall. At low concentrations of the more volatile component in binary systems, the dominating influence of mass diffusion is demonstrated by the following effects: (i) asymptotic bubble growth is slowed down substantially; (ii) the formation of dry areas beneath bubbles is prevented, even at subatmospheric pressures; (iii) the lower part of the bubble is contracted; (iv) the evaporation microlayer contribution to bubble growth is negligible at atmospheric and at elevated pressures.

Abstract: The Isotherm Migration Method is extended to two dimensions. The equations are formulated and a convenient finite-difference method of solution is described for a variety of initial and boundary conditions. Particular attention is devoted to Stefan problems in which phase changes occur on a moving interface. As an example the solidification of a square prism of fluid is solved in detail and the numerical results are compared with those obtained by earlier authors.

Abstract: The parameters which control the momentum- and heat-transfer performance of a rough surface in a uniform channel flow are presented in a novel way. A new efficiency parameter is denned for optimising this performance. Using a recently developed analysis a wide range of rough surfaces are investigated and design charts presented.

Abstract: The convective heat transfer resulting from a granular flow over a heated surface is investigated The specific type of flow considered is that in which adjacent material particles are in physical contact The qualitative features of this type of flow are discussed, and the existing equations of motion are extended With regard to the equations of motion, an exact solution is shown which has applications concerning the mass flow rate of granular materials through hoppers The particular heat transfer problem investigated is convection from a flat plate with its long axis parallel to the flow field An approximate analytical solution, which takes into account the particulate nature of the medium, is developed and experimental measurements obtained The theory was found to correctly predict the trends of the experimental data The results indicate that the Nusselt number for this configuration is influenced substantially, under certain conditions, by the noncontinuous nature of the medium A semi-empirical correlation is presented, based on experimental results obtained with four different granular materials

Abstract: The growth rate of vapour bubbles has been investigated experimentally up to departure in water boiling at pressures varying from 26·7 to 2·0 kPa (the corresponding Jakob number increasing from 108 to 2689). Comparison of the data with existing theory shows the substantial influence of liquid inertia during initial growth, in agreement with previous results of Stewart and Cole [1]on water boiling at 4·9 kPa, the Jakob number varying from 955 to 1112. As an extreme case, at a pressure of 2·0 kPa, large “Rayleigh” bubbles are observed during the entire adherence time. During advanced growth, bubble behaviour is gradually governed by heat diffusion, especially at relatively high (subatmospheric) pressures. Experimental bubble growth in the investigated pressure range is in quantitative agreement with the van Stralen, Sohal, Cole and Sluyter theory [10]. This model combines the Rayleigh solution with a diffusion-type solution, which accounts for the contributions to bubble growth due to both the relaxation microlayer (around the bubble dome) and the evaporation microlayer (beneath the bubble). Finally, a curious bubble cycle is observed at the lowest investigated pressures, which is attributed to the combined action of a high-velocity liquid jet (originating in the wake following a large primary bubble) and a succeeding secondary vapour column (generated at the adjacent dry spot at the heating wall beneath the primary bubble).

Abstract: Heat transfer from a horizontal fine cylinder by pure forced convection at small Reynolds numbers or by pure free convection at small Grashof numbers is analyzed without restriction on Prandtl number by the method of joining the circumferential average temperature in the concentric layer around the cylinder governed mainly by conduction to that in the wake or plume governed mainly by convection. The agreement between analysis and experiment is satisfactory.

Abstract: The rotating heat pipe is a device which utilises a two-phase heat-transfer cycle. Rotation about the longitudinal axis generates a centrifugal force field and a component of this acting along the tapered wall pumps the condensate back to the evaporator. A theoretical Nusselt type analysis is proposed for the condensate film taking into account the drag effects of contra-flowing vapour. A performance prediction relates rates of heat transfer, rotational speeds, temperature differences across condensate films, fluid properties and heat pipe geometry. Experimental investigation tests the analysis with good agreement for the two Arcton 113 and 21 fluids but no agreement with water. An explanation for this is proposed.

Abstract: Explicit matrix formulae are derived for the calculation of total exchange areas in the context of Hottel's zone method Working relations are obtained for the case of a uniform grey absorbing-emitting/isotropically-scattering medium confined in a Lambert enclosure The approach readily leads to limiting cases and significantly reduces computational labor For an enclosure zoned into n volume and r non-black surface zones the general procedure requires evaluation of one ( n × n ) and one ( r × r ) inverse matrix Sufficient conditions for the existence of the latter are shown to be wholly non-restrictive

Abstract: Local impingement cooling effectiveness and heat-transfer coefficients are measured over the interaction area of an air jet impinging on a wall and subjected to a cross flow of air. Impingement cooling effectiveness decreases with the blowing rate and at low blowing rates, there is, near the stagnation point, a definite influence of the density ratio. Effectiveness values as high as 60 per cent are obtained at the stagnation point with blowing rate of 12 and nozzle to plate distance of six diameters. The heat-transfer coefficient can be as high as 700W/(m2 K) for a blowing rate of twelve with the jet only six diameters above the surface on which it impinges.

Abstract: This paper presents a technique for the analysis of unsteady, two-dimensional diffusive heat- or mass-transfer problems characterized by moving irregular boundaries. The technique includes an immobilization transformation and a numerical scheme for the solution of the transformed equations. Specifically, the immobilization consists of transforming the governing partial differential equations into a coordinate system where the phase boundaries correspond to fixed coordinate surfaces. An example problem involving the solidification or melting of a finite cylinder is analyzed, and results for a range of conditions are presented.

Abstract: A systematic approach for the exact calculation of multi-dimensional radiative heat flux in a cylindrical emitting-absorbing non-isothermal medium with non-isothermal bounding walls is described. Closed form exact solutions are obtained for radiative transfer inside (finite and infinite) cylinders and concentric cylinders with prescribed three-dimensional temperature distribution. For the special case of one-dimensional cylindrically symmetric situation, the exact solution obtained in the present work is shown to be equivalent to the exact solution obtained in a previous study, although the solution presented here is much more elegant in approach and simpler in form. Numerical results are also presented for the case of isothermal media bounded by piecewise isothermal walls.

Abstract: A correlation to determine the initial point of net vapor generation for water and Refrigerant-22 is given. The range of data correlated is as follows: geometry: circular tubes, rectangular channels and annuli; pressure: 0·1–15·8 MN/m2; hydraulic diameter: 0·004–0·020 m; subcooling: 3·2–42 K; heat flux: 0·02–1·92 MW/m2; mass velocity: 132–2818 kg/m2s; accuracy: 30 per cent. A scaling law to predict this point for other liquids than those mentioned above has also been established. Experimental determination of the initial point of net vapor generation for water has been carried out with a high-speed photographic technique at 13·9 and 15·8 MN/m2.

Abstract: The maximum evaporation time and Leidenfrost point for discrete drops of water deposited on smooth surfaces of stainless steel, brass and Monel, at pressures ranging to 75 lb/in2 are obtained and compared. The results suggest that, contrary to expectation, thermal diffusivity of the hot surface is not the controlling factor. The evaporation time-surface temperature correlation due to Baumeister et al. is substantially confirmed.

Abstract: Exact solutions are obtained for temperature and moisture distribution as well as the position of the moving evaporation front in a porous half-space. Two mathematical models, corresponding to the drying of the moist body in the period of decreasing rate and the intensive drying in the presence of molar transfer in the region of evaporation are considered. It is shown that the problem solved in ]1[ is a very special case of the solution presented here. The influence of some of the nondimensional parameters is illustrated by examples.

Abstract: Zusammenfassung Potentialverteilungen sind fur eine Reihe von Anordnungen berechnet und in der Literatur angegeben. Diese Losungen werden kritisch gesichtet und ihre Gemeinsamkeiten herausgearbeitet. Die Abtrennung von anwendungsspezifischen Stoffgrossen fuhrt auf den Formfaktor, der allein von der geometrischen Anordnung abhangt und fur alle Vorgange Gultigkeit hat, denen skalare Potentialfelder zugrundeliegen. Die Berechnung des Warmestromes bei stationarer Warmeleitung stand hier im Vordergrund. Sie ist, bei Kenntnis des Formfaktors auch fur komplizierte geometrische Anordnungen sehr einfach. Da Angaben uber Formfaktoren in der Literatur gelegentlich verwirrend und mehrdeutig siad, ist hier auf eine konsequente Einteilung entsprechend den auf analytische Losungen zuruckgehenden Fallen der planparallelen Platte, der koaxialen Rohre und der Kugel geachtet. Die Charakteristika dieser Losungen sind in jedem angegebenen Formfaktor enthalten. Eine besonders einfache Moglichkeit der Ermittlung von Formfaktoren fur Anordnungen von Einzelkorpern wird gezeigt. Damit und mit der Moglichkeit der Vertauschung von Isothermen und Adiabaten, sowie der symmetrischen Erganzung konnen die hier angegebenen rund 50 Formfaktoren Grundlage einer Vielzahl von geometrischen Anordnungen sein.

Abstract: Resume Cette etude est relative a l'elaboration de principes theoriques de mesures et a la realisation d'une cellule permettant d'obtenir simplement les proprietes thermophysiques de fluides et plus particulierement de liquides non-Newtoniens. Apres un rappel concernant l'emploi du regime thermique permanent etabli pour determiner les conductivites thermiques, une theorie relative au regime transitoire, est proposee et detaillee. La methode originale presentee conduit en particulier a l'evaluation des chaleurs specifiques. Elle fait intervenir un calcul de valeurs propres, commodement traite grâce a l'emploi de methodes variationnelles. Le projet et la realisation du conductivimetre sont ensuite presentes: la mise au point de l'appareil a ete effectuee grâce a des liquides “standard” et des essais critiques successifs ont permis d'obtenir un tarage precis du modele. Une place importante est attribuee a l'evaluation des erreurs dues aux defauts de centrage ou aux fuites thermiques par exemple. La cellule ainsi elaboree et les developpements theoriques qui lui sont relatifs sont utilises pour determiner les conductivites et chaleurs specifiques de solutions aqueuses a comportement non-Newtonien pour diverses concentrations et differentes temperatures. Les resultats obtenus sont rassembles et interpretes. L'analyse des limites et des possibilites de la methode conduit enfin a des considerations prospectives.