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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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Partial differential equations for interpenetrating continua
DOI 10.1615/hedhme.a.000099
1.2 DEFINITIONS AND RELATIONSHIPS
1.2.6 Partial Differential Equations for Interpenetrating Continua
D. Brian Spalding
A. INTRODUCTION
The differential equations given in Section 98 are useful if the two fluids flow in parallel or counter flow, or in some combination of these. They cannot be used, however, in cross-flow situations, for these give rise to 2D or 3D temperature variations, see Section 101.
The task of the present section is to develop the differential equations that govern the temperature distribution in more complex situations. Mass transfer and phase-change effects will be neglected for simplicity; a more advanced treatment, allowing for these effects, is to be found in Spalding (1980).
It has been common practice for heat exchanger theorists to suppose that they know quantitatively the pattern of flow adopted by the fluids in the equipment, and that their task is to predict the resulting temperature distributions. This is the first level at which the differential equations can be approached: the velocities appearing in them can be regarded as known functions of position.
However, knowledge of actual flow patterns in, say, baffled shells, is in fact very unreliable; little more is known than that the common assumptions are considerably at fault. It therefore becomes desirable to be able to calculate the velocity fields on the basis of the best general information that is available concerning flows in media containing distributed resistances (such as baffles per banks of tubes).
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