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Cabin heater,
Caetano, EF
Calcium carbonate, fouling of heat exchangers by,
Calcium sulphate, fouling of heat exchangers by,
CALFLO, heat transfer media,
Calorically perfect gas,
CANDU Reactor, fouling problems in,
Carbon dioxide:
Carbon disulfide:
Carbon monoxide:
Carbon steel:
Carbon-manganese steels
Carbon-molybdenum steels,
Carbon tetrachloride:
Carbonyl sulfide:
Carboxylic acids:
Carnot cycle in refrigeration,
Carnot factor,
Carreau fluid (non-Newtonian),
Carryover of solids in fluidized beds,
Cashman, B L,
Cast iron, thermal and mechanical properties,
Cavitation as source of damage in heat exchangers,
Cell method, for heat exchanger effectiveness,
Cement kilns,
CEN code for pressure vessels,
Centrifugal dryer,
Ceramics
Certification of heat exchangers,
Chan, S H,
Channel emissivity,
Chapman-Rubescin formula for viscosity variation with temperature,
Chemical exergy,
Chemical formulas of commonly used fluids
Chemical industry, fouling of heat exchangers in,
Chemical reactions, exergy analysis of,
Chemical reaction fouling,
Chen correlation for forced convective boiling,
Chen method, for enthalpy of vaporisation,
Chenoweth, J M,
Chevron troughs as corrugation design in plate heat exchangers,
Chillers, construction features of,
Chilton-Colburn analogy,
Chisholm, D
Chisholm correlations:
Chlorine:
Chloroacetic acid:
Chlorobenzene:
Chlorobutane:
Chlorodifluoromethane (see Refrigerant 22)
1-Chloro-1,1-difluoroethane (Refrigerant 142b):
Chloroethane (Refrigerant 160):
Chloromethane (Refrigerant 40):
Chloropentane:
1,2-Chloropentafluoroethane (Refrigerant 115):
Chloroprene (2-Chloro-1,3-butadiene):
1-Chloropropane:
2-Chloropropane:
m-Chlorotoluene:
o-Chlorotoluene:
Chlorotrifluoroethylene:
Chlorotrifluoromethane (see Refrigerant 13)
Chromium-molybdenum steels,
Chudnovsky, Y,
Chugging flow (gas-liquid), in shell-and-tube heat exchangers,
Chung et al method, for viscosity of low pressure gases,
Church and Prausnitz methods:
Churchill, S W,
Churchill and Chu correlations for free convective heat transfer:
Churn flow, regions of occurrence of,
Circles, radiative heat transfer shape factors between parallel coaxial,
Circular girth flanges, design according to ASME VIII code,
Circulating fluidized beds,
Circulation, modes of in free convection: in enclosures heated from below,
CISE correlations for void fractions,
Clausius-Clapeyron relationship:
Cleaning:
Climbing film evaporator,
Closed circuit cooling towers,
Coalescence of bubbles in fluidized beds,
Coatings for corrosion protection
Cocurrent flow:
Codes, mechanical design:
Cogeneration
Colburn and Drew method for binary vapor condensation,
Colburn and Hougen method for condensation in presence of noncondensable gases
Colburn equation for single-phase heat transfer outside tube banks,
Colburn j factor:
Colebrook-White equation for friction factor in rough circular pipe,
Coles, law of the wake,
Collier, J G,
Combined free and forced convection heat transfer:
Combined heat and mass transfer,
Combining flow, loss coefficients in,
Combustion model for furnaces,
Compact heat exchangers (see Plate fin heat exchangers)
Compartment dryers,
Composite curves, in the pinch analysis method for heat exchanger network analysis:
Compressed liquids, density of:
Compressible flow:
Compression, exergy analysis of
Compressive stress, in heat exchanger tubes,
Computer-aided design, of evaporators,
Computer program for Monte Carlo calculations of radiative heat transfer,
Computer simulation, of fouling,
Computer software for mechanical design,
Concentration, choice of evaporator type for,
Concentric spheres, free convective heat transfer in,
Concurrency corrections in plate heat exchangers,
Condensation:
Concrete, lightweight, submerged combustion system for,
Condensation curves:
Condenser/preheater tubes, in multistage flash evaporation,
Condensers:
Conduction, heat:
Conductors, thermal conductivity of,
Cones, under internal pressure, EN13445 guidelines for,
Cones, vertical:
Conical shells, mechanical design of:
Conjugate radiation interactions
Connors equation for fluid elastic instability,
Conservation equations:
Constantinon and Gani method, for estimating normal boiling point,
Contact angle,
Contact resistance:
Continuity equation:
Continuum model, for fluids,
Continuum theories, for non-Newtonian fluids,
Contraction, sudden, pressure drop in:
Control:
Control volume method, in finite difference solutions for conduction,
Convection, interaction of radiation with,
Convection effects, on heat transfer in kettle reboilers,
Convective heat transfer, single-phase:
Conversion factors:
Conveyor, gravity:
Cooling curves, in condensation,
Cooling towers:
Cooling water fouling,
Cooper correlation, for nucleate boiling,
Cooper, Anthony,
Copper, thermal and mechanical properties,
Copper alloys,
Correlation, general nature of,
Corresponding states principle
Corrosion:
Corrugation design, for plate heat exchangers
Costing of heat exchangers:
Countercurrent flow:
Coupled thermal fields, in transient conduction,
Cowie, R C,
Crank-Nicolson differencing scheme, in finite difference method,
Creeping flow, in combined free and forced convection around immersed bodies,
m-Cresol:
o-Cresol:
p-Cresol:
Crevice corrosion, in stainless steels,
Critical constants
Critical density, of commonly used fluids,
Critical flow, in gas-liquid systems,
Critical heat flux:
Critical pressure:
Critical Rayleigh number, in free convection,
Critical temperature:
Critical velocity, in stratification in bends and horizontal tubes,
Critical volume (see also Critical density)
Cross counterflow heat exchangers,
Crossflow:
Crude oil, fouling of heat exchangers:
Cryogenic plant, entropy generation in,
Crystallization
Crystallization fouling,
Curved ducts:
Cut-and-twist factor, in enhancement of heat transfer in double pipe heat exchangers,
C-value method for heat exchanger costing,
Cycling, of expansion bellows,
Cyclobutane:
Cyclohexane:
Cyclohexanol:
Cyclohexene:
Cyclopentane:
Cyclopentene:
Cyclopropane:
Cylinders:
boiling from outside horizontal in crossflow,
characteristics of as packings for fixed beds,
combined free and forced convective heat transfer from,
fixed beds of, heat transfer in
flow across,
free convective heat transfer from,
free convective heat transfer inside horizontal,
pool boiling from,
radiative heat transfer on nonisothermal gas in,
single-phase heat transfer in flow over,
steady-state thermal conduction in,
transient conduction in,
under internal pressure, EN13445 guidelines for,
EN13445 guidelines for,
PD5500 guidelines for,
Cylindrical contacts, thermal contact resistance in,
Cylindrical coordinates, finite difference equations for conduction in,
Cylindrical shell, analytical basis of code rules for,
Index
HEDH
A
B
C
Cabin heater,
Caetano, EF
Calcium carbonate, fouling of heat exchangers by,
Calcium sulphate, fouling of heat exchangers by,
CALFLO, heat transfer media,
Calorically perfect gas,
CANDU Reactor, fouling problems in,
Carbon dioxide:
Carbon disulfide:
Carbon monoxide:
Carbon steel:
Carbon-manganese steels
Carbon-molybdenum steels,
Carbon tetrachloride:
Carbonyl sulfide:
Carboxylic acids:
Carnot cycle in refrigeration,
Carnot factor,
Carreau fluid (non-Newtonian),
Carryover of solids in fluidized beds,
Cashman, B L,
Cast iron, thermal and mechanical properties,
Cavitation as source of damage in heat exchangers,
Cell method, for heat exchanger effectiveness,
Cement kilns,
CEN code for pressure vessels,
Centrifugal dryer,
Ceramics
Certification of heat exchangers,
Chan, S H,
Channel emissivity,
Chapman-Rubescin formula for viscosity variation with temperature,
Chemical exergy,
Chemical formulas of commonly used fluids
Chemical industry, fouling of heat exchangers in,
Chemical reactions, exergy analysis of,
Chemical reaction fouling,
Chen correlation for forced convective boiling,
Chen method, for enthalpy of vaporisation,
Chenoweth, J M,
Chevron troughs as corrugation design in plate heat exchangers,
Chillers, construction features of,
Chilton-Colburn analogy,
Chisholm, D
Chisholm correlations:
Chlorine:
Chloroacetic acid:
Chlorobenzene:
Chlorobutane:
Chlorodifluoromethane (see Refrigerant 22)
1-Chloro-1,1-difluoroethane (Refrigerant 142b):
Chloroethane (Refrigerant 160):
Chloromethane (Refrigerant 40):
Chloropentane:
1,2-Chloropentafluoroethane (Refrigerant 115):
Chloroprene (2-Chloro-1,3-butadiene):
1-Chloropropane:
2-Chloropropane:
m-Chlorotoluene:
o-Chlorotoluene:
Chlorotrifluoroethylene:
Chlorotrifluoromethane (see Refrigerant 13)
Chromium-molybdenum steels,
Chudnovsky, Y,
Chugging flow (gas-liquid), in shell-and-tube heat exchangers,
Chung et al method, for viscosity of low pressure gases,
Church and Prausnitz methods:
Churchill, S W,
Churchill and Chu correlations for free convective heat transfer:
Churn flow, regions of occurrence of,
Circles, radiative heat transfer shape factors between parallel coaxial,
Circular girth flanges, design according to ASME VIII code,
Circulating fluidized beds,
Circulation, modes of in free convection: in enclosures heated from below,
CISE correlations for void fractions,
Clausius-Clapeyron relationship:
Cleaning:
Climbing film evaporator,
Closed circuit cooling towers,
Coalescence of bubbles in fluidized beds,
Coatings for corrosion protection
Cocurrent flow:
Codes, mechanical design:
Cogeneration
Colburn and Drew method for binary vapor condensation,
Colburn and Hougen method for condensation in presence of noncondensable gases
Colburn equation for single-phase heat transfer outside tube banks,
Colburn j factor:
Colebrook-White equation for friction factor in rough circular pipe,
Coles, law of the wake,
Collier, J G,
Combined free and forced convection heat transfer:
Combined heat and mass transfer,
Combining flow, loss coefficients in,
Combustion model for furnaces,
Compact heat exchangers (see Plate fin heat exchangers)
Compartment dryers,
Composite curves, in the pinch analysis method for heat exchanger network analysis:
Compressed liquids, density of:
Compressible flow:
Compression, exergy analysis of
Compressive stress, in heat exchanger tubes,
Computer-aided design, of evaporators,
Computer program for Monte Carlo calculations of radiative heat transfer,
Computer simulation, of fouling,
Computer software for mechanical design,
Concentration, choice of evaporator type for,
Concentric spheres, free convective heat transfer in,
Concurrency corrections in plate heat exchangers,
Condensation:
Concrete, lightweight, submerged combustion system for,
Condensation curves:
Condenser/preheater tubes, in multistage flash evaporation,
Condensers:
Conduction, heat:
Conductors, thermal conductivity of,
Cones, under internal pressure, EN13445 guidelines for,
Cones, vertical:
Conical shells, mechanical design of:
Conjugate radiation interactions
Connors equation for fluid elastic instability,
Conservation equations:
Constantinon and Gani method, for estimating normal boiling point,
Contact angle,
Contact resistance:
Continuity equation:
Continuum model, for fluids,
Continuum theories, for non-Newtonian fluids,
Contraction, sudden, pressure drop in:
Control:
Control volume method, in finite difference solutions for conduction,
Convection, interaction of radiation with,
Convection effects, on heat transfer in kettle reboilers,
Convective heat transfer, single-phase:
Conversion factors:
Conveyor, gravity:
Cooling curves, in condensation,
Cooling towers:
Cooling water fouling,
Cooper correlation, for nucleate boiling,
Cooper, Anthony,
Copper, thermal and mechanical properties,
Copper alloys,
Correlation, general nature of,
Corresponding states principle
Corrosion:
Corrugation design, for plate heat exchangers
Costing of heat exchangers:
Countercurrent flow:
Coupled thermal fields, in transient conduction,
Cowie, R C,
Crank-Nicolson differencing scheme, in finite difference method,
Creeping flow, in combined free and forced convection around immersed bodies,
m-Cresol:
o-Cresol:
p-Cresol:
Crevice corrosion, in stainless steels,
Critical constants
Critical density, of commonly used fluids,
Critical flow, in gas-liquid systems,
Critical heat flux:
Critical pressure:
Critical Rayleigh number, in free convection,
Critical temperature:
Critical velocity, in stratification in bends and horizontal tubes,
Critical volume (see also Critical density)
Cross counterflow heat exchangers,
Crossflow:
Crude oil, fouling of heat exchangers:
Cryogenic plant, entropy generation in,
Crystallization
Crystallization fouling,
Curved ducts:
Cut-and-twist factor, in enhancement of heat transfer in double pipe heat exchangers,
C-value method for heat exchanger costing,
Cycling, of expansion bellows,
Cyclobutane:
Cyclohexane:
Cyclohexanol:
Cyclohexene:
Cyclopentane:
Cyclopentene:
Cyclopropane:
Cylinders:
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
boiling from outside horizontal in crossflow,
characteristics of as packings for fixed beds,
combined free and forced convective heat transfer from,
fixed beds of, heat transfer in
flow across,
free convective heat transfer from,
free convective heat transfer inside horizontal,
pool boiling from,
radiative heat transfer on nonisothermal gas in,
single-phase heat transfer in flow over,
steady-state thermal conduction in,
transient conduction in,
under internal pressure, EN13445 guidelines for,
EN13445 guidelines for,
PD5500 guidelines for,
Cylindrical contacts, thermal contact resistance in,
Cylindrical coordinates, finite difference equations for conduction in,
Cylindrical shell, analytical basis of code rules for,
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Packed beds with fluid flow
DOI 10.1615/hedhme.a.000201
2.8 HEAT TRANSFER TO GAS-SOLID SYSTEMS
2.8.2 Packed Beds with Fluid Flow
E.Tsotsas
A. Influence of the Wall on Porosity and Flow
The structure and randomness of packed beds are disturbed in the vicinity of a rigid wall. While this effect has been neglected in the discussion of stagnant beds (Section 200) it has to be taken into account in connection with fluid flow. Radial porosity profiles in circular tubes filled with almost perfect spheres are depicted in Figure 1. As expected, porosity is very high at the wall and reaches its minimum at a distance of half a particle diameter from it. Thereafter, damped oscillations are observed. Computer simulations of packed beds (Cheng et al., 2000) lead to results similar to those of Figure 1. However, increasing deviations from sphericity, size dispersity, and surface roughness of the particles surpress the oscillations. For such imperfect spheres, which are typical for many practical applications, the behavior of Figure 2 is obtained. Now, a monotonic function is sufficient for the approximation of the porosity profile, namely the function
\[\label{eq1} \psi\,(r)=\psi_{\infty} \Bigg [ 1+ 1.36 \,\exp \left( -5.0\frac{R-r}{d} \right) \Bigg] \tag{1}\]
after Giese (1997). According to Equation 1 the void fraction of the bed is increased considerably in a relatively narrow zone in the vicinity of the wall. Outside this zone, the porosity of the undisturbed (infinitely extended) bed ψ∞ prevails. For technical (imperfect) cylinders with a length that does not differ very much from their geometrical diameter (l ≈ da), the analogous relationship
\[\label{eq2} \psi\,(r)=\psi_{\infty} \Bigg [ 1+\left( {\frac{0.65}{\psi_{\infty } }-1} \right) \,\exp \left( -6.0\frac{R-r}{d} \right) \Bigg] \tag{2}\]
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