Showing papers on "Nusselt number published in 1976"
516 citations
TL;DR: In this paper, a Nusselt number correlation is proposed to determine the flow transition from the initial annular regime to the final stratified regime, which exhibits errors of similar magnitude to established methods for annular and stratified flow condensation.
198 citations
TL;DR: In this article, the heat transport and structure of convection in a high Prandtl number fluid layer whose viscosity varies by up to a factor of 300 between the boundary temperatures was investigated.
Abstract: This paper experimentally investigates the heat transport and structure of convection in a high Prandtl number fluid layer whose viscosity varies by up to a factor of 300 between the boundary temperatures. An appropriate definition of the Rayleigh number R uses the viscosity at the average of the top and bottom boundary temperatures. With rigid boundaries and heating from below, the Nusselt number N normalized with the Nusselt number N0 of a constant-viscosity fluid decreases slightly as the viscosity ratio increases. The drop is 12% at a variation of 300. A slight dependence of N/N0 on R is consistent with a decrease in the exponent in the relation N ∝ Rβ from its constant-viscosity value of 0·281 to 0·25 for R [lsim ] 5 × 104. This may be correlated with a transition from three- to two-dimensional flow. At R ∼ 105 and viscosity variation of 150, the cell structure is still dominated by the horizontal wavelength of the marginally stable state. This is true with both free and rigid upper boundaries. The flow is strongly three-dimensional with a free upper boundary, while it is nearly two-dimensional with a rigid upper boundary.
180 citations
TL;DR: In this article, the spacing between the hot solar absorber and successive glass covers should be in the range 4 to 8 cm to assure minimum gap conductance, based on the theory and some experimental measurements.
Abstract: A useful solar-thermal converter requires effective control of heat losses from the hot absorber to the cooler surroundings. Based upon the theory and some experimental measurements it is shown that the spacing between the tilted hot solar absorber and successive glass covers should be in the range 4 to 8 cm to assure minimum gap conductance. Poor choice of spacing can significantly affect thermal conversion efficiency, particularly when the efficiency is low or when selective black absorbers are used. Recommended data for gap Nusselt number are presented as a function of the Rayleigh number for the high aspect ratios of interest in solar collector designs. It is also shown that a rectangular cell structure placed over a solar absorber is an effective device to suppress natural convection, if designed with the proper cell spacing d, height to spacing ratio L/d and width to spacing ratio W/d needed to give a cell Rayleigh number less than the critical value.
169 citations
TL;DR: In this article, a model for simultaneous heat transfer, mass transfer, and chemical reaction in the oxidation of carbon monoxide over platinum containing monoliths is presented. But the model is not suitable for predicting the behavior of the Nusselt number.
Abstract: Mathematical models are developed which account for simultaneous heat transfer, mass transfer, and chemical reaction in the oxidation of carbon monoxide over platinum containing monoliths. A two-dimensional model is shown to predict unusual behavior of the Nusselt number in the presence of rapid reaction. However, a simpler one-dimensional model is adequate for predicting monolith behavior.
149 citations
TL;DR: In this article, transient, laminar free convection along a vertical, isothermal flat plate arising from buoyancy forces created by both temperature and concentration gradients is investigated.
104 citations
TL;DR: In this article, the authors studied axisymmetric convection in a Boussinesq fluid contained in a cylindrical cell with free boundaries, and obtained the solution from a perturbation expansion, valid only if both the Reynolds number and the PBclet number are small.
Abstract: In three-dimensional BBnard convection regions of rising and sinking fluid are dissimilar. This geometrical effect is studied for axisymmetric convection in a Boussinesq fluid contained in a cylindrical cell with free boundaries. Near the critical Rayleigh number R, the solution is obtained from a perturbation expansion, valid only if both the Reynolds number and the PBclet number are small. For values of the Nusselt number N 1 there is a viscous regime with N M 2(R/Rc)i; when R/R, 2 pb, N increases more rapidly, approximately as R0.4. At high Rayleigh numbers a large isothermal region develops, in which the ratio of vorticity to distance from the axis is nearly constant.
95 citations
TL;DR: In this article, a 3·5 by 3.5 m variable-height, closed convection box with conditions ranging from a Rayleigh number of 4 × 104 up to 7 × 109, using air as the working fluid.
Abstract: An experiment was performed in a 3·5 by 3·5 m variable-height, closed convection box, with conditions ranging from a Rayleigh number of 4 × 104 up to 7 × 109, using air as the working fluid. Heat-flux measurements made at Rayleigh numbers up to 7 × 109 yielded a Nusselt number Nu = 0·13Ra0·30. Velocities and temperatures were measured up to Ra = 1·7 × 107, and Fourier spectra calculated to find the predominant horizontal scales of the motion midway between the boundaries. The predominant scale at Ra ∼ 105 was approximately four times the distance between plates, changing to six as Ra increased to 106. With side walls introduced so that the transverse aspect ratio was equal to five, Fourier spectra indicated considerable smaller scale motions, approximately equal to the layer depth. These motions decreased in size as Ra was increased. The results are discussed in relation to previous experimental and theoretical work.
92 citations
72 citations
67 citations
TL;DR: In this article, the authors used the heat-mass transfer analogy, in conjunction with the naphthalene sublimation technique, to investigate the transfer capabilities and transfer mechanisms in two-row plate fin and tube heat exchanger configurations.
TL;DR: In this paper, the assumption of temperature/concentration being center-symmetric in solid particles in packed beds was found to be faulty at low flow rate, and anomalously low transfer coefficients measured at low Reynolds numbers were considered to result from the erroneous assumption.
TL;DR: In this paper, a correlating equation was developed which provides a continuous representation for all Pr and Re and different constants were suggested for the local and mean Nusselt numbers and for uniform wall temperature and heating.
Abstract: A correlating equation was developed which provides a continuous representation for all Pr and Re. Different constants are suggested for the local and mean Nusselt numbers and for uniform wall temperature and heating. These constants are based on the best available theoretical and experimental results.
TL;DR: In this article, a theory for the dependence of the Nusselt number on the Rayleigh number in turbulent thermal convection in horizontal fluid layers is developed, which is based on a number of assumptions regarding the behaviour in the molecular boundary layers and on the assumption of a buoyancy-defect law in the interior analogous to the velocity defect law in flow in pipes and channels.
Abstract: A theory is developed for the dependence of the Nusselt number on the Rayleigh number in turbulent thermal convection in horizontal fluid layers. The theory is based on a number of assumptions regarding the behaviour in the molecular boundary layers and on the assumption of a buoyancy-defect law in the interior analogous to the velocity-defect law in flow in pipes and channels. The theory involves an unknown constant exponent s and two unknown functions of the Prandtl number. For either s = ½ or s = 1/3, corresponding to two different theories of thermal convection, and for a given Prandtl number, constants can be chosen to give excellent agreement with existing data over nearly the whole explored range of Rayleigh numbers in the turbulent case. Unfortunately, comparisons with experiment do not permit a definite choice of s, but consistency with the chosen form of the buoyancy-defect law seems to suggest s = 1/3, corresponding to similarity theory.
TL;DR: In this paper, the temperature profile and the radiative and convective wall-heat fluxes for a hydro-dynamically established flow of a nongray gas in a cylinder are calculated numerically for laminar or turbulent flow.
Abstract: The temperature profile and the radiative and convective wall-heat fluxes for a hydro-dynamically established flow of a nongray gas in a cylinder are calculated numerically for laminar or turbulent flow. Turbulent eddy viscosity is represented by a two-region model having a near-wall-region and a far-from-wall region. Gas properties are represented by the exponential-winged band model. Qualitatively the results for a gas with a single major band agree with a previous solution for a cylinder with internal heat generation.
TL;DR: In this paper, an experimental study of mass transfer to a rotating disk electrode has been employed to determine an empirical correlation for the mass transfer rate in the Reynolds number regime lying between simple laminar and turbulent flows.
Abstract: An experimental study of mass transfer to a rotating disk electrode has been employed to determine an empirical correlation for the mass transfer rate in the Reynolds number regime lying between simple laminar and turbulent flows. This domain, apparently characterized by a regular vortex pattern, was found to extend from a Reynolds number of to approximately. The resultant correlation for the average tranfser rate, in terms of dimensionless Nusselt, Reynolds, and Schmidt numbers, isThe result is strictly applicable to the case of a uniform surface concentration; that is, to the limiting‐current condition.
Journal Article•
TL;DR: In this paper, the authors used the limiting current technique to obtain mass transfer coefficients at very low Reynolds numbers (Re less than 0.1) in a packed bed consisting of stainless steel spheres.
Abstract: The limiting current technique is used to obtain mass transfer coefficients at very low Reynolds numbers (Re less than 0.1) in a packed bed consisting of stainless steel spheres. The data show that for Re less than 0.015, the Nusselt numbers are below those predicted by existing empirical correlations. The results are discussed in the light of some mathematical models for packed beds reported in the literature and show semiquantitative agreement with the values predicted by Sorensen and Stewart (1974a).
01 Nov 1976
TL;DR: An analysis of the mass transfer effects on the free convective flow of an incompressible, dissipative, viscous fluid past an infinite, vertical porous plate with constant suction, has been carried out in this paper.
Abstract: An analysis of the mass transfer effects on the free convective flow of an incompressible, dissipative, viscous fluid past an infinite, vertical porous plate with constant suction, has been carried out. Approximate solutions to coupled non-linear equations governing the flow are derived. The velocity and the temperature profiles are shown graphically for air (P=0·71). The effects of Gr (Grashof number), Gc (the modified Grashof number), Sc (Schmidt number), E (Eckert number) are discussed qualitatively during the course of discussion. It is observed that due to the addition of the foreign mass, there is a rise in the velocity and a fall in the temperature. But the skin-friction increases when Sc≶1 and it decreases when Sc ∼1. The rate of heat transfer increases for Sc 1.
01 Jun 1976
TL;DR: In this article, the Kantorowich method of variational calculus is introduced to solve the problem of laminar forced heat convection in a channel of an arbitrary cross section, and the development of the temperature field and the heat transfer data in the thermal entrance region of elliptical and rectangular channels are determined.
Abstract: The Kantorowich method of variational calculus is introduced to solve the problem of laminar forced heat convection in a channel of an arbitrary cross section. Employing this procedure, the development of the temperature field and the heat transfer data in the thermal entrance region of elliptical and rectangular channels are determined, assuming a linear variation of wall temperature in the direction of flow. The uniform and the fully developed velocity profiles are considered. The local Nusselt numbers are tabulated for different aspect ratios.
TL;DR: In this article, the effects of both liquid film inertia and shear force at the condensing vapor-liquid film interface were taken into account for the condensation of a saturated vapor on a vertical melting surface, with emphasis on departures from a previous treatment produced by: (a) arbitrary liquid Prandtl numbers and (b) condensation melting systems involving two materials of immiscible liquids.
Abstract: Laminar film condensation of a saturated vapor on a vertical melting surface is treated theoretically, with emphasis on departures from a previous treatment produced by: (a) arbitrary liquid Prandtl numbers and (b) condensation-melting systems involving two materials of immiscible liquids. An integral method is utilized which takes full account of the effects of both liquid film inertia and shear force at the condensing vapor-liquid film interface. For a one-component system accurate numerical results for the melting rates are displayed graphically and define the range of validity of a simple treatment of this problem based on Nusselt’s method. For a two-component system, illustrative calculations are made for the condensation of a refrigerant vapor on melting ice.
TL;DR: In this paper, the authors present numerical solutions for heat transfer in the unsteady laminar boundary layer resulting from incompressible flow past an impulsively-started semi-infinite wedge.
TL;DR: In this article, a combined free and forced laminar convection with upward flow in inclined rectangular channels under the thermal boundary condition of axially uniform wall heat flux or constant wall temperature gradient is studied by a numerical method using an improved formulation where three independent physical parameters Pr, Re∗0, Ra∗ appear instead of four in previous investigations dealing with the inclined circular tubes.
TL;DR: In this article, a heat transfer problem for an infinitely long heated cylinder and a small heated sphere, each freely suspended in a general linear flow at Reynolds numbers Re ⪡ 1, is solved, and asymptotic solutions to the convection problem are developed for very large values of the Peclet number Pe.
TL;DR: In this paper, the influence of the developing flow in a circular duct on the laminar forced convection heat transfer was analyzed by employing the Galerkin-Kantorowich method of variational calculus.
TL;DR: In this paper, a numerical and experimental study of convective heat transfer in a vertical layer of a ferromagnetic fluid is presented, and an effect of the direction of a horizontal gradient of magnetic field strength relative to that of the temperature gradient on convective motion is investigated.
TL;DR: In this article, a boundary layer solution is presented for fully developed laminar flow in a horizontal circular tube, assuming large Prandtl number and temperature-dependent viscosity and density.
Abstract: A boundary layer solution is presented for fully developed laminar flow in a horizontal circular tube, assuming large Prandtl number and temperature-dependent viscosity and density. The solution is given by Nu = C1 Ra1/4 , where C1 is a function of a nondimensional viscosity parameter and the heat flux boundary condition. The heat transfer predictions for large values of the viscosity parameter are 50 percent above the constant viscosity predictions. The present analysis is in good agreement with experimental data for water and ethylene glycol flowing in electrically heated tubes which approximate the boundary conditions assumed in the analysis.
TL;DR: In this paper, a flow of steam/air containing a fraction of suspended mist was swept across a roughened heated tube, and the average heat-transfer coefficients were characterized by a dryness parameter, defined as; φ=qwo(Ao.