306
Index
Conduction (Continued)
heat rate, 7
multidimensional heat, 54
1-D, 2, 22
one-dimensional, 22
through plane walls, 13, 14
radiation effect, 26, 30
thermal resistance, 14
through thermal–electrical network
analogy, 14
2-D conduction equation, 45
with uniform cross-sectional area, 21
Conservation of energy, 130, 135,
152, 199
in differential control volume, 6, 7
fully developed flow, 209
general form, 6
for incompressible flow, 136
similarity, 146, 188
steady-state constant properties, 134
uniform wall temperature, 175
unsteady state, 134
Conservation of mass, 130, 131
boundary layer, 150
integral method, 151
Reynolds time-averaged method, 197
Conservation of momentum, 130,
132, 133
Continuity equation. See Conservation
of mass
Contour integration, 251–253
Convection, 2
advanced heat, 150, 179
boundary condition, 23, 51
boundary on surface nodes, 106
external forced, 141
heat convection equations, 130
heat transfer, combined modes of, 4, 5
heat transfer coefficient, 3
internal forced, 167
natural, 185
Newton’s cooling law, 2
surface, 9, 11
thermal resistance, 14
type, 3
Crossed-string method, 243–246
Cryogenic thermal insulation, 289–290
Cylindrical coordinate system, 8
heat conduction equation, 8
2-D heat conduction, 53–54
Cylindrical medium, 20
D
Differential element
hemispheric radiation from, 223
radiation exchange, 268
Diffuse surface, 224
blackbody, 225
brick wall, 231
Dimensional analysis. See Boundary
layer—similarity
Dissipation function, 130
Double-area integration, 243, 250
E
Earth’s atmosphere, 231
Eddy diffusivity, 200, 201
Electric network analogy, 259
furnaces with reradiating surface, 262
gas radiation problems, 285–289
radiant heater panel problem, 263
radiation between two-surface,
259, 261
radiation heat transfer
applications, 259
reradiating surfaces, 261
Electric network analogy, 259–263
Emissivity, 224. See also Surface
radiation—properties
average, 227, 230
gas, 275, 277, 279
of metal, 4
monochromatic, 224
surface, 4, 227
Enclosure
elemental surface for radiation, 280
energy balance, 271
of gray hot surface, 288
radiation exchange, 257, 282
Reciprocity rule, 240
three-surface, 247, 265
two-surface, 260
view factor for N-surface, 240
Energy
integral equation, 152, 210
storage, 7, 117
Energy balance, 264
at boundary nodes, 106
in enclosure, 271
finite-difference, 105, 114
at interior nodes, 106, 117
Index
Conduction (Continued)
heat rate, 7
multidimensional heat, 54
1-D, 2, 22
one-dimensional, 22
through plane walls, 13, 14
radiation effect, 26, 30
thermal resistance, 14
through thermal–electrical network
analogy, 14
2-D conduction equation, 45
with uniform cross-sectional area, 21
Conservation of energy, 130, 135,
152, 199
in differential control volume, 6, 7
fully developed flow, 209
general form, 6
for incompressible flow, 136
similarity, 146, 188
steady-state constant properties, 134
uniform wall temperature, 175
unsteady state, 134
Conservation of mass, 130, 131
boundary layer, 150
integral method, 151
Reynolds time-averaged method, 197
Conservation of momentum, 130,
132, 133
Continuity equation. See Conservation
of mass
Contour integration, 251–253
Convection, 2
advanced heat, 150, 179
boundary condition, 23, 51
boundary on surface nodes, 106
external forced, 141
heat convection equations, 130
heat transfer, combined modes of, 4, 5
heat transfer coefficient, 3
internal forced, 167
natural, 185
Newton’s cooling law, 2
surface, 9, 11
thermal resistance, 14
type, 3
Crossed-string method, 243–246
Cryogenic thermal insulation, 289–290
Cylindrical coordinate system, 8
heat conduction equation, 8
2-D heat conduction, 53–54
Cylindrical medium, 20
D
Differential element
hemispheric radiation from, 223
radiation exchange, 268
Diffuse surface, 224
blackbody, 225
brick wall, 231
Dimensional analysis. See Boundary
layer—similarity
Dissipation function, 130
Double-area integration, 243, 250
E
Earth’s atmosphere, 231
Eddy diffusivity, 200, 201
Electric network analogy, 259
furnaces with reradiating surface, 262
gas radiation problems, 285–289
radiant heater panel problem, 263
radiation between two-surface,
259, 261
radiation heat transfer
applications, 259
reradiating surfaces, 261
Electric network analogy, 259–263
Emissivity, 224. See also Surface
radiation—properties
average, 227, 230
gas, 275, 277, 279
of metal, 4
monochromatic, 224
surface, 4, 227
Enclosure
elemental surface for radiation, 280
energy balance, 271
of gray hot surface, 288
radiation exchange, 257, 282
Reciprocity rule, 240
three-surface, 247, 265
two-surface, 260
view factor for N-surface, 240
Energy
integral equation, 152, 210
storage, 7, 117
Energy balance, 264
at boundary nodes, 106
in enclosure, 271
finite-difference, 105, 114
at interior nodes, 106, 117