Showing papers on "Natural convection published in 1992"

Heat transfer in condensation and boiling

Abstract: A Heat Transfer in Condensation.- 1 Fundamentals.- 2 Film Condensation of Stagnant Vapors.- 3 Drop Condensation of Stagnant Vapors.- 4 Condensation of Flowing Vapors.- 5 Condensation of Metal Vapors.- 6 Condensation of Vapors of Miscible Liquids.- 7 Condensation of Vapors of Immiscible Liquids.- 8 Enhancement of Heat Transfer During Condensation.- B Heat Transfer in Boiling.- 9 The Different Types of Heat Transfer During Boiling.- 10 Physical Fundamentals of Vapor Bubble Formation.- 11 Heat Transfer During Boiling of Pure Substances in Free Convection.- 12 Heat Transfer in Falling Film Evaporators.- 13 Heat Transfer During Boiling of Pure Substances in Forced Flow.- 14 Heat Transfer During Boiling of Mixtures in Free Convection.- 15 Heat Transfer During Boiling of Mixtures in Forced Flow.- 16 Enhancement of Heat Transfer During Boiling.- Index of Names.

Heat transfer in rotating serpentine passages with trips normal to the flow

Abstract: Experiments were conducted to determine the effects of buoyancy and Coriolis forces on heat transfer in turbine blade internal coolant passages. The experiments were conducted with a large scale, multipass, heat transfer model with both radially inward and outward flow. Trip strips on the leading and trailing surfaces of the radial coolant passages were used to produce the rough walls. An analysis of the governing flow equations showed that four parameters influence the heat transfer in rotating passages: coolant-to-wall temperature ratio, Rossby number, Reynolds number, and radius-to-passage hydraulic diameter ratio. The first three of these four parameters were varied over ranges which are typical of advanced gas turbine engine operating conditions. Results were correlated and compared to previous results from stationary and rotating similar models with trip strips. The heat transfer coefficients on surfaces, where the heat increased with rotation and buoyancy, varied by as much as a factor of four. Maximum values of the heat transfer coefficients with high rotation were only slightly above the highest levels obtained with the smooth wall model. The heat transfer coefficients on surfaces, where the heat transfer decreased with rotation, varied by as much as a factor of three due to rotation and buoyancy. It was concluded that both Coriolis and buoyancy effects must be considered in turbine blade cooling designs with trip strips and that the effects of rotation were markedly different depending upon the flow direction.

Coupled buoyancy and Marangoni convection in acetone: experiments and comparison with numerical simulations

Abstract: This paper presents a study of the convection in acetone due jointly to the thermocapillary (Marangoni) and thermogravitational effects. The liquid (acetone) is submitted to a horizontal temperature difference. Experiments and numerical simulations both show the existence of three different states : monocellular steady states, multicellular steady states and spatio-temporal structures. The results are discussed and compared with the linear stability analysis of Smith & Davis (1983).

Chaos in models of double convection

Abstract: In certain parameter regimes, it is possible to derive third-order sets of ordinary differential equations that are asymptotically exact descriptions of weakly nonlinear double convection and that exhibit chaotic behaviour. This paper presents a unified approach to deriving such models for two-dimensional convection in a horizontal layer of Boussinesq fluid with lateral constraints. Four situations are considered: thermosolutal convection, convection in an imposed vertical or horizontal magnetic field, and convection in a fluid layer rotating uniformly about a vertical axis. Thermosolutal convection and convection in an imposed horizontal magnetic field are shown here to be governed by the same sets of model equations, which exhibit the period-doubling cascades and chaotic solutions that are associated with the Shil'nikov bifurcation (Proctor & Weiss 1990). This establishes, for the first time, the existence of chaotic solutions of the equations governing two-dimensional magneto-convection. Moreover, in the limit of tall thin rolls, convection in an imposed vertical magnetic field and convection in a rotating fluid layer are both modelled by a new third-order set of ordinary differential equations, which is shown here to have chaotic solutions that are created in a homoclinic explosion, in the same manner as the chaotic solutions of the Lorenz equations. Unlike the Lorenz equations, however, this model provides an accurate description of convection in the parameter regime where the chaotic solutions appear.

Linear-Eddy Modeling of Turbulent Transport. Part 4. Structure of Diffusion Flames

Abstract: A simulation model of the axial structure of turbulent jet diffusion flames is formulated for the purpose of interpreting flame-structure measurements. The model, based on the linear-eddy approach, incorporates spatial and temporal variation of the air entrainment rate, reflecting buoyancy effects, and an implementation of turbulent mixing using a novel stochastic representation of convective stirring in conjunction with Fick's law governing molecular diffusion. Simulation results are compared to axial profiles of mixing-cup density measured in propane flames. The comparisons suggest that the measured Froude-number dependences reflect the combined effect of finite-rate mixing and the transition from forced to natural convection. Predictions for hydrogen flames are presented in order to assess the generality of inferences based on the propane results.

Experimental Heat Transfer Rates of Natural Convection of Molten Gallium Suppressed Under an External Magnetic Field in Either the X, Y, or Z Direction

Abstract: The heat transfer rates of natural convection of molten gallium were measured under various strengths of heating rates and three coordinate directional magnetic fields. Molten gallium (Pr = 0.024) was filled in a cubic enclosure of 30 mm {times} 30 mm {times} 30 mm whose one vertical wall was uniformly heated and an opposing wall was isothermally cooled, with otherwise insulated walls. An external magnetic field was impressed either perpendicular and horizontal to the heated wall (x direction) or in parallel and horizontal to the heated wall (y direction) of the enclosure or in a vertical direction (z direction). For the modified Grashof number, based on the heat flux, less than 4.24 {times} 10{sup 6} and the Hartmann number less than 461, the average Nusselt numbers were measured. These results proved that our previous three-dimensional numerical analyses for an isothermal hot wall boundary were in good qualitative agreement. A much higher suppression effect is given in the x- and z-directional magnetic fields than that in the y-directional one.

Models of convection-driven tectonic plates: a comparison of methods and results

Abstract: Recent numerical studies of convection in the earth's mantle have included various features of plate tectonics. This paper describes three methods of modeling plates: through material properties, through force balance, and through a thin power-law sheet approximation. The results obtained are compared using each method on a series of simple calculations. From these results, scaling relations between the different parameterizations are developed. While each method produces different degrees of deformation within the surface plate, the surface heat flux and average plate velocity agree to within a few percent. The main results are not dependent upon the plate modeling method and herefore are representative of the physical system modeled.

Wave properties of natural-convection boundary layers

Abstract: The thermal boundary layer on the wall of a side-heated cavity at early time is known to exhibit a complex travelling wave during growth to steady state and a similar feature is observed on isolated heated semi-infinite plates. Direct numerical solutions of the Navier–Stokes equations together with a linearized stability analysis are used to study the character of the flow at early time in detail. It is demonstrated that the cavity flow is essentially identical to the plate flow, and that for early time the flow is one-dimensional. Using the stability results it has been possible to accurately describe the form of the observed instability, as well as to reconcile a previously unexplained discrepancy in the speed of development of the flow.

Packaging structure of small-sized computer

Abstract: In a small-sized computer of a natural air-cooling type, a high-temperature radiator promotes natural convection so as to increase a quantity of heat radiation and to raise the allowable limit of heat generation of LSI chips, thereby improving the processing speed of the computer. For this purpose, a casing and fins are utilized as heat radiators at relatively low temperatures of about 40° C. which are safe even if they are touched by an operator's hands. On the other hand, the high-temperature radiator set at about 50° to 60° C. is provided inside of the casing, thus preventing the operator's hands from touching it directly. Heat generated by the LSI chips and so forth is transmitted to the high-temperature radiator through heat conduction or the like, and heat exchange is performed between the high-temperature radiator increased in temperature and the air introduced into the casing, in order to promote natural convection inside of the casing.

Three-dimensional convection of an infinite-Prandtl-number compressible fluid in a basally heated spherical shell

Abstract: A numerical investigation is made of the effects of compressibility on threedimensional thermal convection in a basally heated, highly viscous fluid spherical shell with an inner to outer radius ratio of approximately 0.55, characteristic of the Earth’s whole mantle. Compressibility is implemented with the anelastic approximation and a hydrostatic adiabatic reference state whose bulk modulus is a linear function of pressure. The compressibilities studied range from Boussinesq cases to compressibilities typical of the Earth’s whole mantle. Compressibility has little effect on the spatial structure of steady convection when the superadiabatic temperature drop across the shell AT,, is comparable to a characteristic adiabatic temperature. When AT,& is approximately an order of magnitude smaller than the adiabatic temperature, compressibility is significant. For all the non-Boussinesq cases, the regular polyhedral convective patterns that exist at large AZ, break down at small AT, into highly irregular patterns ; as AZ, decreases convection becomes penetrative in the upper portion of the shell and is strongly time dependent at Rayleigh numbers only ten times the critical Rayleigh number, (Ra),,. Viscous heating in the compressible solutions is concentrated around the upwelling plumes and is greatest near the top and bottom of the shell. Solutions with regular patterns (and large AEJ remain steady up to fairly high Rayleigh numbers (100(Ra),,), while solutions with irregular convective patterns are time dependent at similar Rayleigh numbers. Compressibility affects the pattern evolution of the irregular solutions, producing fewer upwelling plumes with increasing compressibility.

Buoyancy- and thermocapillary-driven flows in differentially heated cavities for low-Prandtl-number fluids

Abstract: The influence of thermocapillary forces on buoyancy-driven convection is numerically simulated for shallow open cavities with differentially heated endwalls and filled with low-Prandtl-number fluid. Calculations are carried out by solving two-dimensional Navier-Stokes equations coupled to the energy equation, for three aspects ratios A = (length/height) = 4, 12.5 and 25, and several values of the Grashof number (up to 6 × 104) and Reynolds number (|Re| ≤ 1.67 × 104). Thermocapillarity can have a quite significant effect on the stability of a primarily buoyancy-driven flow. The result of the combination of the two basic mechanisms (thermo-capillarity) and buoyancy) depends on whether their effects are additive (positive Re) or opposing (negative Re); counter-acting mechanisms yield more complex flow patterns. The critical Grashof number Grc for the onset of the unsteady regime is found to decrease substantially within a small range of negative Re, and to increase for positive Re (and also for large negative Re). For Gr = 4 × 104, A = 4 and small negative Reynolds numbers, −2.4 × 103 ≤ Re < 0, mono-periodic and bi- or quasi-periodic regimes are shown to exist successively, followed by a reverse transition. The development of the instabilities from an initial steady-state regime has been investigated by varying Re for Gr = 1.5 × 104 (below Grc at Re = 0); the onset of buoyant instabilities is enhanced in a narrow range of Re only (-1200 < Re < -200). It is also noteworthy that for small enough Grashof numbers (e.g. Gr = 3 × 103), a steady-state solution prevails over the whole range of Reynolds numbers investigated. This means that a critical Grashof number exists below which the effect of the thermocapillary forces is no longer destabilizing.

Convection velocity measurements in a cylinder wake

Abstract: The convection velocity of vortices in the wake of a circular cylinder has been obtained by two different approaches. The first, implemented in a wind tunnel using an array of X-wires, consists in determining the velocity at the location of maximum spanwise vorticity. Four variants of the second method, which estimates the transit time of vortices tagged by heat or dye, were used in wind and water tunnels over a relatively large Reynolds number range. Results from the two methods are in good agreement with each other. Along the most probable vortex trajectory, there is only a small streamwise increase in the convection velocity for laminar conditions and a more substantial variation when the wake is turbulent. The convection velocity is generally greater than the local mean velocity and does not depend significantly on the Reynolds number.

Method and apparatus for immersion cooling or an electronic board

Abstract: A liquid heat sink is provided that employs natural convection of a liquid coolant (18') to cool a printed circuit board (14) on which are mounted a plurality of heat-generating components (12). In particular, the spacing d between the heat-generating components and a cold plate (20) used to cool the liquid must be such as to provide a Rayleigh number of at least about 1700 in the Rayleigh equation: ##EQU1## In the above equation, g is the acceleration of gravity, β is the volumetric coefficient of expansion of the liquid coolant, T1 is the temperature of the cold plate, T2 is the temperature of the component to be cooled, ν is the kinematic viscosity of the liquid coolant, and α is the thermal diffusivity of the liquid coolant. The novel heat sink of the present invention allows complete immersion of the component in the liquid to provide maximum heat transfer, while at the same time providing a mounting/packaging scheme that allows full utilization of the desired heat transfer properties.

Natural convection heat transfer in rectangular cavities partially heated from below

Abstract: Natural convection in an enclosed cavity with localized heating from below has been investigated by a finite difference procedure. The upper surface is cooled at a constant temperature and a portion of the bottom surface is isothermally heated while the rest of the bottom surface and the vertical walls are adiabatic. Parameters of the problem are the cavity aspect ratio (A = 1 and 2), dimensionless length (B = 0.06 to 1.0) and position of the heat source with respect to the vertical symmetry line of the cavity (e = -0.6 to 0.7), the Prandtl number and the Rayleigh number (Ra = 0 to 5 x 10 6). The effects of the thermophysical and geometrical parameters on the fluid flow and temperature fields have been studied. The existence of multiple steady-state solutions and the oscillatory behavior for a given set of the governing parameters are demonstrated. Nomenclature A = aspect ratio, L'lH' B = dimensionless length of heat source, t'/L' g = acceleration due to gravity, m/s2 H' = cavity height, m h = local heat transfer coefficient, W/m2-K h = average heat transfer coefficient, W/m2-K k = thermal conductivity of fluid, W/m-K L' = cavity width, m €' = length of heat source, m m, n = wave numbers of initial disturbance, Eq. (15) Nu = Nusselt number based on cavity height, hH'/K Pr = Prandtl number,'via p'_ = pressure, Pa

The Effect of Plate Spacing on Free Convection Between Heated Parallel Plates

Abstract: In the past, considerable attention has been given to free convection between heated vertical parallel plates. This problem is considerable interest to engineers because of its application to electronic equipment cooling and solar energy. Some attempts have been made to optimize the spacing between parallel plates in the past. Bodoia and Osterle analytically derived a criterion for an optimum plate spacing for which the heat dissipation is maximum. The objective of this paper is to predict the optimum plate spacing for single channels by using the governing equations for a continuous system model. No heat transfer coefficient known a priori will be used in these calculations, but will be calculated as part of the solution.

An experimental study of oscillatory thermocapillary convection in cylindrical containers

Abstract: An experimental study of oscillatory thermocapillary convection in small cylindrical containers with a heating wire placed along the center axis is performed by investigating the flow structures and temperature distributions under various conditions. To supplement the flow visualization the surface is scanned using an infrared imager. Here 2 cS viscosity (Pr=27) silicone oil is used as the test fluid. It is observed that beyond a certain temperature difference between the container wall and the heating wire, a distinctive unsteady flow pattern appears. This unsteady phenomenon is identified as oscillatory thermocapillary. After the onset of oscillations the flow structure becomes nonaxisymmetric and wave motion is observed at the free surface. It is shown that the critical temperature difference is independent of container dimensions if the aspect ratio is fixed.

Convection in superposed fluid and porous layers

Abstract: Thermal convection due to heating from below in a porous layer underlying a fluid layer has been analyzed using the Navier-Stokes equations for the fluid layers and the extended Darcy equation (including Brinkman and Forchheimer terms) for the porous layer. The flow is assumed to be two-dimensional and periodic in the horizontal direction. The numerical scheme used is a combined Galerkin and finite-difference method, and appropriate boundary conditions are applied at the interface. Results have been obtained for depth ratios of 0, 0.1, 0.2, 0.5, and 1.0, where this ratio is defined as the ratio of the thickness of the fluid layer to that of the porous layer. For the depth ratio of 0.1, the convection is dominated by the porous layer, similar to the situation at onset, even though the Rayleigh number for the fluid layer is well into the supercritical regime.

Natural convection in a differentially heated square cavity with internal heat generation

Abstract: A high-resolution, finite-difference numerical study is reported on natural convection in a square cavity. The vertical sidewatts of the cavity are differentially heated, and a uniform internal heat generation is also present. Two principal parameters are considered, the internal Rayleigh number RaI, which represents the strength of the internal heat generation, and the external Rayleigh number Rag, which denotes the effect due to the differential heating of the side walls. The internal Rayleigh number varies in the range 1010 RaI ≤ 107, while the external Rayleigh number is set at RaE = 5 x 107 for most computations. As the relative strength of the internal heat generation increases, the flows near the tap portion of the heated sidewall are directed downward. When the effect of the internal heat generation is dominant, the thermal energy leaves the system for the surroundings over the top portion of the heated wall. Only in the bottom pari of the heated wall is heat transfer directed into the system. The...

Numerical models of mantle convection

Abstract: An overview of numerical methods describing the structure and dynamics of the mantle is presented with attention given to novel 3D modeling techniques. The paper reviews 3D spherical and Cartesian models for constant viscosity emphasizing the assumptions regarding style of convection, time dependence, and implications for the mantle. Similarly treated are 3D Cartesian models with temperature-dependent viscosities, and briefly examined are models that are based on compressibility, nonlinear viscosity, or plates. Extensive illustrations are presented detailing: (1) temperature variations from models of 3D thermal convection in spherical shells; (2) thermal anomalies in equatorial cross sections; and (3) temperature variations in a spherical shell heated from within. The discussion relates the numerical results of the models with real mantle-convection events, and the simulations are shown to yield increasingly realistic representations of material behavior.

The effects of multiple phase transitions on Venusian mantle convection

Abstract: The effects of multiple phase-transitions on the dynamics of the Venusian mantle have been investigated with a two-dimensional finite-element method. A depth-dependent thermal expansivity has been employed in a purely basal heating configuration with an aspect-ratio of four. The addition of the olivine → spinel transition promotes layered convection more so than models with a single spinel → perovskite phase-change. The shifts in the phase-transition depths and the presence of a conductive lid increase the tendency of the Venusian mantle circulation to flow through the transition zone. The potentially lower Rayleigh number in Venus from lack of volatiles will also enhance whole mantle convection. The style of convection in Venus may have changed from layered convection in the past to whole-mantle convection today. This transition might have been responsible for the major resurfacing event on Venus.