Index
313
multidimensional heat conduction, 75
problem, 54
spherical coordinate system, 8
steady-state, 54
unsteady, 69
Three-surface enclosure, 264–267
Total hemispherical emissivity, 224, 235
Transient heat conduction, 69, 93–104
engineering application problems, 86
Fourier’s conduction law, 1
lumped capacitance method, 70–73
with moving boundaries, 86–93
multidimensional, 75–76, 77
1-D, 76–86, 91, 114–117, 118
3-D, 12, 76
2-D, 117–121
variable separation method, 73–78
Transmissivity, 224, 225, 278. See also
Absorptivity; Beer’s law;
Reflectivity
gas, 282
Transport equation, 290–292
Turbulent diffusivity. See Eddy
diffusivity
Turbulent flow heat transfer, 172, 195,
208–219
in circular tube, 209
energy equation, 209
energy integral equation, 210–211
final heat transfer coefficient, 213, 215
law of wall, 205
method, 196
Nusselt number, 213
Prandtl mixing length theory, 205
RANS equation, 195–197
Stantan number, 215
velocity and temperature profile, 196
Turbulent mixing, 126, 128, 195
2-D. See Two-dimension (2-D)
Two-dimension (2-D), 1
boundary-layer equations, 3, 185–186
boundary-layer flow, 2, 203, 207
conduction equation, 45
energy conservation, 134
heat convection equations, 131–135
mass conservation, 131
momentum conservation, 132
temperature distribution, 49
Two-dimension (2-D) steady-state heat
conduction, 45, 56–63, 64–68
boundary conditions, 46
equations, 45
finite-difference energy balance
method, 105, 106
finite-differential format, 108
with heat generation, 108
nonhomogeneous BCs superposition,
52, 54
problem, 56
temperature distribution, 49, 50, 51
variable separation, 45, 49
Two-dimension (2-D) transient heat
conduction, 117–121. See also
Finite-difference energy
balance method
finite difference, 118, 119
multidimensional heat conduction, 75
U
Uniform heat flux, 107
V
Variable separation method, 45, 49
boundary conditions, 45–46, 50
Laplace’s equation, 51
multidimensional transient
conduction problems, 75
1-D transient conduction problems,
73–74, 76–78
solution, 69
superposition, 46–47
surface convection BC, 51
surface heat flux BC, 49
temperature BC, 45
2-D temperature distribution, 49
View factor, 239–243, 256
algebraic method, 253, 255
applications, 255
calculation, 263, 274
between circular tubes, 246
contour integration, 251–253
crossed-string method, 243–246
between differential areas, 241
between disks, 242
double-area integration, 250
evaluation, 243
geometrical resistance, 259
N-surface enclosure, 240
between plates, 245
radiation heat transfer determination,
257, 273
313
multidimensional heat conduction, 75
problem, 54
spherical coordinate system, 8
steady-state, 54
unsteady, 69
Three-surface enclosure, 264–267
Total hemispherical emissivity, 224, 235
Transient heat conduction, 69, 93–104
engineering application problems, 86
Fourier’s conduction law, 1
lumped capacitance method, 70–73
with moving boundaries, 86–93
multidimensional, 75–76, 77
1-D, 76–86, 91, 114–117, 118
3-D, 12, 76
2-D, 117–121
variable separation method, 73–78
Transmissivity, 224, 225, 278. See also
Absorptivity; Beer’s law;
Reflectivity
gas, 282
Transport equation, 290–292
Turbulent diffusivity. See Eddy
diffusivity
Turbulent flow heat transfer, 172, 195,
208–219
in circular tube, 209
energy equation, 209
energy integral equation, 210–211
final heat transfer coefficient, 213, 215
law of wall, 205
method, 196
Nusselt number, 213
Prandtl mixing length theory, 205
RANS equation, 195–197
Stantan number, 215
velocity and temperature profile, 196
Turbulent mixing, 126, 128, 195
2-D. See Two-dimension (2-D)
Two-dimension (2-D), 1
boundary-layer equations, 3, 185–186
boundary-layer flow, 2, 203, 207
conduction equation, 45
energy conservation, 134
heat convection equations, 131–135
mass conservation, 131
momentum conservation, 132
temperature distribution, 49
Two-dimension (2-D) steady-state heat
conduction, 45, 56–63, 64–68
boundary conditions, 46
equations, 45
finite-difference energy balance
method, 105, 106
finite-differential format, 108
with heat generation, 108
nonhomogeneous BCs superposition,
52, 54
problem, 56
temperature distribution, 49, 50, 51
variable separation, 45, 49
Two-dimension (2-D) transient heat
conduction, 117–121. See also
Finite-difference energy
balance method
finite difference, 118, 119
multidimensional heat conduction, 75
U
Uniform heat flux, 107
V
Variable separation method, 45, 49
boundary conditions, 45–46, 50
Laplace’s equation, 51
multidimensional transient
conduction problems, 75
1-D transient conduction problems,
73–74, 76–78
solution, 69
superposition, 46–47
surface convection BC, 51
surface heat flux BC, 49
temperature BC, 45
2-D temperature distribution, 49
View factor, 239–243, 256
algebraic method, 253, 255
applications, 255
calculation, 263, 274
between circular tubes, 246
contour integration, 251–253
crossed-string method, 243–246
between differential areas, 241
between disks, 242
double-area integration, 250
evaluation, 243
geometrical resistance, 259
N-surface enclosure, 240
between plates, 245
radiation heat transfer determination,
257, 273