An opaque, diffuse, gray ( 200 mm× 200 mm ) plate with an emissivity of 0.8 is placed over the opening of a furnace and is known to be at 400 K at a certain instant. The bottom of the furnace, having the same dimensions as the plate, is black and operates at 1000 K. The sidewalls of the furnace are well insulated. The top of the plate is exposed to ambient air with a convection coefficient of 25 W/m 2 ⋅ K and to large surroundings. The air and surroundings are each at 300 K. (a) Evaluate the net radiative heat transfer lo the bottom surface of the plate. (b) If the plate has mass and specific heat of 2 kg and 900 J/kg ⋅ K , respectively, what will be the change in temperature of the plate with time, d T p / d t ? Assume convection to the bottom surface of the plate to be negligible. (c) Extending the analysis of part (b), generate a plot of the change in temperature of the plate with time, d T p / d t , as a function of the plate temperature for 350 ≤ T p ≤ 900 K and all other conditions remaining the same. What is the steady-state temperature of the plate?
An opaque, diffuse, gray ( 200 mm× 200 mm ) plate with an emissivity of 0.8 is placed over the opening of a furnace and is known to be at 400 K at a certain instant. The bottom of the furnace, having the same dimensions as the plate, is black and operates at 1000 K. The sidewalls of the furnace are well insulated. The top of the plate is exposed to ambient air with a convection coefficient of 25 W/m 2 ⋅ K and to large surroundings. The air and surroundings are each at 300 K. (a) Evaluate the net radiative heat transfer lo the bottom surface of the plate. (b) If the plate has mass and specific heat of 2 kg and 900 J/kg ⋅ K , respectively, what will be the change in temperature of the plate with time, d T p / d t ? Assume convection to the bottom surface of the plate to be negligible. (c) Extending the analysis of part (b), generate a plot of the change in temperature of the plate with time, d T p / d t , as a function of the plate temperature for 350 ≤ T p ≤ 900 K and all other conditions remaining the same. What is the steady-state temperature of the plate?
Solution Summary: The author explains the net radiative heat transfer to the bottom surface of the plate.
An opaque, diffuse, gray
(
200
mm×
200
mm
)
plate with an emissivity of 0.8 is placed over the opening of a furnace and is known to be at 400 K at a certain instant. The bottom of the furnace, having the same dimensions as the plate, is black and operates at 1000 K. The sidewalls of the furnace are well insulated. The top of the plate is exposed to ambient air with a convection coefficient of
25
W/m
2
⋅
K
and to large surroundings. The air and surroundings are each at 300 K.
(a) Evaluate the net radiative heat transfer lo the bottom surface of the plate. (b) If the plate has mass and specific heat of 2 kg and
900
J/kg
⋅
K
, respectively, what will be the change in temperature of the plate with time,
d
T
p
/
d
t
? Assume convection to the bottom surface of the plate to be negligible. (c) Extending the analysis of part (b), generate a plot of the change in temperature of the plate with time,
d
T
p
/
d
t
, as a function of the plate temperature for
350
≤
T
p
≤
900
K
and all other conditions remaining the same. What is the steady-state temperature of the plate?
A furnace is shaped like a 1-m-diameter and 1-m-long vertical cylinder. The base surface has an emissivity of 0.7 and is maintained at a uniform
temperature of 525 K. The side surface has an emissivity of 0.3 and is maintained at a uniform temperature of 600 K. The top surface has an emissivity
of 0.5 and is maintained at a uniform temperature of 450 K. If Fbase-top=0.62; Fside-base=0.31, determine the net radiation heat transfer FROM the side
surface to the top surface (W).
O a. -1986
O b. -1651
O C.
-999
O d.
1986.
O e.
1651
O f. 999
An electric hot plate is placed in a room which is maintained at a temperature of 297 K. The plate is maintained at a temperature of 403 K and has an emissivity of 0.8. If the plate surface resembles a circular disc of diameter 250 mm, electrical power consumed by the hot plate will be?
Two parallel rectangular surfaces 1m x 2m are opposite to each other at adistance of 4 m. The surfaces are black and at 100 °C and 200 °C, respectively.Calculate the heat exchange by radiation between the two surfaces.
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