The diameter and surface emissivity of an electricallyheated plate are D = 300 mm and ∈ = 0.80 , respectively. (a) Estimate the power needed to maintain a surfacetemperature of 200°C in a room [or which the airand the walls are at 25°C. The coefficient characterizing heat transfer by natural convection depends on the surface temperature and, in units of W/m 2 ⋅ K , may be approximated by an expression ofthe form h = 0.80 ( T s − T ∞ ) 1 / 3 . (b) Assess the effect of surface temperature on thepower requirement, as well as on the relative contributions of convection and radiation to heat transfer from the surface.
Solution Summary: The author explains the power needed to maintain the surface temperature of heated plate at 200°C in a room.
The diameter and surface emissivity of an electricallyheated plate are
D
=
300
mm
and
∈
=
0.80
,
respectively. (a) Estimate the power needed to maintain a surfacetemperature of 200°C in a room [or which the airand the walls are at 25°C. The coefficient characterizing heat transfer by natural convection depends on the surface temperature and, in units of
W/m
2
⋅
K
, may be approximated by an expression ofthe form
h
=
0.80
(
T
s
−
T
∞
)
1
/
3
. (b) Assess the effect of surface temperature on thepower requirement, as well as on the relative contributions of convection and radiation to heat transfer from the surface.
The emissivity of galvanized steel sheet, a common roofing material, is ε = 0.13 at temperatures around 300 K, while its absorptivity for solar irradiation is αS = 0.65. Would the neighborhood cat be comfortable walking on a roof constructed of the material on a day when GS = 750 W/m2, T∞ = 16°C, and h = 7 W/m2 · K? Assume the bottom surface of the steel is insulated.
Chips of width L _ 15 mm on a side are mounted to a substrate that is installed in an enclosurewhose walls and air are maintained at a temperature of Tsur=T∞=25oC. The chips have an emissivity ofε=0.60 and a maximum allowable temperature of Ts=85oC.(a) If heat is rejected from the chips by radiation and natural convection, what is the maximum operatingpower of each chip? The convection coefficient may be approximated as h=11.7 W/m2K.(b) If a fan is used to maintain airflow through the enclosure and heat transfer is by only forcedconvection, with h=250 W/m2K, what is the maximum operating power?
Chips of width L _ 15 mm on a side are mounted to a substrate that is installed in an enclosure
whose walls and air are maintained at a temperature of Tsur=T∞=25oC. The chips have an emissivity of
ε=0.60 and a maximum allowable temperature of Ts=85oC.
(a) If heat is rejected from the chips by radiation and natural convection, what is the maximum operating
power of each chip? The convection coefficient may be approximated as h=11.7 W/m2K.
(b) If a fan is used to maintain airflow through the enclosure and heat transfer is by only forced
convection, with h=250 W/m2K, what is the maximum operating power
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