A B C D E F G H I J K L M
M J BOX COMPLEX METHOD MACH LINES MACH NUMBER MACH NUMBER, IN NOZZLES MACH WAVES MACH, ERNST 1838-1916 MACH-ZEHNDER INTERFEROMETRY MACHINE LANGUAGE MACLAURIN SERIES MACRO-POROUS AND MACRO-RETICULAR RESINS MAGNESIUM MAGNETIC FIELDS MAGNETIC FUSION REACTORS Magnetic Prandtl number MAGNETIC REYNOLDS NUMBER Magnetic Reynolds number Magnetic Reynolds number MAGNETIC SEALS MAGNETICALLY DRIVEN ARC MAGNETO ACOUSTIC WAVES MAGNETOHYDRODYNAMIC ELECTRICAL POWER GENERATORS MAGNETOHYDRODYNAMIC FLOWS OF A SECOND GRADE FLUID MAGNETOHYDRODYNAMIC METHODS Magnetohydrodynamics MAGNETOHYDRODYNAMICS AND RADIATIVE EFFECTS ON FREE CONVECTION FLOW OF FLUID MAGNETOHYDRODYNAMICS IN LIQUID METALS MAGNOX MAGNOX POWER STATION Magnus Force MAGNUSSEN AND HJERTAGER MODEL MAINFRAME COMPUTERS MALDISTRIBUTION OF FLOW MALVERN, SCATTERING, METHOD FOR PARTICLE SIZING MANOMETERS MANOMETRY MARANGONI CONVECTION Marangoni effect MARGULES EQUATION MARINE FUEL OILS MARINE GAS TURBINES MARIOTTE LAW MASS ACTION LAW MASS FLOW METERS MASS MEDIAN DIAMETER, MMD MASS SPECTROSCOPY MASS TRANSFER MASS TRANSFER COEFFICIENTS MASS TRANSFER UNDER REDUCED GRAVITY MASS TRANSFER, ELECTROCHEMICAL, PROBE MASSACHUSETTS INSTITUTE OF TECHNOLOGY, MIT Mathematical formulation MATHEMATICAL METHODS MATHEMATICAL MODELING Matrix operator method MATTE MAXI-COMPUTERS MAXIMUM HEAT FLUX MAXIMUM HYGROSCOPIC MOISTURE CONTENT MAXIMUM LIQUID TEMPERATURE MAXWELL EQUATION MAXWELL EQUATION FOR ELECTRICAL CONDUCTIVITY MAXWELL FLUIDS MAXWELL MODEL FOR ACCOMMODATION COEFFICIENT MAXWELL RELATIONS MAXWELL'S EQUATIONS MAXWELL-BOLTZMANN DISTRIBUTION MAXWELL-STEFAN EQUATIONS McCABE - THIELE METHOD McCABE-THlELE METHOD McREYNOLDS CONSTANT Mean absorption coefficients (Planck, Rosseland) Mean Free Path MEAN PHASE CONTENT MEAN TEMPERATURE DIFFERENCE MEAN TEMPERATURE DRIVING FORCE MEASUREMENT TECHNIQUES MEASURING ELECTRIC FIELDS WITH LASER-INDUCED FLUORESCENCE-DIP STARK SPECTROSCOPY MECHANICAL DESIGN OF HEAT EXCHANGERS MECHANICAL HEART VALVE MEISSNER EFFECT MELT FILMS MELTING MELTING HEAT MELTING OF ICE MEMBRANE POLARIZATION MEMBRANE PROCESSES MEMBRANE TYPE FILTERS MEMBRANES, ION EXCHANGE MENDELEEV-CLAPEYRON EQUATION MERCURY MERKEL'S EQUATION MESOSCOPIC ENERGY SYSTEMS MESOSPHERE METAL POWDERS METAL SURFACES Metal-coated polymer fibers in infrared and microwave METALLURGICAL PLASMA REACTORS METALS METHANE METHANOL METHOD OF CHARACTERISTICS METHODS OF SUPERPOSED GRIDS AND OF VIRTUAL Z-MESHES METHYLAMINE METHYLCHLORIDE METRE METZNER-OTTO CONSTANTS FOR IMPELLERS MICELLAR CATALYSIS MICELLES MICHAELIS-MENTEN RELATIONSHIP MICHELSON INTERFEROMETRY MICROBUBBLE MICROCHANNEL FLOW MICROCHANNELS MICROCIRCULATORY CELL OF THE PLANT LEAF MICROCOMPUTERS MICRODAMAGE MICROELECTRONIC EQUIPMENT MICROFILTRATION MICROFIN TUBES MICROGRAVITY CONDITIONS MICROLEVEL FLOWS MICROORGANISM MICROPOLAR FLUID MICROSCALE PHENOMENA Microscale/nanoscale radiative heat transfer MICROSTRUCTURAL EVOLUTION MICROSTRUCTURE OF HETEROGENEOUS MIXTURE MICROSYSTEMS MICROWAVE DRYING MICROWAVE HEATING MICROWAVE PLASMA TREATMENT MICROWAVES MIE SCATTERING MIE SERIES Mie solution for spherical particles MIE THEORY MIKIC, ROHSENOW AND GRIFFITH EQUATION, FOR BUBBLE GROWTH MINIATURE HEAT PIPES MINIATURE OSCILLATING HEAT PIPES MINICOMPUTERS MINIMUM FILM BOILING TEMPERATURE MINIMUM FLUIDIZATION VELOCITY MIROPOLSKII FORMULA, FOR POST DRYOUT HEAT TRANSFER MIST COOLING MIST ELIMINATORS MISTS MIT MIXED (COMBINED) CONVECTION MIXED SPECTRAL-FINITE DIFFERENCE TECHNIQUE MIXER SETTLERS MIXER-HEAT EXCHANGERS MIXERS MIXERS, STATIC MIXING MIXING GAS-LIQUID MIXING IN ROD BUNDLES MIXING LENGTH MIXING LENGTH HYPOTHESIS MIXING LENGTH MODELS MIXING OF PARTICLES IN FLUIDIZED BEDS MIXING REYNOLDS NUMBER MIXTURE CONSERVATION EQUATIONS MIXTURES MODEL BANDWIDTH MODELING SUBSURFACE FLOW MODELING TECHNIQUES MODERATING RATIO MODERATORS Modified discrete ordinates and finite volume methods Modified Mach number (velocity coefficient) MODULUS OF THE SOLID MOIRÉ FRINGES MOISTURE ISOTHERM MOISTURE MEASUREMENT MOISTURE METER MOLALITY OF A SOLUTION MOLAR MASS MOLD CONSTANT MOLE MOLECULAR DIFFUSION MOLECULAR DYNAMICS MOLECULAR FLOW OF GAS MOLECULAR INTERACTIONS MOLECULAR MASS MOLECULAR PARTITION FUNCTION MOLECULAR PHYSICS MOLECULAR SCALE VISUALIZATION OF MICRO-FLOWS MOLECULAR SCATTERING MOLECULAR SIEVES Molecular spectra in the infrared MOLECULAR SPECTROSCOPY MOLECULAR SPEEDS MOLECULAR WEIGHT MOLECULE MOLLIER DIAGRAM MOLTEN DROPLET MOLYBDENUM Momentum thickness MONOCHROMATIC LIGHT MONOD MODEL OF CELL GROWTH MONODISPERSE AEROSOLS Monte Carlo method Monte Carlo method Monte Carlo method Monte Carlo method for exchange among diffuse-gray surfaces MONTE CARLO MODELING, OF TURBULENCE Monte Carlo simulation of radiative transfer MONTREAL PROTOCOL MOODY CHART MOODY, OR WEISBACH, FRICTION FACTOR MOSSBAUER SPECTROSCOPY MOTOR GASOLINE MOULD MOUNTAIN DRAG MOVEMENT OF TWO CONSECUTIVE TAYLOR BUBBLES MOVING BOUNDARY PROBLEMS MOVING FRONT OF AN INSTANTANEOUS IRREVERSIBLE REACTION MTBE MUFFLE FURNACE MULTI FLUID MODELS MULTICOMPONENT MIXTURES, BOILING IN MULTICOMPONENT MIXTURES, DIFFUSION IN MULTICOMPONENT SYSTEMS THERMODYNAMICS MULTICOMPONENT VAPOR CONDENSATION MULTIGRID SOLUTION OF MODIFIED REYNOLDS EQUATION MULTILINGUAL PROGRAMMING MULTIMODE FIBRE MULTIPHASE DENSITY Multiphase Flow Multiphase medium MULTIPLE BEAMLETS MULTISCALE ANALYSIS MULTISCALE DIFFUSION MULTISCALE ELECTROMAGNETIC SIMULATION MULTISCALE MODELING MULTISCALE SIMULATION MULTISCALE TRANSPORT MULTISTAGE TURBINES MULTISTART HELICALLY COILED TUBE BOILER MURPHREE EFFICIENCY MUTUAL DIFFUSION COEFFICIENT
N O P Q R S T U V W X Y Z

MIXED (COMBINED) CONVECTION

Interlinking between Articles
Visual Navigation

Mixed (combined) convection is a combination of forced and free convections which is the general case of convection when a flow is determined simultaneously by both an outer forcing system (i.e., outer energy supply to the fluid-streamlined body system) and inner volumetric (mass) forces, viz., by the nonuniform density distribution of a fluid medium in a gravity field. The most vivid manifestation of mixed convection is the motion of the temperature stratified mass of air and water areas of the Earth that the traditionally studied in geophysics. However, mixed convection is found in the systems of much smaller scales, i.e., in many engineering devices. We shall illustrate this on the basis of some examples referring to channel flows, the most typical and common cases. On heating or cooling of channel walls, and at the small velocities of a fluid flow that are characteristic of a laminar flow, mixed convection is almost always realized. Pure forced laminar convection may be obtained only in capillaries. Studies of turbulent channel flows with substantial gravity field effects have actively developed since the 1960s after their becoming important in engineering practice by virtue of the growth of heat loads and channel dimensions in modern technological applications (thermal and nuclear power engineering, pipeline transport).

In a mathematical description of mixed convection in the equations of motion (the Navier-Stokes equations), both the term characterizing the pressure head loss dp/dx and the term characterizing mass forces ρg are retained. The simplest case allowing an analytical solution of the problem refers to the steady-state laminar flow at a distance from the tube inlet with a constant heat flux on a wall (qw = const). Figure 1 shows the calculated velocity and temperature distributions both in an ascending flow, i.e., when the directions of forced and free near-wall convections coincide (case "a"), and in a descending flow in heated tubes, i.e., when the directions of forced and free near-wall convections are opposite (case "b"). The curves refer to different values of the Rayleigh number RaA = gβD4 (dT/dx)/ν2 = 4 Grq/Re = (4/Re)(gβqwD4/λν2). In the case of an ascending fluid flow, velocity profiles peak near the wall giving an M-like shape which becomes sharper with the growth of the effect of thermogravitation convection until instability of the laminar flow occurs before the calculated values of the axis velocity have vanished (Figure 1a, RaA = 625). In a descending flow the stability is disturbed rather quickly, as indicated by the velocity profiles (Figure 1b) which even at relatively small growth of the bouyancy effect acquire zero values of the velocity gradient on the wall. A remarkable property of temperature distributions should be noted for all the cases considered (Figure 1a and b); even with strong deformation of velocity distribution, the temperature profiles only differ slightly from the profiles for pure forced convection. The shown specific features of velocity and temperature shown in Fig. 1 are reflected on the corresponding variation of the relative heat transfer value presented in the left portion of Fig. 2 where Nu0 means the Nusselt number for a "purely" forced flow.

Velocity and temperature profiles in mixed convection.

Figure 1. Velocity and temperature profiles in mixed convection.

The variation of heat transfer with Grq in turbulent and laminar mixed convection is considerably different (Figure 2). In the case of a descending flow (b) (Nu/Nu0), falls with Grq in laminar mixed convection due to the retardation near a wall, but with turbulent mixed convection (Nu/Nu0) grows as the heat load increases due to additional flow turbulization. For an ascending turbulent flow the behavior of the curve (Nu/Nu0) — Grq is nonmonotonic. First, heat transfer deteriorates with increasing Grq. This is caused by the attenuation of turbulent momentum and heat transfer as a result of the effect of buoyancy forces on the shear stress profile and hence as the generation of turbulence. With further increase in the Grashof number, heat transfer begins to grow, thus reflecting an intensive development of the free convection effect on the flow as a whole as also takes place in the laminar mode (case "a"). In turbulent flow, the velocity profiles also acquire a typical M-like shape, but the quantitative characteristics, as well as the mechanism of momentum and heat transfer, are quite different for turbulent and laminar mixed convection. In the region of a strong effect of free convection the mode of thermal turbulent convection with the dependence of the Nusselt number on the Grashof number, characteristic to turbulent free convection Nu = A(Pr)Gr1/4 and excluding the effect of a geometry parameter on heat transfer, is established. Line B in Figure 2 is constructed by the relation for the Nusselt number with developed free convection on a vertical plate. Under normal conditions (in particular, for air at atmospheric pressure and temperatures close to room ones, the data of which are given in Figure 2) the effect of the gravity field on a forced turbulent flow manifests itself only at relatively small Reynolds numbers, of the order of 104 for tubes, and with channels of rather large dimensions equal with characteristic equivalent diameters of the order of 1 m and more. However, for media with strong density variation, e.g., under near-critical conditions where density varies from the values typical of gases to the values characteristic for a liquid, mixed convection is realized in tubes of small diameters (of the order of several millimeters) and at large values of the Reynolds number (see Figure 3 for a water flow p/pc = 1.1 in a diameter 3 mm tube at Re = (2−3) × 104).

Variation of Nusselt number Nu (= αD/λ, where α = least transfer coefficient, D = tube diameter and λ = thermal conductivity) with Grq (= gβ D4/λw).

Figure 2. Variation of Nusselt number Nu (= αD/λ, where α = least transfer coefficient, D = tube diameter and λ = thermal conductivity) with Grq (= gβ Variation of Nusselt number Nu (= αD/λ, where α = least transfer coefficient, D = tube diameter and λ = thermal conductivity) with Grq (= gβ D4/λw). D4/λw).

Temperature profiles as a function of fluid enthalphy (hGC) for ascending (a) and descending (b) flow in a 3 mm tube at (p/pc) = 1.1. (Tw = wall temperature, Gct = mean fluid temperature).

Figure 3. Temperature profiles as a function of fluid enthalphy (hGC) for ascending (a) and descending (b) flow in a 3 mm tube at (p/pc) = 1.1. (Tw = wall temperature, Gct = mean fluid temperature).

In a turbulent flow in the presence of heat transfer, the gravity field leads not only to the manifestation of large-scale free convection covering the entire flow as in the laminar mode, but also to the manifestation of local effects on turbulence that radically change the character of heat transfer (see Figure 2). One may judge the character of the manifestation of the effect of the buoyancy forces on turbulence from the velocity distributions given in Figure 4. These velocity profiles are plotted in the near-wall region in terms of the universal parameters u+ = u/u* and γ = u*ρy/η, where u* is the friction velocity ( ) and y+ the distance from the wall. The data are for a horizontal channel. The channel can either be heated from above giving stable stratification or from below giving unstable stratification. Points 1 and 2 represent the profile near the bottom wall for a case with stable density distribution (stable stratification) and from points 4 and 5 show the profile with unstable density distribution (unstable stratification); those results may be compared with the universal velocity distribution in an equilibrium wall flow (points 3). Points 2 and 4 indicate to a small effect of density stratification on turbulence. With strong stable stratification, turbulent transport of fluid particles is retarded and a turbulent flow, which occurred under isothermal conditions, laminarizes at the same Reynolds number and the velocity distribution in this case (points 1) approaches the distribution typical of a laminar flow (a dashed line). With a strong unstable stratification (points 5) the buoyancy forces additionally turbulize the flow and in the limited case the wall logarithmic law for a velocity is transformed to the "−1/3"-law, viz.: u ~ y−3 (line 6) found when studying the near-Earth atmospheric turbulence. The data indicate that in physical studies and mathematical simulation of mixed convection, one should simultaneously take into account both the global effect of gravitation on the flow as a whole and its direct effect on turbulence.

Dimensionless velocity profiles in mixed convection.

Figure 4. Dimensionless velocity profiles in mixed convection.

REFERENCES

Petukhov, B. S. and Poliakov, A. F. (1988) Heat Transfer in Turbulent Mixed Convection, Hemisphere Publishing Corp., N.Y.

References

  1. Petukhov, B. S. and Poliakov, A. F. (1988) Heat Transfer in Turbulent Mixed Convection, Hemisphere Publishing Corp., N.Y.

Following from:

CONVECTIVE HEAT TRANSFER

This article belongs to the following areas:

M in A-Z Index
Number of views: 7194 Article added: 2 February 2011 Article last modified: 14 February 2011 © Copyright 2010-2014 Back to top