312
Index
Similarity solution (Continued)
laminar natural convection, 185–190
momentum equation, 186–187
numerical integration, 144–145
similarity function, 146
similarity momentum equation, 143
stream lines, 142
temperature profile, 148
velocity and temperature profiles,
188–189
velocity profile, 146
Similarity variable, 79, 142, 143, 187
Single black enclosure
net radiation heat transfer, 286
radiation between hot gases
and, 287
Single-surface enclosure, 281
radiation between hot gases and, 286
Solar collector, 232, 233, 236, 237
solar radiation, 231
Solar flux, 231
in Earth’s atmosphere, 231
house with skylight, 233
radiation gain, 72
Solar radiation, 231–233
absorption, 232
maximum emission, 227
spectral blackbody emissive
power, 226
Solar spectra, 232
Solid angle, 223
unit, 221, 239
Spectral blackbody emissive power, 226
Spectral radiation, 222
absorption, 277
Spherical coordinate system, 8, 64
St. See Stantan number (St)
Stantan number (St), 139, 215
Steady-state, 10–11
ablation velocity, 91, 92
constant properties, 134
constant-property flow, 133–134
cylindrical medium, 20
heat conduction, 1, 12, 13, 15, 18, 27,
45, 105
solid material, 121
Stefan–Boltzmann law, 4, 226
Superposition, 46–47, 54
multidimensional heat conduction,
54, 75
for nonhomogeneous BCs, 52
3-D heat conduction, 54, 56
2-D heat conduction, 53–54
Surface radiation, 221. See also Thermal
radiation
blackbody radiation, 225
diffuse surface, 224
emissive power, 223, 224
flux, 221, 222
gray surface, 224
hemispherical emissivity, 224
monochromatic emissivity, 224
properties, 223–231, 239, 257
radiation transport equation, 291
spectral blackbody emissive
power, 226
Wien’s displacement law, 227
Surface temperature boundary
condition, 83
T
Temperature, nondimensional, 291
Thermal
conductivity, 8
energy generation, 7
resistance, 14
Thermal boundary layer, 126, 129, 146,
168. See also Hydrodynamic
boundary layer
over flat plate, 126, 127
for flow entering circular tube, 167
heat flux, 128, 129
heat transfer coefficient, 128, 129
integral method, 153
over solid surface, 130, 131
thickness, 128, 139, 140, 157, 158
uniformwall heat flux, 172, 173
Thermal radiation, 221
for blackbody, 234
in hemispheric radiation, 222
intensity and emissive power, 221
Thermally fully developed flow,
167, 174
3-D. See Three-dimension (3-D)
Three-dimension (3-D), 1
Three-dimension (3-D) heat conduction,
8. See also Transient heat
conduction
in cylindrical coordinates, 53–54
equation, 8
finite difference method, 113
Index
Similarity solution (Continued)
laminar natural convection, 185–190
momentum equation, 186–187
numerical integration, 144–145
similarity function, 146
similarity momentum equation, 143
stream lines, 142
temperature profile, 148
velocity and temperature profiles,
188–189
velocity profile, 146
Similarity variable, 79, 142, 143, 187
Single black enclosure
net radiation heat transfer, 286
radiation between hot gases
and, 287
Single-surface enclosure, 281
radiation between hot gases and, 286
Solar collector, 232, 233, 236, 237
solar radiation, 231
Solar flux, 231
in Earth’s atmosphere, 231
house with skylight, 233
radiation gain, 72
Solar radiation, 231–233
absorption, 232
maximum emission, 227
spectral blackbody emissive
power, 226
Solar spectra, 232
Solid angle, 223
unit, 221, 239
Spectral blackbody emissive power, 226
Spectral radiation, 222
absorption, 277
Spherical coordinate system, 8, 64
St. See Stantan number (St)
Stantan number (St), 139, 215
Steady-state, 10–11
ablation velocity, 91, 92
constant properties, 134
constant-property flow, 133–134
cylindrical medium, 20
heat conduction, 1, 12, 13, 15, 18, 27,
45, 105
solid material, 121
Stefan–Boltzmann law, 4, 226
Superposition, 46–47, 54
multidimensional heat conduction,
54, 75
for nonhomogeneous BCs, 52
3-D heat conduction, 54, 56
2-D heat conduction, 53–54
Surface radiation, 221. See also Thermal
radiation
blackbody radiation, 225
diffuse surface, 224
emissive power, 223, 224
flux, 221, 222
gray surface, 224
hemispherical emissivity, 224
monochromatic emissivity, 224
properties, 223–231, 239, 257
radiation transport equation, 291
spectral blackbody emissive
power, 226
Wien’s displacement law, 227
Surface temperature boundary
condition, 83
T
Temperature, nondimensional, 291
Thermal
conductivity, 8
energy generation, 7
resistance, 14
Thermal boundary layer, 126, 129, 146,
168. See also Hydrodynamic
boundary layer
over flat plate, 126, 127
for flow entering circular tube, 167
heat flux, 128, 129
heat transfer coefficient, 128, 129
integral method, 153
over solid surface, 130, 131
thickness, 128, 139, 140, 157, 158
uniformwall heat flux, 172, 173
Thermal radiation, 221
for blackbody, 234
in hemispheric radiation, 222
intensity and emissive power, 221
Thermally fully developed flow,
167, 174
3-D. See Three-dimension (3-D)
Three-dimension (3-D), 1
Three-dimension (3-D) heat conduction,
8. See also Transient heat
conduction
in cylindrical coordinates, 53–54
equation, 8
finite difference method, 113