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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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Finite-Difference Methods for Conduction
DOI 10.1615/hedhme.a.000165
2.4.7 Finite-Difference Methods for Conduction
F. W. Schmidt
A. Introduction
The widespread use of numerical techniques for the solution of heat conduction problems is very well documented in the technical literature. A number of factors have contributed to the popularity of numerical techniques. They are capable of handling complex geometrical configurations, composite media, both nonlinear and linear boundary conditions, and variable termophysical properties. Transient as well as steady-state conduction problems can be analyzed. Perhaps the most important factor, however, has been the rapid increase in the availability of digital computers to practicing engineers, enabling them easily to apply numerical techniques for the solution of everyday engineering problems.
Numerical techniques, as applied to conduction heat transfer, can be classified as either finite-difference or finite-element methods. This section will deal only with finite-difference methods; Section 166 concentrates on finite-element methods.
A general discussion of finite-difference methods and their use for flow predictions has been presented in Section 1.4. This section will concentrate on the application of these methods to conduction problems, in which the geoemtrical configuration of the region is of considerable importance. Although a number of generalized conduction programs are commercially available, the practicing engineer can easily employ the techniques to be described to obtain satisfactory accuracy with computational power as small as that provided by a desktop personal computer (PC).
The steps used to obtain a finite-difference solution can be categorized as follows:
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