Surrounding wall, T sur , ε sur
Air flow
q conv ′′
q rad,net ′′
Machine or equipment
T ∞ h
Surface A at T s , ε, A s
5
Heat Conduction Equations
FIGURE 1.4
Heat transfer between two surfaces involving radiation and convection.
Assume: surface A « surrounding sky or building wall surface, T ∞ = T sur
(or, T ∞ = T sur )
Total heat flux from the surface A is due to convection and radiation, and
can be found as
""
""
""
q = q
+ q
(1.5)
conv
rad,net
where
""
q
= h(T s − T ∞ )
conv
""
q
= εσT
4
− αε sur σT
4
rad,net
s
sur
= εσ(T
4
− T
4 ), if ε = α,
s
sur
ε sur= 1
= εσ(T
2
+ T
2
s
sur )(T s + T sur )(T s − T sur )
= h r (T s − T sur )
Therefore, from Equation 1.5
""
q = h(T s − T ∞ ) + h r (T s − T sur )
(1.6)
where
h r = εσ(T
2
+ T
2
(1.7)
s
sur )(T s + T sur )
Also
q
""
≡
"" A s
q
or q = q
A s
where α is the absorptivity, T sur the surrounding wall temperature ( ◦ C or
K), ε sur the emissivity of the surrounding wall, h r the radiation heat transfer
coefficient (W/m 2 K), and A s the surface area for radiation (m 2 ). Total heat
transfer rate can be determined by knowing T s , T sur , h, ε, ε sur , σ, and A s .