Showing papers on "Natural convection published in 1970"
TL;DR: In this paper, the authors consider optical methods in which the temperature dependence of the refractive index is used to make the temperature field visible, and compare shadowgraph and schlieren methods.
Abstract: Publisher Summary This chapter considers optical methods in which the temperature dependence of the refractive index is used to make the temperature field visible. The optical methods considered are divided into two groups: the shadow and schlieren techniques, utilizing the deflection of light in the measurement media, and the interference methods based on differences in lengths of the optical paths. Compared with shadowgraph and schlieren methods, the interference methods offer more detailed information about the model that is to be investigated; these allow a greater accuracy. The laws governing the propagation of light through a medium with locally varying refractive index have also been considered. The total information on the region of optical inhomogeneity being investigated comes from the deformation of a wave front, whose shape was originally known, as it passes through the region. The chapter provides examples of boundary-layer problems in the region of natural convection and combined convection. To fully demonstrate how the results are evaluated, some selected examples have been presented.
348 citations
210 citations
TL;DR: Experimental average heat transfer coefficients for free-convection cooling of arrays of isothermal fins on horizontal surfaces over a wider range of spacings than previously available are reported in this article.
Abstract: Experimental average heat-transfer coefficients for free-convection cooling of arrays of isothermal fins on horizontal surfaces over a wider range of spacings than previously available are reported. A simplified correlation is presented and a previously available correlation is questioned. An optimum arrangement for maximum heat transfer and a preliminary design method are suggested, including weight considerations.
177 citations
TL;DR: In this article, the authors describe experimental work on the mixed convection regime with flow normal to electrically heated cylinders and propose a correlation for the combined forced and natural convection region by a vectorial addition of the flow parameters, which gives good agreement with the experiments except over a limited range in the contraflow regime.
Abstract: This article describes experimental work on the mixed convection regime with flow normal to electrically heated cylinders. The forcing velocities used were in the range 0·0085–3 ft./sec (i.e. 10−2 < Ref < 45) and temperature differences in the range 30°C to 200°C (i.e. 10−3 < Ra < 10) were covered.Correlations are proposed for the forced convection and natural convection conditions. A correlation is also developed for the combined forced and natural convection region by a vectorial addition of the flow parameters, which gives good agreement with the experiments except over a limited range in the contraflow regime.
165 citations
TL;DR: In this paper, numerical methods are used to solve the field equations for heat transfer in a porous medium filled with gas and bounded by plane rectangular surfaces at different temperatures, and the relative increases in heat transfer rate, corresponding to natural convection, are obtained as functions of 3-dimensional parameters: the Darcy number Da, the Rayleigh number Ra and a geometric aspect ratio L/D.
Abstract: Numerical methods are used to solve the field equations for heat transfer in a porous medium filled with gas and bounded by plane rectangular surfaces at different temperatures. The results are presented in terms of theoretical streamlines and isotherms. From these the relative increases in heat transfer rate, corresponding to natural convection, are obtained as functions of 3- dimensionless parameters: the Darcy number Da, the Rayleigh number Ra, and a geometric aspect ratio L/D. A possible correlation using the lumped parameter Da Ra is proposed for Da Ra greater than about 40. (33 refs.)
155 citations
TL;DR: In this article, surface temperature distributions of flat copper plates were matched to those of real leaves in a very low-speed wind tunnel, and they were measured at wind velocities of < 1, 10, and 30 cm s_1 from below and laterally with horizontal and vertical plate orientations.
Abstract: Circular, abstractly lobed, and leaf-shaped flat copper plates were heated in a very low-speed wind tunnel. Surface temperature distributions of the plates were matched to those of real leaves. With the centres of the plates 15 °C above ambient temperature, their heat dissipation was measured at wind velocities of < 1, 10, and 30 cm s_1 from below and laterally with horizontal and vertical plate orientations. Even very slight forced-air movements markedly increased heat dissipation in this range of mixed free and forced convection. Lobed plates were more effective dissipators than circles, with the greatest differences occurring where flow was normal to the plate. Circular plates dissipated about one-fourth more heat when vertical than when horizontal in still air (free convection). By contrast, dissipation was essen tially independent of orientation for extensively lobed models. Under some circumstances, maximum dissipation occurred with lobed plates oblique to a forced air stream. Physical explanations and biological implications of these results are discussed.
135 citations
TL;DR: In this paper, a simple formulation of the boundary value problem for a wide range of values of the Prandtl number has been proposed, and results of experiments with plumes are included to emphasize the various properties of plume flow and to indicate that the large thickness of boundary region in the range of stable laminar plumes (i.e. at relatively low local Grashof numbers) should encourage the calculation of higher order approximate of the flow.
129 citations
112 citations
TL;DR: In this paper, local heat transfer coefficients along a flat plate in natural convection in air were measured using Boelter-Schmidt type heat flux meters, and the results were presented in terms of local Nusselt number as a function of the local Grashof number "tangential component".
111 citations
TL;DR: In this paper, the relationship between the nature of flow instability and the inclination angle of the plate was established, and the angular dependence of the Rayleigh number characterizing the onset of instability was also determined.
Abstract: Experiments are carried out to establish the relationship between the nature of the flow instability and the inclination angle of the plate. The angular dependence of the Rayleigh number characterizing the onset of instability is also determined. An electrochemical flow visualization technique is utilized to expose the patterns of fluid motion. It is found that for inclination angles of less than 14° (relative to the vertical), waves are the mode of instability. On the other hand, for inclination angles in excess of 17°, the instability is characterized by longitudinal vortices. The range between 14° and 17° is a zone of continuous transition, with the two modes of instability co-existing.
110 citations
TL;DR: In this article, an experimental investigation is described concerning natural convection between two isothermal concentric spheres of various diameter ratios ranging from 1.09 to 2.81, and a k eff k vs. Rayleigh number heat transfer correlation is presented for each of the three fluids individually, and an overall expression based solely on modified Rayleigh numbers is presented which correlates all three liquids as well as air.
TL;DR: In this article, the authors considered the problem of fully developed free convection in the atmospheric boundary layer and derived an expression for the height of unstable Ekman layers, as a function of the time of day and the stability conditions at the top of the boundary layer.
Abstract: This paper deals with the problem of fully developed free convection in the atmospheric boundary layer. In free convection, the height of the Ekman layer is much larger than the absolute value of the Monin-Oboukhov length. The kinetic energy budget of the turbulence above the surface layer shows that the standard deviations of vertical velocity and of temperature are related to h/L by σw/u*∝(−h/L)⅓ and σθ/θ*∝(−h/L)⅓. Because convection has no natural length scale, the height of the neutral Ekman layer (h∝u*/f) is used to explore the consequences of the proposed expressions for σw and σθ. The dissimilarity between the heat flux and the momentum flux is studied in terms of time- and length-scale ratios and in terms of a flux Richardson number. A definitive solution of the problem, however, cannot be formulated until an expression for the height of unstable Ekman layers, as a function of the time of day and the stability conditions at the top of the boundary layer, can he found.
TL;DR: In this paper, a cylindrical cell was investigated experimentally using two different fluids heated from below, and the flow pattern was found to consist of concentric rolls in the case of buoyancy-driven convection, and of hexagonal cells for surface-tension driven flow.
01 Aug 1970
TL;DR: In this article, a formulation is given and computed solutions are presented for transient solidification accompanied by natural convection in a vertical slot, where the simplifying assumptions made limit the validity of the solutions to systems where GrPr < 500, i.e., to narrow slots or to low values of the superheat.
Abstract: A formulation is given and computed solutions are presented for transient solidification accompanied by natural convection in a vertical slot. It was found that appreciable fluid velocities may be produced by natural convection, the values of which could be comparable to the terminal rising velocities of typical nonmetallic inclusions. The simplifying assumptions made limit the validity of the solutions to systems where GrPr < 500,i.e., to narrow slots or to low values of the superheat; nonetheless, the results should be indicative of the effects of convection at much higher values of GrPr.
01 May 1970-Metallurgical and Materials Transactions B-process Metallurgy and Materials Processing Science
TL;DR: In this paper, the effect of natural convection on the controlled solidification of lead under conditions of nearly unidirectional heat flow within the system was investigated and the experimentally found shape and position of the solid-melt interface was reasonably well predicted by the consideration of heat transfer from the melt to the solid surface.
Abstract: Experiments are reported on the study of the effect of natural convection on the controlled solidification of lead under conditions of nearly unidirectional heat flow within the system. The experimentally found shape and position of the solid-melt interface was reasonably well predicted by the consideration of heat transfer by natural convection from the melt to the solid surface. Transient runs were also carried out and here the rate of movement of the melt-solid interface was readily predicted from the (numerical) solution of the appropriate unsteady state conduction equation.
TL;DR: In this article, buoyancy-driven convection in horizontal layers of dilute water solutions of ionic and nonionic polyacrylamides confined between rigid, parallel, conducting surfaces was studied experimentally.
Abstract: Buoyancy-driven convection in horizontal layers of dilute water solutions of ionic and nonionic polyacrylamides confined between rigid, parallel, conducting surfaces was studied experimentally. By determining the temperature difference at the point where convection first sets in, values of the zero shear rate viscosity were calculated in good agreement with those obtained from rheogoniometer data. Beyond this point, the heat transfer characteristics of the solutions and the associated convective flow patterns were found to be rather similar to those of a viscous Newtonian fluid forRayleigh numbers up to 5 × 104, the range covered by the present experiments. However, theNusselt numbers at any givenRayleigh number were slightly but consistently higher than those of a Newtonian fluid of comparable viscosity. Also, the regularity of the flow patterns was more pronounced.
TL;DR: In this paper, the problem of magnetohydrodynamic free convection of an electrically conducting fluid in a strong cross field is investigated by using a singular perturbation technique, and the solutions presented cover the range of Prandtl numbers from zero to order one.
Abstract: The problem of magnetohydrodynamic free convection of an electrically conducting fluid in a strong cross field is investigated. It is solved by using a singular perturbation technique. The solutions presented cover the range of Prandtl numbers from zero to order one. This includes both the important cases of liquid metals and ionized gases. A general examination is given of the role of the important parameters: Hartmann, Grashof and Prandtl numbers of the problem. This provides clear insight into its singular character and yields the correct expansion parameters. The boundary-layer approximations are derived from the complete Navier-Stokes and energy equations. The conditions for these approximations to be valid will be explicitly stated. Attention is given to ‘power law’ wall-temperatures and magnetic fields, and an assessment is given of the range of application.
TL;DR: In this paper, the authors investigated the natural convection wake arising from a heated horizontal line source in liquids and in air using a 20 cm Mach-Zehnder interferometer.
TL;DR: In this paper, the stability of the laminar flow solution for given values of the three governing parameters, the Rayleigh number A = γ g Δ TL 3 /κν, the aspect ratio h = H/L and the Prandtl number σ = ν/κ.
Abstract: The study of natural convection in a rectangular cavity whose side walls are maintained at different fixed temperatures can be regarded as one of the classical problems of thermal convection (see Batchelor 1954; Elder 1965 and Gill 1966). One aspect of this problem is the question of stability of the laminar flow solution for given values of the three governing parameters, the Rayleigh number A = γ g Δ TL 3 /κν, the aspect ratio h = H/L and the Prandtl number σ = ν/κ. Here H is the height and L the width of the cavity, T is the temperature difference between the two walls and g the acceleration due to gravity. The fluid filling the container has coefficient of expansion γ, thermal diffusivity κ and kinematic viscosity ν. Instead of studying the stability of the exact laminar flow solution, which is not a parallel flow, the stability of the following solution of the governing eauations is examined instead:
TL;DR: In this article, the heat and mass transfer coefficients for laminar free convection driven by simultaneous differences in temperature and composition were derived for horizontal cylinders or vertical axisymmetric bodies with arbitrary body contours.
Abstract: Expressions are derived for the heat and mass transfer coefficients for laminar free convection driven by simultaneous differences in temperature and composition for the asymptotic cases of equal Schmidt and Prandtl numbers approaching zero, equal Schmidt and Prandtl numbers approaching infinity, Schmidt number approaching infinity and Prandtl number approaching zero, and Schmidt number larger than Prandtl number and Prandtl number approaching infinity.
The results are applicable for horizontal cylinders or vertical axisymmetric bodies with arbitrary body contours insofar as the approximations of boundary-layer theory are valid. The results compare favorably with existing solutions and experimental results for particular conditions.
01 Jan 1970
TL;DR: In this paper, the effects of radiative transfer in the thermal convection of a thin fluid layer bounded by rigid horizontal planes and heated from below were investigated and the critical values (for instability of the motionless fluid) of the Rayleigh number and wavenumber were computed for a gray, transparent medium including the effect of nonlinear initial temperature profiles.
Abstract: Linear stability theory is applied to determine the effects of radiative transfer in the thermal convection of a thin fluid layer bounded by rigid horizontal planes and heated from below. The critical values (for instability of the motionless fluid) of the Rayleigh number and wavenumber are computed for a gray, transparent medium including the effect of nonlinear initial temperature profiles. Limited results are given for the whole range of optical thickness showing that molecular heat conduction is negligible in the whole range except when the optical thickness approaches zero (a nonuniform limit). An estimate for the convective heat transport in a transparent medium is made using the “shape assumption” and compared with nonradiative convection.
TL;DR: In this paper, the fundamental equations of free convection in a compressible viscous heat-conducting fluid were derived and the difference between these and the equations for an incompressible fluid has been reduced to two dimensionless parameters with recpect to which the transitions to limit yield the Rayleigh and the Schwarzchild criteria.