Coatings applied to long metallic strips are cured by installing the strips along the walls of a long oven of square cross section. Thermal conditions in the oven are maintained by a long silicon carbide rod (heating element), which is of diameter D = 20 mm and is operated at T 1 = 1700 K . Each of two strips on one side wall has the same orientation relative to the rod ( s 1 = 60 mm , s 2 = 20 mm , L = 80 mm ) and is operated at T 2 = 600 K . All surfaces are diffuse and gray with ε 1 = 0.9 and ε 2 = 0.4 . Assuming the oven to be well insulated al all but the strip surfaces and neglecting convection effects, determine the heater power requirement per unit length (W/m).
Coatings applied to long metallic strips are cured by installing the strips along the walls of a long oven of square cross section. Thermal conditions in the oven are maintained by a long silicon carbide rod (heating element), which is of diameter D = 20 mm and is operated at T 1 = 1700 K . Each of two strips on one side wall has the same orientation relative to the rod ( s 1 = 60 mm , s 2 = 20 mm , L = 80 mm ) and is operated at T 2 = 600 K . All surfaces are diffuse and gray with ε 1 = 0.9 and ε 2 = 0.4 . Assuming the oven to be well insulated al all but the strip surfaces and neglecting convection effects, determine the heater power requirement per unit length (W/m).
Solution Summary: The author explains the heater power requirement per unit length, the distance between heating element and strip, and the expression for reciprocity theorem.
Coatings applied to long metallic strips are cured by installing the strips along the walls of a long oven of square cross section.
Thermal conditions in the oven are maintained by a long silicon carbide rod (heating element), which is of diameter
D
=
20
mm
and is operated at
T
1
=
1700
K
. Each of two strips on one side wall has the same orientation relative to the rod
(
s
1
=
60
mm
,
s
2
=
20
mm
,
L
=
80
mm
)
and is operated at
T
2
=
600
K
. All surfaces are diffuse and gray with
ε
1
=
0.9
and
ε
2
=
0.4
. Assuming the oven to be well insulated al all but the strip surfaces and neglecting convection effects, determine the heater power requirement per unit length (W/m).
[2] An array of electronic chips is mounted within a sealed rectangular enclosure, and cooling is implemented by
attaching an aluminum heat sink (k = 180 W/m K). The base of the heat sink has dimensions of w1 = W2 = 100 mm,
while the 6 fins are of thickness t = 10 mm and pitch S = 18 mm. The fin length is Lr = 50 mm, and the base of the heat
sink has a thickness of Lb = 10 mm.
L
-Chips
Water u T
Electronic
package,
P
elec
If cooling is implemented by water flow through the heat sink, with uo = 3 m/s and To =
temperature Tb of the heat sink when power dissipation by the chips is Pelec = 1800 W? The average convection
coefficient for surfaces of the fins and the exposed base may be estimated by assuming parallel flow over a flat plate.
Properties of the water may be approximated as k = 0.62 W/m-K, p = 995 kg/m3, Cp = 4178 J/kg-K, v = 7.73 x 10-7 m2/s,
and Pr = 5.2.
17°C, what is the base
a.) Base temperature.
А. 37.8°C
B. 43.9°C
С. 31.4°С
D. 46.2°C
2. In an experiment to measure the thermal conductivity of beef was formed into a square section
block 5 cm x 5 cm and 1 cm thick. The edges of the block were insulated, and heat was supplied
continuously to one face of the block at a rate of 0.80 W. The temperatures of each face were
measured with thermocouples and found to be 28.5°C and 23.3°C, respectively. What is the
thermal conductivity of beef?
Question 5: A copper bar 35 cm long, with square cross-section 2 cm x 2 cm is fitted with a
resistive heater at one end, and a large heat sink at the other. The bar itself is ideally thermally
lagged.
(i)
(ii)
Sketch how you think the two thermometers would behave when the heater is switched
on;
(ii) Calculate the thermal conductivity if in the steady-state, T1=64.7 deg C and T2=40.0
deg C.
Hint: rate of flow of heat = k*A*AT/X
V=6 V,
I=2.5A
heater
T1
25 cm
T2
Heat
sink
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