A small sphere (2.5 cm-diam) is placed in a heating oven. The oven cavity is a 30 cm cube filled with air at 101 kPa(abs); it contains 3 % water vapor at 810 K, and its walls are at 1370 K. The emissivity of the sphere is equal to 0.44 – 0.00018 T, where T is the surface temperature in K. When the surface temperature of the sphere is 810 K determine (a) the total irradiation received by the walls of the oven from the sphere, (b) the net heat transfer by radiation between the sphere and the walls of the oven, and (c) the radiant heat transfer coefficient.
GIVEN
A small sphere in a 30 cm cubic heat oven filled with air
Sphere diameter (D) = 30 cm – 2.5 cm= 27.5 cm
Air pressure = 101 kPa(abs) = 1.01*105 Pa
Air contains 3% water vapor
Air temperature (Tm) = 810 K
Oven wall temperature (T2) = 1370 K
Sphere emissivity (?1) = 0.44 – 0.00018 T (T in K)
Sphere surface temperature (T1) = 810 K
FIND
(a) Total irradiation received by the walls from the sphere (q2)
(b) The net heat transfer by radiation between the sphere and the walls (q12)
(c) The radiant heat transfer coefficient (hr)
ASSUMPTIONS
The gas is a gray body
The oven walls are black (?2 = 1)
The sphere is near the center of the oven
SKETCH
PROPERTIES AND CONSTANTS
the Stephan-Boltzmann constant
(a)
The surface area of the sphere is
Since the air and the oven completely enclose the sphere, F12 = 1.0 and F1g = 1.0
the portion of the total radiation leaving the sphere that is received by the walls
where tm is the transmissivity of the air and the radio sity of the sphere, J1, is
Since the air temperature is the same as the sphere temperature, there will be no net heat transfer between the air and the sphere and the heat transfer from the sphere (q1) will be the same as the net heat transfer between the sphere and the walls (q12). Simplifying with the shape factors above and
Since the sphere is near the center of the cube, one half the beam length for a cube will be used
The partial pressure of the water vapor is
The emissivity of the water vapor (?m) can be calculated where Tm = 810 K
By Kirchoff’s radiation law
(b) The net radiation between the sphere and walls is 146.5 W from the walls to the sphere.
(c) The radiative heat transfer coefficient must satisfy the following equation
You might also like to view...
In a nuclear reactor, how many neutrons [on the average] created during the fission of a 235U nucleus cause further fission in other uranium nuclei?
A) None B) Less than one C) More than one D) One E) Ten
Energy Conservation With Conservative Forces: The figure shows a famous roller coaster ride. You can ignore friction. If the roller coaster leaves point Q from rest, what is its speed at the top of the 25-m peak (point S)
A. 10 m/s B. 22 m/s C. 44 m/s D. 62 m/s E. 120 m/s
Three resistors connected in parallel have individual values of 4.0, 6.0, and 10.0 ?, respectively. If this combination is connected in series with a 12-V battery and a 2.0-? resistor, what is the current in the 10.0-? resistor?
a.
0.55 A
b.
1.0 A
c.
11 A
d.
16 A
A 40-kg boy is standing on the edge of a stationary 30-kg circular platform that is free to rotate. The boy tries to walk around the platform in a counterclockwise direction. As he does:
a. the platform doesn't rotate. b. the platform rotates in a clockwise direction just fast enough so that the boy remains stationary relative to the ground. c. the platform rotates in a clockwise direction while the boy goes around in a counterclockwise direction relative to the ground. d. both go around with equal angular velocities but in opposite directions.