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Taborek, J, xlv-lvi
Taitel and Dukler flow regime map, for horizontal and inclined gas- liquid flows,
Tamura et al correlation, for surface tension of mixtures,
Taylor Forge method, for mechanical design of flanges, comparison with EN13445 method,
Taylor series expansion,
Teflon, use in heat transfer enhancement:
TEMA (Tubular Exchanger Manufacturers Association):
Temperature distribution:
Tenders for heat exchangers,
Terminal free fall velocity, in fluidization,
Testing and inspection of heat exchangers:
Tetrabromomethane:
1,1,2,2-Tetrachloroethane:
Tetrachloroethylene:
Tetradecane:
Tetradecene:
Tetrachlorodifluoroethane (Refrigerant 112):
1,1,1,2-Tetrafluoroethane (Refrigerant R134a):
Tetrafluoromethane (Refrigerant 14):
Tetrahydrofuran:
1,2,3,4-Tetramethylbenzene:
1,2,3,5-Tetramethylbenzene:
1,2,4,5-Tetramethylbenzene:
Thermal conductivity:
Thermal contact conductance (TCC),
Thermal contact resistance (TCR),
Thermal design, constructional features affecting, in shell-and-tube heat exchangers
Thermal diffusivity:
Thermal expansion coefficient:
Thermal leakage in F-type shell-and-tube heat exchangers,
Thermal mixing in plate heat exchangers,
Thermal stress:
Thermocal, heat transfer media,
Thermodynamic cycles in refrigeration,
Thermodynamic properties:
Thermodynamic surface in radiative heat transfer,
Thermoexel surface, for enhancement of boiling,
Thermofluids, heat transfer medium,
Thermosiphon
Theta-NTU method:
Thickness of boundary layers (displacement, momentum, energy, density, temperature),
Thin-wall-type expansion bellows,
Thiophene:
Thome, J R
Three-phase flows:
Tie rods in shell-and-tube heat exchangers,
Tinker method for shell-side heat transfer in shell-and-tube heat exchangers,
Titanium and titanium alloys,
T-junctions, loss coefficients in,
Tolerances
Toluene:
m-Toluidine:
Tong F-factor method, for critical heat flux with nonuniform heating,
Tooth, A S,
Total emissivity in gases,
Transcendental equations in transient conduction,
Transient behavior:
Transition boiling:
Transition flow, heat transfer in free convective flow over vertical surfaces in,
Transitional flow, in combined free and forced convection,
Transmission of thermal radiation in solids:
Transmissivity of solids:
Transport properties:
Transverse flow, combined free and forced convection in,
Treated surfaces, for augmentation of heat transfer,
Triangular duct:
Triangular fins, in plate fin exchangers,
Triangular relationship, in annular gas-liquid flow,
Tribromomethane:
1,1,1-Trichloroethane (Refrigerant 140a):
Trichloroethylene:
Trichlorofluoromethane (Refrigerant 11)
Trichloromethane (Chloroform) (Refrigerant 20):
1,1,2-Trichlorotrifluoroethane (Refrigerant 113):
Tridecane:
Tridecene:
Triethylamine:
1,1,1-Trifluoroethane (Refrigerant 143a):
Trifluoromethane (Refrigerant 23):
Trimethylamine:
1,2,3-Trimethylbenzene:
1,2,4-Trimethylbenzene:
1,3,5-Trimethylbenzene:
2,2,4-Trimethylpentane (Isooctane):
Triphenylmethane:
Triple interface (gas/solid/liquid),
True temperature difference, in double pipe exchangers,
Truelove, J S,
Tsotsas, E
Tube-baffle damage, in heat exchangers,
Tube banks, finned:
Tube banks, plain:
Tube banks, roughened tubes, effect of roughness on Euler number in,
Tube bundles:
Tube counts, in shell-and-tube heat exchangers:
Tube end attachment, in shell-and-tube heat exchangers,
Tube inserts, heat exchangers with,
Tube-in-plate extended surface configurations, fin efficiency of,
Tube plates, in shell-and-tube heat exchangers:
Tube rupture in shell-and-tube heat exchangers,
Tube-to-tubesheet attachment, in shell-and-tube heat exchangers,
Tubes:
Tucker, R J,
Tunnel dryer,
Turbine exhaust condensers:
Turbines, lost work in
Turbulence:
Turbulent boundary layers:
Turbulent buffeting, as source of tube vibration,
Turbulent energy, integral equation for,
Turbulent flow:
Turnarounds, in heat exchangers,
Turner, C W,
Twisted tapes:
Twisted tube heat exchangers,
Twisted tubes
Two-equation models, for turbulent boundary layers,
Two-phase loop with capillary pump,
Two-phase flows:
Index
HEDH
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
Taborek, J, xlv-lvi
Taitel and Dukler flow regime map, for horizontal and inclined gas- liquid flows,
Tamura et al correlation, for surface tension of mixtures,
Taylor Forge method, for mechanical design of flanges, comparison with EN13445 method,
Taylor series expansion,
Teflon, use in heat transfer enhancement:
TEMA (Tubular Exchanger Manufacturers Association):
Temperature distribution:
Tenders for heat exchangers,
Terminal free fall velocity, in fluidization,
Testing and inspection of heat exchangers:
Tetrabromomethane:
1,1,2,2-Tetrachloroethane:
Tetrachloroethylene:
Tetradecane:
Tetradecene:
Tetrachlorodifluoroethane (Refrigerant 112):
1,1,1,2-Tetrafluoroethane (Refrigerant R134a):
Tetrafluoromethane (Refrigerant 14):
Tetrahydrofuran:
1,2,3,4-Tetramethylbenzene:
1,2,3,5-Tetramethylbenzene:
1,2,4,5-Tetramethylbenzene:
Thermal conductivity:
Thermal contact conductance (TCC),
Thermal contact resistance (TCR),
Thermal design, constructional features affecting, in shell-and-tube heat exchangers
Thermal diffusivity:
Thermal expansion coefficient:
Thermal leakage in F-type shell-and-tube heat exchangers,
Thermal mixing in plate heat exchangers,
Thermal stress:
Thermocal, heat transfer media,
Thermodynamic cycles in refrigeration,
Thermodynamic properties:
Thermodynamic surface in radiative heat transfer,
Thermoexel surface, for enhancement of boiling,
Thermofluids, heat transfer medium,
Thermosiphon
Theta-NTU method:
Thickness of boundary layers (displacement, momentum, energy, density, temperature),
Thin-wall-type expansion bellows,
Thiophene:
Thome, J R
Three-phase flows:
Tie rods in shell-and-tube heat exchangers,
Tinker method for shell-side heat transfer in shell-and-tube heat exchangers,
Titanium and titanium alloys,
T-junctions, loss coefficients in,
Tolerances
Toluene:
m-Toluidine:
Tong F-factor method, for critical heat flux with nonuniform heating,
Tooth, A S,
Total emissivity in gases,
Transcendental equations in transient conduction,
Transient behavior:
Transition boiling:
Transition flow, heat transfer in free convective flow over vertical surfaces in,
Transitional flow, in combined free and forced convection,
Transmission of thermal radiation in solids:
Transmissivity of solids:
Transport properties:
Transverse flow, combined free and forced convection in,
Treated surfaces, for augmentation of heat transfer,
Triangular duct:
Triangular fins, in plate fin exchangers,
Triangular relationship, in annular gas-liquid flow,
Tribromomethane:
1,1,1-Trichloroethane (Refrigerant 140a):
Trichloroethylene:
Trichlorofluoromethane (Refrigerant 11)
Trichloromethane (Chloroform) (Refrigerant 20):
1,1,2-Trichlorotrifluoroethane (Refrigerant 113):
Tridecane:
Tridecene:
Triethylamine:
1,1,1-Trifluoroethane (Refrigerant 143a):
Trifluoromethane (Refrigerant 23):
Trimethylamine:
1,2,3-Trimethylbenzene:
1,2,4-Trimethylbenzene:
1,3,5-Trimethylbenzene:
2,2,4-Trimethylpentane (Isooctane):
Triphenylmethane:
Triple interface (gas/solid/liquid),
True temperature difference, in double pipe exchangers,
Truelove, J S,
Tsotsas, E
Tube-baffle damage, in heat exchangers,
Tube banks, finned:
Tube banks, plain:
Tube banks, roughened tubes, effect of roughness on Euler number in,
Tube bundles:
Tube counts, in shell-and-tube heat exchangers:
Tube end attachment, in shell-and-tube heat exchangers,
Tube inserts, heat exchangers with,
Tube-in-plate extended surface configurations, fin efficiency of,
Tube plates, in shell-and-tube heat exchangers:
Tube rupture in shell-and-tube heat exchangers,
Tube-to-tubesheet attachment, in shell-and-tube heat exchangers,
Tubes:
Tucker, R J,
Tunnel dryer,
Turbine exhaust condensers:
Turbines, lost work in
Turbulence:
Turbulent boundary layers:
Turbulent buffeting, as source of tube vibration,
Turbulent energy, integral equation for,
Turbulent flow:
Turnarounds, in heat exchangers,
Turner, C W,
Twisted tapes:
Twisted tube heat exchangers,
Twisted tubes
Two-equation models, for turbulent boundary layers,
Two-phase loop with capillary pump,
Two-phase flows:
U
V
W
X
Y
Z
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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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