Showing papers in "International Journal of Heat and Mass Transfer in 1963"

Heat and momentum transfer in smooth and rough tubes at various prandtl numbers

Abstract: Results are presented from an experimental investigation of the relation between heat transfer and friction in smooth and rough tubes. Three rough tubes and one smooth tube were formed from electroplated nickel. The rough tubes contained a close-packed, granular type of surface with roughness-height-to-diameter ratios ranging from 0.0024 to 0.049. Measurements of the heat-transfer coefficients (CH) and the friction coefficients (CF) were obtained with distilled water flowing through electrically heated tubes. A Prandtl number range of 1.20–5.94 was investigated by adjusting the bulk temperature of the water. Results were obtained for Reynolds numbers from 6 × 104 to 5 × 106 and from 1.4 × 104 to 1.2 × 105 at the lowest and highest Prandtl numbers respectively. A similarity rule for heat transfer was used to correlate, interpret, and extend the experimental results. The results were compared with previously existing results, both theoretical and experimental. Increases in CH due to roughness of as high as 270 per cent were obtained. These increases were, in general, accompanied by even larger increases in CF. An exception to this general behavior occurs at high Prandtl number in the region of transition between the “smooth” and the “fully rough” CF characteristic.

Nucleate boiling. The region of isolated bubbles and the similarity with natural convection

Abstract: Experimental data indicate that nucleate boiling consists of two regions, (a) the region of isolated bubbles and (b) the region of interference. The vapor removal pattern, the flow pattern and the mechanisms of heat transfer in the two regions are discussed and analysed. A criterion for the change from one region to another is presented. In the regime of isolated bubbles, bubbles do not interfere with each other and at any particular point vapor is produced intermittently. Jakob's description of the natural flow circulation in nucleate pool boiling from a horizontal surface is similar to Malkus' and Townsend's description of the flow regime in turbulent natural convection from a horizontal surface. In both cases the heat transfer is caused by the “up-draught” induced circulation. It is shown that the same equations which predict the heat-transfer coefficient and the average turbulent velocity fluctuation in natural turbulent convection from a horizontal surface can be used in the regime of isolated bubbles if the vapor void coefficient i.e. the vapor hold-up is taken into account in evaluating the mean density of the fluid. Equations relating the vapor void coefficient to the heat-transfer coefficient or to the bubble population density and liquid superheat temperature are presented. It is shown that an upper limit exists for the heat-transfer mechanism induced by the “up-draught” circulation. Equations predicting the limiting value of the heat-transfer coefficient and of the heat flux density in the regime of isolated bubbles are presented also. All these results, predicted by the analysis, are shown to be in qualitative and quantitative agreement with experimental data presently available. In the region of interference, bubbles interfere with each other to form continuous vapor columns and patches. Vapor is continuously produced by vaporization of a pulsating micro-layer (proposed and described by Moore and Mesler) at the base of a vapor column or of a vapor patch. In this regime the dominant heat-transfer mechanism is, most probably, the latent heat transport process (formulated by Gaertner) and the latent heat transport associated with the large bursts of vapor caused by collapsing vapor patches. The results of the analysis indicate that a particular regime of nucleate pool boiling (a two-phase problem) can be analysed as a turbulent natural convection problem (a single-phase problem). Applications of similar considerations to other aspects of the two-phase flow appear therefore promising. The important effect of the two-phase flow patterns on the mechanism of heat transfer and on the coefficient of heat transfer for a two-phase mixture is demonstrated again, emphasized and discussed.

Heat transfer in tube coils with laminar and turbulent flow

Abstract: Friction and heat transfer results are presented for the laminar flow of oil and the turbulent flow of water in tube coils having ratios of coil to tube diameter of 17 and 104, for Reynolds numbers from 12 to 65 000. A correlation for the asymptotic heat transfer coefficient for laminar flow is supported by the indication of theory, and the coefficients for turbulent flow depend on the coil diameter in the way indicated by available results for air.

Heat transfer in annular passages—hydrodynamically developed turbulent flow with arbitrarily prescribed heat flux

Abstract: The problem of turbulent flow heat transfer in a concentric circular tube annulus with fully developed velocity profile and constant heat rate per unit of length is considered. Experimentally obtained solutions are presented for the thermal entry length for a fluid with Pr = 0·7. Asymptotic solutions (fully developed velocity and temperature profiles) are developed for a wide range of radius ratio, Reynolds number, and Prandtl number. The solutions are based on empirical velocity and eddy diffusivity profiles, and the validity of the solutions is demonstrated experimentally for Pr = 0·7. A superposition method is demonstrated for solving the problem of asymmetric heating from the two surfaces of an annulus, and experimental data on asymmetric heating are presented which are in excellent agreement with the analysis. This paper is the third in a series (1, 2) culminating a four year study of heat transfer in annular passages.

Theory of the steady laminar natural convectiol above a horizontal line heat source and a point heat source

Abstract: Steady laminar natural convection above a horizontal line heat source and a point heat source are analysed mathematically. The solutions of elementary functions are given for Pr = 2, and also for the flow above a point source for Pr = 1. The velocity and temperature distributions for the case of Prandtl number equal to 0.01, 0.7 and 10 are computed with an electronic computer, and differences, caused by different Prandtl number, among the velocity distributions or the temperature distributions are described in detail.

Heat transfer in annular passages. hydrodynamically developed laminar flow with arbitrarily prescribed wall temperatures or heat fluxes

Abstract: Eigenvalue problem solved for the thermal problem of a hydrodynamically fully developed flow

Heat transfer across turbulent, incompressible boundary layers

Abstract: The paper contains a survey of the present status of knowledge concerning the transfer of heat by forced convection across incompressible turbulent boundary layers. The foundations of the semi-empirical theory are examined from first principles and the limitations of the theory are carefully noted. Elementary theories are described and an outline of D.B. Spalding's mathematically exact theory is given. The limiting cases of very high and very low Prandtl numbers are discussed. Finally, an outline of W. V. R. Malkus' theory of turbulent processes is sketched. A conscientious attempt has been made to clarify all physical assumptions, to identify the major fundamental problems which require attention and to indicate directions in which the semi-empirical theory can be extended.

Measurements of convective heat transfer from a horizontal cylinder rotating in a tank of water

Abstract: The present paper deals with measurements of heat transfer from a horizontal cylinder rotating in water. The experimental results have been correlated by the equation Nu = 0.133Re23 · Pr13 for a range of rotating Reynolds numbers from 1000 to 46 000, and Prandtl numbers from 2.2 to 6.4. This equation compares very well with the experimental and theoretical information available for air, water and oil in published works. The analogy suggested by Anderson and Saunders between natural convection from a horizontal plate and the present type of flow has been used to predict the Nusselt numbers. The analogy solution and the present experimental results have been found to compare very well with each other.

Heat transfer in annular passages- general formulation of the problem for arbitrarily prescribed wall temperatures or heat fluxes

Abstract: Effects of asymmetry in the heat flux of wall temperatures in the heat transfer along annular passages

Natural convection mass-transfer measurements on spheres and horizontal cylinders by an electrochemical method

Abstract: In the electrolysis of cupric sulphate with sulphuric acid as supporting electrolyte the limiting current is directly proportional to the mass-transfer coefficient. Using spheres and horizontal cylinders as cathodes, limiting currents were measured for ( Gr · Sc ) numbers between 1.22 × 10 7 and 1.51 × 10 10 . By insulating electrically a small area on the cathode local mass-transfer coefficients and also the transition laminar-turbulent of the hydrodynamic boundary layer could be determined. The accuracy of the method is estimated to be ±5 per cent with the instrumentation used

Convection heat transfer and flow phenomena of rotating spheres

Abstract: The flow engendered by and the convection heat transfer to or from a rotating sphere have been investigated experimentally and theoretically over ranges of Reynolds numbers from zero to 9 × 105, Grashof numbers from 7 × 104 to 3 × 109, and Prandtl numbers from 0.024 to 217. For Prandtl numbers between 4.0 and 217 and Reynolds numbers below 5 × 104 the average Nusselt number for cooling as well as heating was found to be in reasonably good agreement with the result of a theoretical analysis based on a solution of the boundary-layer equations in which the boundary-layer thickness around the sphere was assumed to be uniform. A detailed study of the boundary-layer flow by means of a hot wire and several visualization methods showed, however, that the thickness of the boundary layer increases with angular distance from the poles and that in the vicinity of the equator where the boundary layers from the upper and lower halves of a rotating sphere meet, a complex flow separation takes place. The extent of the separation region was determined and some unusual transition phenomena were observed

The thermal conductance of uranium dioxide/stainless steel interfaces

Abstract: The thermal conductance of uranium dioxide/stainless steel interfaces was investigated in a disc-type apparatus under vacuum and with different interface gases (helium, argon, neon), and ranges of surface roughness (STA11 to 1417! x 10/sup -6/ cm, arithmetical mean height measured from Talysurf profile records), interface gas pressure (7 to 1226 mm Hg), contact pressure (0 to 570 lb/ in/sup 2/), mean interface temperature (55 to 410 deg C), and heat flux (1 to 5.5 cal/s cm/sup 2/). To obtain consistent results, the contact faces of the 2-cm diameter specimens were lapped optically flat and then roughened to a controlled amount. The thermal conductance is the sum of the soiid conductance through the small areas of true contact, and the conductance through the gas in the interface (thermal radiation made a negligible contribution). The experimental values obtained for the solid conductance were of the same order as that predicted by the theory of Cetinkale and Fishenden. It was found, as expected, that the solid conductance between uranium dioxide and stainless steel was very low, owing to the hardness of the materials and the poor thermal conductivity of the uranium dioxide. Predicted values of the gas conductance, based on several simple geometricalmore » models of the roughness, and allowing for accommodation effects in collisions between the gas molecules and the surfaces, have been compared with the present experimental results and with other published data. In nearly all cases the measured conductance is within a factor two of the predicted value, which is considered to represent good agreement in view of the very wide range of variables covered by the data and the inaccuracies inherent in this type of measurement. (auth)« less

Turbulent heat transfer in a circular tube with variable circumferential heat flux

Abstract: An analysis for hydrodynamically and thermally fully developed heat transfer in a circular tube with variable circumferential heat flux is presented. The results allow prediction of temperature variations when the tube is heated uniformly in the axial direction and non-uniformly around its perimeter. A surprising conclusion is that the effects of circumferential heat flux variation in turbulent flow are sometimes more pronounced than in laminar flow. An example shows the striking importance of these effects.

The effect of axially varying and unsymmetrical boundary conditions on heat transfer with turbulent flow between parallel plates

Abstract: The solution is presented to the heat-transfer problem with turbulent flow between parallel plates with heating on one side only. The configuration has some practical significance when considered as a limiting case of the annulus with a heated core. The velocity and eddy diffusivity variations due to Deissler are used but are modified in the central region of the passage by assuming a constant eddy diffusivity. In solving the energy equation the eddy diffusivities for heat and momentum are taken equal. The eigenvalues and functions necessary to calculate the variation of Nusselt number with distance along the passages are tabulated for three Reynolds and three Prandtl numbers. From the two basic solutions of uniform temperature and uniform heat flux the analysis is extended to certain axial variations which are of practical interest and finally, by using superposition, the result is obtained for unequal uniform heat fluxes on each side of the passage.

Mass minimization of radiating trapezoidal fins with negligible base cylinder interaction

Abstract: An optimization procedure is presented for achieving maximum dissipation from a longitudinal fin system of trapezoidal profile with mutual irradiation. The fins are conceived to be arranged symmetrically around a small base cylinder of uniform temperature. The governing equation for the temperature field along the fin is formulated in terms of finite summation and differences. The resulting set of simultaneous, non-linear, algebraic equations was solved by iteration using the Newton-Raphson method. A new dimensionless parameter is proposed to characterize the total dissipating capacity of a fin system with mutual irradiation. Its use has advantage over the conventional fin effectiveness in design application. Trapezoidal fins, including triangular and rectangular profiles, were investigated for a wide range of emissivities and incident space radiation. Optimum fin number and their proportions were determined and charts of dissipation capacity were presented. This analysis also leads to an expression suitable for comparing performance of fin systems fabricated of materials of different conductivity and density. For a fixed total mass of the fin material, the maximum dissipation varies as the 1 3 power of the quantity k ρ , other factors remain unaltered.

The influence of electrostrictive forces in natural thermal convection

Abstract: The free convection of an electrostrictive fluid enclosed between a horizontally heated wire and a coaxial, cooled cylinder, under an applied nonuniform radial electric field, is examined. An approximate solution is obtained by extending Langmuir's conduction model for fine wires to the electrostrictive case. It is found that the increase in Nusselt number due to the additional circulation produced by the electrostrictive force depends on the Grashof number, Prandtl number and a third characteristic non-dimensional number of the same nature as the Grashof number but based on an electrostatic rather than gravitational field. The theoretical results are compared with available experimental data and are found in good agreement.

Turbulent heat transfer and temperature fluctuations in a field with uniform velocity and temperature gradients

Abstract: Turbulent heat and momentum transfer for uniform velocity and temperature gradients in a flow field

Effect of discontinuity of surface catalycity on boundary layer flow of dissociated gas

Abstract: The catalytic recombination of atoms along a surface with a discontinuous variation of the surface catalytic activity is studied. The catalycity is considered to have a discrete jump from either zero or infinity to an arbitrary but constant value at a given location. Highly cooled hypersonic laminar boundary layers are considered for general two-dimensional and axisymmetric bodies. Two approaches are used in the study: a Volterra integral equation which is solved by both a series method and a numerical method and a modified Pohlhausen integral method. The effect of a non-catalytic up-stream surface on the heat transfer to down-stream surfaces with a finite catalycity is discussed. Also, a method is advanced to increase the sensitivity of a differential catalytic gage used for the determination of local atom concentrations of high temperature experimental facilities.

A flame zone model for chemical reaction in a laminar boundary layer with application to the injection of hydrogen-oxygen mixtures

Abstract: There is suggested a model for chemical reaction within a boundary layer based on the concept of a critical temperature to distinguish between regions of frozen and equilibrium flow. The model, which is termed the flame zone model, is applied to the injection of hydrogen-oxygen mixtures through a porous surface into a laminar boundary layer with uniform external conditions in air. It is shown that the model is less restrictive than the frequently applied flame sheet model to which it reduces in special cases and with a simplifying approximation concerning the equilibrium condition. The results of several numerical examples corresponding to hypersonic wind tunnel and to hypersonic flight conditions are presented.

Calculation of the spalding function over a range of prandtl numbers

Abstract: : An extensive tabulation is presented of the Spalding function = SP/square root (.5c), where S = Stanton number, P = Prandtl number, c = skin-friction coefficient. This tabulation is useful in the calculation of heat transfer rates into fully developed turbulent boundary layers. Numerical data are presented for P = 0.71, 1, 7, 30, 100, and 1,000. (Author)

Mathematical model for heat or mass transfer at the bubble-stirred interface of two immiscible liquids

Abstract: A mathematical model is proposed to describe the mechanism of heat or mass transfer at the bubble-stirred interface of two immiscible liquids. On the assumption of unsteady-state condition (diffusion) between the arrival of successive bubbles, an expression is derived for the overall transfer coefficient. One practical application of the proposed model is the interpretation of slag-metal interactions in an open-hearth furnace.

The effect of transverse mass flow on heat transfer and friction drag in a turbulent flow of compressible gas along an arbitrarily shaped surface

Abstract: Experimental investigations were carried out on the friction drag and heat transfer of a porous surface in a heated air flow at dp dx = 0 and dp/dx ≠ 0 with the injection of various gases (helium, air, carbon dioxide and freon-12). The effect of relative flow of injected gases on a flat plate and of longitudinal pressure gradient (the case dp/dx ≠ 0) on heat transfer and friction drag is found. It is shown that with increase of molecular weight of injected gases, their effect on heat transfer and friction drag decreases. Longitudinal pressure gradient considerably influences friction drag rather strongly, but it has no effect on heat transfer rate. Experimental data and their correlation by relations between dimensionless parameters of friction, pressure gradient and injection allowed the relation between the main characteristic quantities for a turbulent boundary layer to be evaluated under conditions of heat and mass transfer and longitudinal pressure gradient.

Use of reference states and constant-property solutions in predicting mass-, momentum-, and energy-transfer rates in high-speed laminar flows

Abstract: Two simple cases of laminar flow with simultaneous transfers of mass, momentum, and energy are studied first in order to obtain insight into the nature of transport phenomena and thermodynamic conditions existing in high-speed boundary layers involving diffusion of a gas added at the wall. In laminar Couette flow, simplifications are realized as a consequence of the nature of the boundary conditions, and information concerning the effects of differences in the heat capacities of the two species and the effects of deviations of Prandtl number, Schmidt number, and Lewis number from unity are obtained. An exact expression for the reference composition is obtained for the case of isothermal flow; a linearized expression for the reference temperature is obtained for the case in which the viscosity is a linear function of temperature and independent of composition. To first order in blowing rates, the reference composition is the arithmetic average of the compositions at the two surfaces, whereas the expression for the reference enthalpy is a simple extension of Eckert's expression for the reference enthalpy for a laminar boundary-layer with no mass addition at the wall. In laminar boundary-layer flow with constant properties, simplifications are realized as a consequence of the fluid properties being constant properties, and information concerning the effects of the two-dimensional character of boundary-layer flow is obtained. The information obtained for these two simple cases is combined then, and applied to the case of laminar boundary-layer flow with variable fluid properties. Basing all fluid properties upon the reference state suggested in the Couette flow study, mass-, momentum-, and energy-transfer rates and recovery factors for fluids with variable fluid properties, are given as functions of blowing rates for several coolants (including H2, with molecular weight 2, and I2, with molecular weight 254) and for several speeds (up to Ma = 12) by only two curves to an approximation adequate for many engineering applications. A Reynolds analogy for boundary-layer flows with mass additions at the wall is found to exist.

Dissociated laminar boundary layer flows over surfaces with arbitrary continuous distributions of catalycity

Abstract: This paper studies several new types of exact series solutions to the diffusion equation for chemically-frozen, dissociated, laminar boundary-layer flows around bodies with arbitrary continuous distributions of a first-order atom recombination rate along the surface. Plate, wedge, and cone flows are considered. The analysis extends the theory of Chambre and Acrivos for constant surface catalytic efficiency and temperature to the case wherein the surface Damkohler number varies as any power of the distance or is distributed as any polynomial involving integer or fractional positive powers of the distance. Furthermore, by imposing the approximation of local similarity in the velocity profile, the resulting solutions are also applied with good accuracy to highly-cooled bluntnosed bodies in hypersonic flow. An approximate method of solution is also developed which provides an extremely simple closedform representation of the exact series solutions throughout the entire flow field by means of a local nonlinear extrapolation of the leading term in the series. It is shown by several examples that this technique yields very accurate results for surface atom concentration, diffusion flux, and heat-transfer distributions for a variety of streamwise variations in the wall catalycity.

Forced convection in a channel with wall heat capacity and with wall heating variable with axial position and time

Abstract: Heat transfer to a fluid with constant properties is analysed for forced convection between two parallel plates. The plates have a finite heat capacity, and heat is supplied to them in an arbitrary manner with both time and axial position. The wall is assumed sufficiently thin or highly conducting so that the temperature variation through the wall thickness can be neglected. The fluid temperature is variable over the channel cross section, but the fluid velocity is assumed constant throughout the channel (slug-flow condition). The energy equation is laminar. A general method of solution is given and then some illustrative examples are carried out. These include uniform wall heating that varies sinusoidally in time, and heating varying sinusoidally with axial distance and exponentially in time.

The mechanism of nucleate boiling heat transfer

Abstract: In nucleate boiling a bubble created at nucleation site on a heating surface grows, leaves the surface and rises. The fluid motion induced in the thermal boundary layer during this process is calculated and the heat flux carried by this liquid motion to a nucleation site is obtained. The heat flux thus calculated is equal to that transferred from the heating surface to the liquid by conduction and to the latent heat carried away by the bubble per unit time. From these relations the following theoretical formula is obtained. Δθ = 0.114 n − 1 4 q 2 3 where Δθ is a temperature difference between the temperature of heating surface and the saturation temperature, n is the number of nucleation sites per unit area and q is average heat flux. This closely resembles in form the following experimental formula which was obtained through measurement by Nishikawa: Δθ exp = 0.448 n − 1 6 q 2 3 The numerical values computed from these two formulas are in fairly good agreement with each other.

Differential methods for studying radiant heat transfer

Abstract: This paper describes novel differential methods for studying radiant heat transfer which might have wide application on the score of simplicity. A new method is put forward, based on tensor representation and yields more accurate results. Comparison between calculated results of radiant heat transfer through a plane absorbing layer obtained with existing and with the proposed methods and those obtained numerically on a computer reveal good agreement.