fundamentals of engineering supplied-reference handbook - Ventech!

RADIATION
The radiation emitted by a body is given by
� 4
= AT , where
Q εσ
T = the absolute temperature (K or °R),
σ = 5.67 × 10 –8 W/(m 2 ⋅K 4 )
[0.173 × 10 –8 Btu/(hr-ft 2 –°R 4 )],
ε = the emissivity of the body, and
A = the body surface area.
For a body (1) which is small compared to its surroundings
(2)
4 4
Q� = εσA
T − T , where
12
( )
1
2
Q12 � = the net heat transfer rate from the body.
A black body is defined as one which absorbs all energy
incident upon it. It also emits radiation at the maximum rate
for a body of a particular size at a particular temperature.
For such a body
α = ε = 1, where
α = the absorptivity (energy absorbed/incident energy).
A gray body is one for which α = ε, where
0 < α < 1; 0 < ε < 1
Real bodies are frequently approximated as gray bodies.
The net energy exchange by radiation between two black
bodies, which see each other, is given by
4 4
Q� = A F σ T − T , where
12
1
12
( )
1
2
F12 = the shape factor (view factor, configuration factor);
0 ≤ F12 ≤ 1.
For any body, α + ρ + τ = 1, where
α = absorptivity,
ρ = reflectivity (ratio of energy reflected to incident
energy), and
τ = transmissivity (ratio of energy transmitted to incident
energy).
For an opaque body, α + ρ = 1
For a gray body, ε + ρ = 1
68
HEAT TRANSFER (continued)
HEAT EXCHANGERS
The overall heat-transfer coefficient for a shell-and-tube
heat exchanger is
1 1 R fi t R fo 1
= + + + + , where
UA h A A kA A h A
i
i
i
avg
A = any convenient reference area (m 2 ),
o
Aavg = average of inside and outside area (for thin-walled
tubes) (m 2 ),
Ai = inside area of tubes (m 2 ),
Ao = outside area of tubes (m 2 ),
hi = heat-transfer coefficient for inside of tubes
[W/(m 2 ⋅K)],
ho = heat-transfer coefficient for outside of tubes
[W/(m 2 ⋅K)],
k = thermal conductivity of tube material [W/(m⋅K)],
Rfi = fouling factor for inside of tube (m 2 ⋅K/W),
Rfo = fouling factor for outside of tube (m 2 ⋅K/W),
t = tube-wall thickness (m), and
U = overall heat-transfer coefficient based on area A and
the log mean temperature difference [W/(m 2 ⋅K)].
The log mean temperature difference (LMTD) for
countercurrent flow in tubular heat exchangers is
( T − T ) − ( T − T )
Ho
Ci
∆Tlm
=
⎛ THo
− TCi
⎞
ln⎜
⎟
⎜ ⎟
⎝ THi
− TCo
⎠
The log mean temperature difference for concurrent
(parallel) flow in tubular heat exchangers is
∆T
lm
=
Hi
o
o
Co
( T − T ) − ( T − T )
Ho
Co
⎛ T
ln
⎜
⎝ T
Ho
Hi
− T
− T
Hi
Co
Ci
⎞
⎟
⎠
Ci
, where
∆Tlm = log mean temperature difference (K),
THi = inlet temperature of the hot fluid (K),
THo = outlet temperature of the hot fluid (K),
TCi = inlet temperature of the cold fluid (K), and
TCo = outlet temperature of the cold fluid (K).
For individual heat-transfer coefficients of a fluid being
heated or cooled in a tube, one pair of temperatures (either
the hot or the cold) are the surface temperatures at the inlet
and outlet of the tube.