Showing papers on "Natural convection published in 1974"

Natural Convection Adjacent to Horizontal Surface of Various Planforms

Abstract: Natural convection adjacent to horizontal surfaces of circular, square, rectangular, and right triangular planforms has been studied experimentally. Electrochemical techniques were employed involving a fluid with a Schmidt number of about 2200. The results encompass a wide range of Rayleigh numbers thus providing information on both the laminar and the turbulent regimes. The data for all planforms are reduced to a single correlation in the laminar and turbulent regimes using the characteristic length, as recommended by Goldstein, Sparrow, and Jones. L* = A/p, where A is the surface area and p is the surface perimeter. The laminar data for all planforms are correlated by the expression Sh = 0.54 Ra1/4 (2.2 × 104 ≤ Ra ≤ 8 × 106) and the data for the turbulent regime are correlated by the expression Sh = 0.15 Ra1/3 (8 × 106 ≤ 1.6 × 109) Transition is found to occur at about Ra = 8 × 106 . The present work thus significantly extends the Rayleigh number range of validity for the use of L* through the 1/4 power laminar regime into the turbulent 1/3 power regime. It also demonstrates the validity of the use of L* to correlate natural convection transfer coefficients for highly unsymmetrical planforms, which heretofore had not been demonstrated. Comparisons to analytical solutions and other experimental heat and mass transfer data are presented.

Natural convection in a shallow cavity with differentially heated end walls. Part 1. Asymptotic theory

Abstract: The problem of natural convection in a cavity of small aspect ratio with differentially heated end walls is considered. It is shown by use of matched asymptotic expansions that the flow consists of two distinct regimes : a parallel flow in the core region and a second, non-parallel flow near the ends of the cavity. A solution valid at all orders in the aspect ratio A is found for the core region, while the first several terms of the appropriate asymptotic expansion are obtained for the end regions. Parametric limits of validity for the parallel flow structure are discussed. Asymptotic expressions for the Nusselt number and the single free parameter of the parallel flow solution, valid in the limit as A → 0, are derived.

Natural convection in enclosed spaces - A review of application to solar energy collection

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.

Natural convection in a shallow cavity with differentially heated end walls. Part 3. Experimental results

Abstract: The steady motion of water in an enclosed rectangular cavity with differentially heated vertical end walls was studied experimentally, and the results are compared with the findings of parts 1 and 2. The depth-to-length ratios of the cavities were 102 and 1·9 × 102, and the Rayleigh number was allowed to vary sufficiently to enable a study to be made of the transition from a flow driven by the vertical wall boundary layers to one sustained by a longitudinal temperature gradient in the central sections of the cavity.

Natural convection in a shallow cavity with differentially heated end walls. Part 2. Numerical solutions

Abstract: Numerical solutions of the full Navier-Stokes equations are obtained for the problem of natural convection in closed cavities of small aspect ratio with differentially heated end walls. These solutions cover the parameter range Pr = 6.983, 10 ≤ Gr ≤ 2x10^4 and 0.05 ≤ A ≤ 1. A comparison with the asymptotic theory of part 1 shows excellent agreement between the analytical and numerical solutions provided that A ≾ 0.1 and Gr^2A^3Pr^2 ≾ l0^5. In addition, the numerical solutions demonstrate the transition between the shallow-cavity limit of part 1 and the boundary-layer limit; A fixed, Gr → ∞.

Finite-amplitude thermal convection in a spherical shell

Abstract: The properties of finite-amplitude thermal convection for a Boussinesq fluid contained in a spherical shell are investigated. All nonlinear terms are retained in the equations, and both axisymmetric and nonaxisymmetric solutions are studied. The velocity is expanded in terms of poloidal and toroidal vectors. Spherical surface harmonics resolve the horizontal structure of the flow, but finite differences are used in the vertical. With a few modifications, the transform method developed by Orszag (1970) is used to calculate the nonlinear terms, while Green's function techniques are applied to the poloidal equation and diffusion terms.

On transition mechanisms in vertical natural convection flow

Abstract: An experimental investigation has been made of the processes occurring during the natural transition from laminar to turbulent flow of natural convection flow of water adjacent to a flat vertical surface where the surface heat flux is uniform. Measurements of both the velocity and temperature fields were made over wide ranges of the heat flux and at various downstream locations. Of principal interest were the definitions of the boundaries of the transition regime and their determination at several values of the surface heat flux. The interaction of the velocity and temperature fields during transition was measured. Our results show that transition events are not correlated in terms of the Grashof number G*. The form G*/xn, where n is of order ½ was found to give satisfactory correlations. Measurements of the frequency and growth rate of disturbances indicate the primacy of the velocity field during transition and show that the growth of turbulence in the temperature field lags behind that in the velocity field. The study of the turbulence growth, in terms of intermittency factors in both the velocity and temperature fields, resulted in unambiguous criteria for the boundaries of the transition regime. Our results suggest a kinetic energy flux parameter E and a single value closely correlates both our measurements of the onset of transition as well as those from all past studies known to us, for both different fluids and heating conditions.

Free convection effects on steady MHD flow past a vertical porous plate

Abstract: An analysis of two-dimensional steady flow of an incompressible, viscous, electrically conducting fluid past an infinite vertical porous plate is carried out under the following assumptions: (i) that the suction velocity normal to the plate is constant, (ii) that the plate temperature is constant, (iii) that the difference between the temperatures of the plate and the free stream is moderately large, causing free convection currents, (iv) that the transversely applied magnetic field and magnetic Reynolds number are very small and hence the induced magnetic field is negligible.Approximate solutions to the coupled nonlinear equations governing the steady velocity and temperature are derived. They are shown graphically. During the course of discussion, the effects of positive and negative G (the Grashof number: G > 0 implies cooling of the plate, G < 0 heating of the plate), of P (the Prandtl number), of positive and negative E (the Eckert number) and of M (the magnetic field parameter) are presented quantitatively.

Free Convection Heat Transfer from Vertical Fin-Arrays

Abstract: A simple but relatively accurate, approximate technique is presented for analyzing the heat transfer due to natural convection and radiation from parallel-fin heat sinks. This technique accounts for a nonuniform base plate temperature. The finned surfaces and the base plate have been considered to be vertical U-shaped channels and a relationship for the NusseJt number has been used which has a suitable form for both very long and very short fins. The accuracy of the technique has been demonstrated by a testing program on a representative sample of heat sinks.

Natural convection in vertical permeable space

Abstract: This article describes the natural convective heat transfer in a vertical space insulated with a permeable material. A numerical solution to the problem is given for Ra0 ⩽ 200, which is the range of interest to building technological applications. The variables and boundary conditions and their influence upon the convective heat transfer are discussed. Comparisons are made with previously published results.

Stress work effects in laminar flat-plate natural convection

Abstract: The effects of both viscous and pressure stress work are considered in laminar natural convection on flat surfaces. Whereas in previous investigations only viscous stress work effects were studied, it is established here that pressure work effects are generally rather more important both for gases and liquids. Variations in the properties of the fluid outside the natural convection boundary layer are shown to occur inevitably in this problem and are found to lead to effects comparable with those produced by pressure work. Property variations in the boundary layer itself are also found to be of importance. Such variations, both inside and outside the boundary layer, have been ignored in previous studies. Examples of flows are discussed in which the fluids are either perfect gases or fluids undergoing small changes in temperature and pressure. For both of these fluids, the effects of conditions of either constant temperature or constant entropy in the fluid outside the boundary layer are examined.

Mass transfer during dissolution of a solid into liquid in the iron-carbon system

Abstract: The rates of dissolution of solid pure iron and a solid iron-carbon alloy into molten iron-carbon alloys were studied “isothermally” as a function of temperature, carbon content and fluid dynamic (stirring) conditions. Experiments were carried out in a resistance-heated tube furnace under an inert atmosphere of argon gas at temperatures ranging from 2165 to 2563°F. A cylindrical specimen of the solid was preheated to the liquid temperature, immersed in the liquid bath contained in a graphite or alumina crucible, and rotated at speeds ranging up to 1800 rpm. The diameter of the specimen after partial solution was determined by direct measurement or calculated from the weight loss of the specimen. The experimental data were fitted with nondimensional correlations of mass transfer for a vertical cylinder, both stationary and rotating. When the specimen was stationary the mass transfer was dominated by natural convection in the liquid bath. When the specimen was rotated, forced convection prevailed and controlled the mass transfer rate.