A small disk of diameter D 1 = 50 mm and emissivity ε 1 = 0.6 is maintained at a temperature of T 1 = 900 K . The disk is covered with a hemispherical radiation shield of the same diameter and an emissivity of ε 2 = 0.02 (both sides). Tue disk and cap are located at the bottom of a large evacuated refractory container ( ε 4 = 0.85 ) , facing another disk of diameter D 3 = D 1 , emissivity ε 3 = 0.4 , and temperature T 3 = 400 K . The view factor F 2 3 of the shield with respect to the upper disk is 0.3. (a) Construct an equivalent thermal circuit for the above system. Label all nodes, resistances, and currents. (b) Find the net rate of heat transfer between the hot disk and the rest of the system.
A small disk of diameter D 1 = 50 mm and emissivity ε 1 = 0.6 is maintained at a temperature of T 1 = 900 K . The disk is covered with a hemispherical radiation shield of the same diameter and an emissivity of ε 2 = 0.02 (both sides). Tue disk and cap are located at the bottom of a large evacuated refractory container ( ε 4 = 0.85 ) , facing another disk of diameter D 3 = D 1 , emissivity ε 3 = 0.4 , and temperature T 3 = 400 K . The view factor F 2 3 of the shield with respect to the upper disk is 0.3. (a) Construct an equivalent thermal circuit for the above system. Label all nodes, resistances, and currents. (b) Find the net rate of heat transfer between the hot disk and the rest of the system.
Solution Summary: The author calculates the equivalent thermal circuit for the given system by labeling all nodes, resistance and currents.
A small disk of diameter
D
1
=
50
mm
and emissivity
ε
1
=
0.6
is maintained at a temperature of
T
1
=
900
K
. The disk is covered with a hemispherical radiation shield of the same diameter and an emissivity of
ε
2
=
0.02
(both sides). Tue disk and cap are located at the bottom of a large evacuated refractory container
(
ε
4
=
0.85
)
, facing another disk of diameter
D
3
=
D
1
, emissivity
ε
3
=
0.4
, and temperature
T
3
=
400
K
. The view factor F23of the shield with respect to the upper disk is 0.3.
(a) Construct an equivalent thermal circuit for the above system. Label all nodes, resistances, and currents. (b) Find the net rate of heat transfer between the hot disk and the rest of the system.
EX3
Two coaxial cylinders of diameters Di = 0.10 m and D: = 0.30 m and emissivities 1 =0.7 and 2 = 0.4
are maintained at uniforn temperatures of T1 = 750 K and T2 = 500 K. respectively. Now a coaxial
radiation shield of diameter D; = 0.20 m and emissivity 3 = 0.2 is placed between the two cylinders.
Determine the net rate of radiation heat transfer berween the two cylinders per unit length of the
cylinders and compare the result with that without the shield.
This experiment is conducted to determine the emissivity of a certain material. A lone cylindrical
rod of diameter D1 = 0.01 m is coated with this new material and is placed in an
evacuated lone cylindrical enclosure of diameter D2 = 0.1 m
and emissivity E2 = 0.95, which is cooled externally and
maintained at a temperature of 200 K at all times. The rod is heated by passing electric current
through it. When steady Operating conditions are reached, it Is observed that the rod
Is dissipating electric power at a rate of 8 W per unit or its leneth and its surface temperature is 500 k, Based on
these measurements, determine the emissivity of the coatine on the rod
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