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McNaught, J M,
Macdonald equation, for fixed-bed pressure drop,
Mach number,
Macleod-Sugden method for surface tension
Macrolayer consumption model for critical heat flux in pool boiling,
Maddox, R N
Magnetic fields, effect on properties of rheologically complex materials,
Magnetic devices, for fouling mitigation,
Magnetohydrodynamcs, inaugmentation of heat transfer in microfluidic systems,
Margarine manufacture, crystallization of edible oils and fats in, scraped surface heat exchangers for,
Marlotherm, heat transfer media,
Martensitic stainless steels,
Martin, H
Martinelli and Boelter equations for combined free and forced convection,
Martinelli and Nelson correlations:
Mass absorption coefficient,
Mass extinction coefficient,
Mass fraction, in multicomponent mixtures,
Mass scattering coefficient,
Mass transfer:
Mass transfer coefficient:
Materials of construction, for heat exchangers,
Low temperature operation, ASME VIII code guidelines for,
Matovosian, Robert,
Matrix inversion techniques, in radiative heat transfer,
Maximum drag reduction
Maximum velocities (in shell-and-tube heat exchangers)
Maxwell model, for non-Newtonian fluid,
Maxwell-Stefan equations, for multicomponent diffusion,
Maxwell's equations, for electromagnetic radiation,
Mean beam length concept, in radiative heat transfer:
Mean phase content,
Mean temperature difference:
Measurement of fouling resistance,
Mechanical design of heat exchangers:
Mechanical draft cooling towers,
Mechanical loads, specifications in EN13445,
Mechanical vapour compression cycles in refrigeration,
Mediatherm, heat transfer medium,
Melo, L F,
Melting, thermal conduction in,
Melting point:
Mercury:
Merilo correlation, for critical heat flux in horizontal tubes,
Merkel's equation, in cooling tower design,
Mertz, R,
Metais and Eckert diagrams, for regimes of convection:
Metals:
Metallurgical industry, kilns and furnaces for,
Metastable equilibrium, of vapor and liquid,
Methane:
Methanol:
Methyl acetate:
Methylacetylene:
Methyl acrylate:
Methyl amine
n-Methylaniline:
Methyl benzoate:
2-Methyl-1,3-Butadiene (Isoprene):
2-Methylbutane (isopentane):
Methylbutanoate:
2-Methyl-2-butene:
Methylcyclohexane:
Methylcyclopentane:
Methylethylketone:
Methyl formate:
Metallurgical slag, use of submerged combustion in reprocessing of,
Methyl fluorate:
2-Methylhexane:
Methylisobutylketone:
Methylmercaptan:
1-Methylnaphthalene:
2-Methylnaphthalene:
2-Methylpentane:
3-Methylpentane:
2-Methylpropane (isobutane):
2-Methylpropene:
Methyl propionate:
Methylpropylether:
Methylpropyl ketone:
Methyl salicylate:
Methyl-t-butyl ether:
Microbubbles, for drag reduction,
Microchannels (see also microfluidics)
Micro-fin tubes:
Microfluidics, enhancement of heat transfer in,
Mie scattering, in pulverized coal combustion,
Miller, C J
Miller, E R
Mineral oils, as heat transfer media, physical properties of,
Mineral wool production, submerged combustion systems for,
Minimum fluidization velocity,
Minimum heat flux in pool boiling:
Minimum tubeside velocity, in shell-and-tube heat exchangers,
Minimum velocity for fluidization,
Minimum wetting rate, for binary mixtures,
Mirror-image concept, in radiative heat transfer,
Mirrors, spectral characteristics of reflectance from,
Mishkinis, D,
Mist flow:
Mitigation of fouling,
Mixed convection occurrence in horiozntal circular pipe, Metais and Eckert diagram for,
Mixing (shell-side), in twisted tube heat exchangers,
Mixing length, in turbulent flow,
Mixtures:
Modelling, of fouling:
Models, theory of,
Modulus of elasticity:
Moffat, R S M,
Molecular gas radiation properties,
Molecular weight:
Mollier chart, for humid air,
Momentum equation:
Monitoring, on line, of fouling,
Monochloroacetic acid:
Monte Carlo methods, in radiative heat transfer,
Moody chart:
Morris, M
Mostinski correlations:
Moving bed, heat transfer to,
Muchowski, E,
Mueller, A C
Muller-Steinhagen, H
Multicomponent mixtures:
Multidimensional systems, heat conduction in,
Multiflux methods, for radiative heat transfer in nonisothermal gases,
Multipass shell-and-tube heat exchangers,
Multiphase fluid flow and pressure drop:
Multiple duties, in plate heat exchangers,
Multiple effect evaporation,
Multiple hairpin heat exchanger,
Multistage flash evaporation (MSF)
Multizone model, for furnaces,
Index
HEDH
A
B
C
D
E
F
G
H
I
J
K
L
M
McNaught, J M,
Macdonald equation, for fixed-bed pressure drop,
Mach number,
Macleod-Sugden method for surface tension
Macrolayer consumption model for critical heat flux in pool boiling,
Maddox, R N
Magnetic fields, effect on properties of rheologically complex materials,
Magnetic devices, for fouling mitigation,
Magnetohydrodynamcs, inaugmentation of heat transfer in microfluidic systems,
Margarine manufacture, crystallization of edible oils and fats in, scraped surface heat exchangers for,
Marlotherm, heat transfer media,
Martensitic stainless steels,
Martin, H
Martinelli and Boelter equations for combined free and forced convection,
Martinelli and Nelson correlations:
Mass absorption coefficient,
Mass extinction coefficient,
Mass fraction, in multicomponent mixtures,
Mass scattering coefficient,
Mass transfer:
Mass transfer coefficient:
Materials of construction, for heat exchangers,
Low temperature operation, ASME VIII code guidelines for,
Matovosian, Robert,
Matrix inversion techniques, in radiative heat transfer,
Maximum drag reduction
Maximum velocities (in shell-and-tube heat exchangers)
Maxwell model, for non-Newtonian fluid,
Maxwell-Stefan equations, for multicomponent diffusion,
Maxwell's equations, for electromagnetic radiation,
Mean beam length concept, in radiative heat transfer:
Mean phase content,
Mean temperature difference:
Measurement of fouling resistance,
Mechanical design of heat exchangers:
Mechanical draft cooling towers,
Mechanical loads, specifications in EN13445,
Mechanical vapour compression cycles in refrigeration,
Mediatherm, heat transfer medium,
Melo, L F,
Melting, thermal conduction in,
Melting point:
Mercury:
Merilo correlation, for critical heat flux in horizontal tubes,
Merkel's equation, in cooling tower design,
Mertz, R,
Metais and Eckert diagrams, for regimes of convection:
Metals:
Metallurgical industry, kilns and furnaces for,
Metastable equilibrium, of vapor and liquid,
Methane:
Methanol:
Methyl acetate:
Methylacetylene:
Methyl acrylate:
Methyl amine
n-Methylaniline:
Methyl benzoate:
2-Methyl-1,3-Butadiene (Isoprene):
2-Methylbutane (isopentane):
Methylbutanoate:
2-Methyl-2-butene:
Methylcyclohexane:
Methylcyclopentane:
Methylethylketone:
Methyl formate:
Metallurgical slag, use of submerged combustion in reprocessing of,
Methyl fluorate:
2-Methylhexane:
Methylisobutylketone:
Methylmercaptan:
1-Methylnaphthalene:
2-Methylnaphthalene:
2-Methylpentane:
3-Methylpentane:
2-Methylpropane (isobutane):
2-Methylpropene:
Methyl propionate:
Methylpropylether:
Methylpropyl ketone:
Methyl salicylate:
Methyl-t-butyl ether:
Microbubbles, for drag reduction,
Microchannels (see also microfluidics)
Micro-fin tubes:
Microfluidics, enhancement of heat transfer in,
Mie scattering, in pulverized coal combustion,
Miller, C J
Miller, E R
Mineral oils, as heat transfer media, physical properties of,
Mineral wool production, submerged combustion systems for,
Minimum fluidization velocity,
Minimum heat flux in pool boiling:
Minimum tubeside velocity, in shell-and-tube heat exchangers,
Minimum velocity for fluidization,
Minimum wetting rate, for binary mixtures,
Mirror-image concept, in radiative heat transfer,
Mirrors, spectral characteristics of reflectance from,
Mishkinis, D,
Mist flow:
Mitigation of fouling,
Mixed convection occurrence in horiozntal circular pipe, Metais and Eckert diagram for,
Mixing (shell-side), in twisted tube heat exchangers,
Mixing length, in turbulent flow,
Mixtures:
Modelling, of fouling:
Models, theory of,
Modulus of elasticity:
Moffat, R S M,
Molecular gas radiation properties,
Molecular weight:
Mollier chart, for humid air,
Momentum equation:
Monitoring, on line, of fouling,
Monochloroacetic acid:
Monte Carlo methods, in radiative heat transfer,
Moody chart:
Morris, M
Mostinski correlations:
Moving bed, heat transfer to,
Muchowski, E,
Mueller, A C
Muller-Steinhagen, H
Multicomponent mixtures:
Multidimensional systems, heat conduction in,
Multiflux methods, for radiative heat transfer in nonisothermal gases,
Multipass shell-and-tube heat exchangers,
Multiphase fluid flow and pressure drop:
Multiple duties, in plate heat exchangers,
Multiple effect evaporation,
Multiple hairpin heat exchanger,
Multistage flash evaporation (MSF)
Multizone model, for furnaces,
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
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Introduction and Fundamentals
DOI 10.1615/hedhme.a.000153
2.3.1 Introduction and fundamentals
G. F. Hewitt
A. Classification of multiphase flows
Surveys carried out on industrial heat exchanger systems have indicated that more than half of these involve multiphase flow in one form or another. Multiphase flow’s are ubiquitous in the power generation and process industries and have a very wide range of applications. Such flows are often extremely complex in nature and it should be stated at the outset that many of the relationships used for multiphase flows are of an essentially empirical nature, are of limited applicability, and reflect the poor physical understanding of many two-phase flow phenomena.
This part of the handbook deals with a variety of multiphase flows in which the phases passing through the system may be solid (denoted by the subscript s), liquid (denoted by ℓ ), or gas 1 (denoted by g ). Some of the characteristic features associated with the behavior of each of these phases in multiphase flows are as follows:
- Solids: Normally, the solid phase is in the form of lumps or particles. To all intents and purposes, the solid phase can be regarded as incompressible and to have a nondeformable interface with the fluid phase or phases with which it is flowing. The flow characteristics are strongly dependent on the size of the individual solid elements and on the motions of the associated fluids. Very small particles follow the fluid motions whereas larger particles are less responsive to turbulent eddies in the fluid. Normally, the size is nonuniform and a knowledge of the particle size distribution is of great significance in studying such flows. More often than not, the solid is denser than the associated fluid phases and, in horizontal flow systems, this can give rise to gravitational separation or stratification. Solid particles may adhere to channel walls as permanent fouling layers, and these layers can often be very significant resistances to heat transfer. Examples here would be the deposition of magnetite particles on the tubes of a boiler or deposition of crystalline solids in a cooler crystallizer.
- Liquid: In multiphase flows containing a liquid phase, the liquid can be the continuous phase, containing dispersed elements of solids (particles), gases (bubbles), or other liquids (drops). The liquid phase can also be discontinuous, for example, in the form of drops suspended in a gas phase or in another liquid phase. With the exception of some special kinds of non-Newtonian liquids, liquids differ greatly from solids in their response to deforming forces. In solids, provided the force is not too high, a small reversible deformation (elastic) occurs, allowing an equal and opposite force to be transmitted through the solid to balance the imposed force, if the solid is to remain at rest. As a fluid, a liquid does not have this property and a balancing force can only exist if the liquid is in motion. A liquid also differs from a solid insofar as its interface with other fluids (gases or other liquids) is readily deformable. The existence of interfacial tension (which may be regarded as the energy required to form a unit area of interface) tends to limit the deformation. For example, there is a tendency to form spherical droplets when the liquid is the discontinuous phase, such droplets representing the minimum interfacial energy per unit volume of the liquid.
Another important property of liquid phases relates to wetting. When a liquid phase is in contact with a solid phase (such as the channel wall) and is adjacent to another phase which is also in contact with the wall, there exists at the wall a triple interface, and the angle subtended at this interface - Gas: As a fluid, a gas lias the same properties as a liquid in its response to forces. However, it has the important additional property of being (in comparison to liquids and solids) highly compressible. Notwithstanding this property, many multiphase flows containing gases can be treated as essentially incompressible, particularly if the pressure is reasonably high and the Mach number with respect to the gas phase is low (e.g., < 0.2).
Having made some general statements about the properties of the various phases that make up multiphase flows, the common forms of multiphase flow will now be considered and examples given of their applications.
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