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E-type shells in shell-and-tube heat exchangers:
Ebert and Panchal equation, for crude oil fouling,
Eckert number,
Eddy viscosity:
Eddy diffusivity, of heat,
Edge, D,
Edwards, D K
EEC code for thermal design of heat exchangers,
Effective diffusivity,
Effective thermal conductivity of fixed beds,
Effective tube length in shell-and-tube heat exchangers,
Effectiveness of a heat exchanger:
Efficiency of fins,
Eicosane:
Eicosene:
Ejectors, in flash distillation plant,
EJMA (Expansion Joint Manufacturers Association), standards for expansion bellows
Elastic properties of solids:
El-Dessouky, H,
Electrical enhancement processes, in heat transfer augmentation,
Electric fields, effect on properties of rheologically complex materials,
Electric fields, in augmentation of condensation,
Electrical process heater, specification of,
Electrokinetics, for heat transfer augmentation in microfluidic systems,
Electromagnetic theory of radiation,
Electrostatic fields in augmentation of heat transfer,
Elements:
Elhadidy relation between heat and momentum transfer,
Embedding methods for radiative heat transfer in nonisothermal gases,
Embittlement, of stainless steels,
Emission of thermal radiation, in solids,
Emissivity:
Emitting media, interaction phenomena with,
Emulsions, viscosity of,
EN13445 (European Pressure Vessel Codes), design of heat exchangers to,
Enclosures:
Energy equation:
in boundary layers,
in compressible duct flow,
differential form in single-phase flow,
in gas-liquid flows,
in heat exchangers,
integral form in single-phase flow,
in multiphase flows: homogeneous,
in non-Newtonian flow,
in turbulent flow,
Energy recovery, maximum, in heat exchanger network design,
Enhanced surfaces, fouling in,
Enhancement devices:
Enlargements in pipes:
Enthalpy:
Entrainment in annular gas-liquid flow
Entrance effects in heat and mass transfer:
Entrance lengths, hydrodynamic in pipe flow,
Entrance losses for tube inlet in shell-and-tube heat exchanger,
Entry losses in plate heat exchangers,
Entropy generation and minimisation
Environmental impact, of fouling,
Eotvos number:
Epstein, N,
Epstein matrix, for fouling,
Equalizing rings, for expansion bellows,
Equilibrium interphase:
Equilibrium vapor nucleus,
Equivalent sand roughness,
Ergun equation, for pressure drop in fixed beds
ESDU correlations:
Esters:
Ethane:
Ethanol:
Ethers:
Ethyl acetate:
Ethylacetylene:
Ethylacrylate:
Ethylamine:
Ethylbenzene:
Ethyl benzoate:
Ethyl butanoate:
Ethylcyclohexane:
Ethylcyclopentane:
Ethyl formate:
Ethylene:
Ethylene diamine:
Ethylene glycol:
Ethylene oxide:
Ethylmercaptan:
1-Ethylnaphthalene:
2-Ethylnaphthalene:
Ethyl proprionate:
Ethyl propylether:
Ettouney, H,
Euler number:
Eutectic mixtures, condensation of forming immiscible liquids,
Evaporation:
Evaporative crystallisers,
Evaporators:
Exergy, definition of,
Exergy analysis,
Exit losses for tubes in shell-and-tube exchanger,
Expansion bellows, for shell-and-tube heat exchangers:
EJMA (Expansion Joint Manufacturers Association), standards for
Expansion joints, mechanical design of:
Expansion of tubes into tube sheets:
Expansion turbine, lost work in,
Explosively clad plate,
Explosive welding of tubes into tube sheets
Explosive expansion joints,
Extended surfaces (see also Fins)
Externally induced convection, in kettle reboilers,
Extinction coefficient,
Extinction efficiency,
Eyring fluid (non-Newtonian),
Index
HEDH
A
B
C
D
E
E-type shells in shell-and-tube heat exchangers:
Ebert and Panchal equation, for crude oil fouling,
Eckert number,
Eddy viscosity:
Eddy diffusivity, of heat,
Edge, D,
Edwards, D K
EEC code for thermal design of heat exchangers,
Effective diffusivity,
Effective thermal conductivity of fixed beds,
Effective tube length in shell-and-tube heat exchangers,
Effectiveness of a heat exchanger:
Efficiency of fins,
Eicosane:
Eicosene:
Ejectors, in flash distillation plant,
EJMA (Expansion Joint Manufacturers Association), standards for expansion bellows
Elastic properties of solids:
El-Dessouky, H,
Electrical enhancement processes, in heat transfer augmentation,
Electric fields, effect on properties of rheologically complex materials,
Electric fields, in augmentation of condensation,
Electrical process heater, specification of,
Electrokinetics, for heat transfer augmentation in microfluidic systems,
Electromagnetic theory of radiation,
Electrostatic fields in augmentation of heat transfer,
Elements:
Elhadidy relation between heat and momentum transfer,
Embedding methods for radiative heat transfer in nonisothermal gases,
Embittlement, of stainless steels,
Emission of thermal radiation, in solids,
Emissivity:
Emitting media, interaction phenomena with,
Emulsions, viscosity of,
EN13445 (European Pressure Vessel Codes), design of heat exchangers to,
Enclosures:
Energy equation:
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
in boundary layers,
in compressible duct flow,
differential form in single-phase flow,
in gas-liquid flows,
in heat exchangers,
integral form in single-phase flow,
in multiphase flows: homogeneous,
in non-Newtonian flow,
in turbulent flow,
Energy recovery, maximum, in heat exchanger network design,
Enhanced surfaces, fouling in,
Enhancement devices:
Enlargements in pipes:
Enthalpy:
Entrainment in annular gas-liquid flow
Entrance effects in heat and mass transfer:
Entrance lengths, hydrodynamic in pipe flow,
Entrance losses for tube inlet in shell-and-tube heat exchanger,
Entry losses in plate heat exchangers,
Entropy generation and minimisation
Environmental impact, of fouling,
Eotvos number:
Epstein, N,
Epstein matrix, for fouling,
Equalizing rings, for expansion bellows,
Equilibrium interphase:
Equilibrium vapor nucleus,
Equivalent sand roughness,
Ergun equation, for pressure drop in fixed beds
ESDU correlations:
Esters:
Ethane:
Ethanol:
Ethers:
Ethyl acetate:
Ethylacetylene:
Ethylacrylate:
Ethylamine:
Ethylbenzene:
Ethyl benzoate:
Ethyl butanoate:
Ethylcyclohexane:
Ethylcyclopentane:
Ethyl formate:
Ethylene:
Ethylene diamine:
Ethylene glycol:
Ethylene oxide:
Ethylmercaptan:
1-Ethylnaphthalene:
2-Ethylnaphthalene:
Ethyl proprionate:
Ethyl propylether:
Ettouney, H,
Euler number:
Eutectic mixtures, condensation of forming immiscible liquids,
Evaporation:
Evaporative crystallisers,
Evaporators:
Exergy, definition of,
Exergy analysis,
Exit losses for tubes in shell-and-tube exchanger,
Expansion bellows, for shell-and-tube heat exchangers:
EJMA (Expansion Joint Manufacturers Association), standards for
Expansion joints, mechanical design of:
Expansion of tubes into tube sheets:
Expansion turbine, lost work in,
Explosively clad plate,
Explosive welding of tubes into tube sheets
Explosive expansion joints,
Extended surfaces (see also Fins)
Externally induced convection, in kettle reboilers,
Extinction coefficient,
Extinction efficiency,
Eyring fluid (non-Newtonian),
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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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