A quartz window of thickness L serves as a viewing port in a furnace used for annealing steel. The inner surface ( x = 0 ) of the window is irradiated with a uniform heat flux q o n due to emission from hot gases in the furnace. A fraction, β , of this radiation may be assumed to be absorbed at the inner surface, while the remaining radiation is partially absorbed as it passes through the quartz. The volumetric heat generation due to this absorption may be described by an expression of the form q . ( x ) = ( 1 − β ) q o n α e − a x where α is the absorption coefficient of the quartz. Convection heat transfer occurs from the outer surface ( x = L ) of the window to ambient air at T ∞ , and is characterized by the convection coefficient h. Convection and radiation emission from the inner surface may be neglected. along with radiation emission from the outer surface. Determine the temperature distribution in the quartz. expressing your result in terms of the foregoing parameters.
A quartz window of thickness L serves as a viewing port in a furnace used for annealing steel. The inner surface ( x = 0 ) of the window is irradiated with a uniform heat flux q o n due to emission from hot gases in the furnace. A fraction, β , of this radiation may be assumed to be absorbed at the inner surface, while the remaining radiation is partially absorbed as it passes through the quartz. The volumetric heat generation due to this absorption may be described by an expression of the form q . ( x ) = ( 1 − β ) q o n α e − a x where α is the absorption coefficient of the quartz. Convection heat transfer occurs from the outer surface ( x = L ) of the window to ambient air at T ∞ , and is characterized by the convection coefficient h. Convection and radiation emission from the inner surface may be neglected. along with radiation emission from the outer surface. Determine the temperature distribution in the quartz. expressing your result in terms of the foregoing parameters.
Solution Summary: The author explains the temperature distribution T in terms of forgoing parameters.
A quartz window of thickness L serves as a viewing port in a furnace used for annealing steel. The inner surface
(
x
=
0
)
of the window is irradiated with a uniform heat flux
q
o
n
due to emission from hot gases in the furnace. A fraction,
β
,
of this radiation may be assumed to be absorbed at the inner surface, while the remaining radiation is partially absorbed as it passes through the quartz. The volumetric heat generation due to this absorption may be described by an expression of the form
q
.
(
x
)
=
(
1
−
β
)
q
o
n
α
e
−
a
x
where
α
is the absorption coefficient of the quartz. Convection heat transfer occurs from the outer surface
(
x
=
L
)
of the window to ambient air at
T
∞
,
and is characterized by the convection coefficient h. Convection and radiation emission from the inner surface may be neglected. along with radiation emission from the outer surface. Determine the temperature distribution in the quartz. expressing your result in terms of the foregoing parameters.
Heat transfer problem.The internal surface area is an enclosure is 50 meter square. The surface is black and maintained at constant temperature. A small opening in the enclosure has area 0.05 meter square. The radiant power emitted from the opening is 52W. (A) what’s the temperature of the interior enclosure wall. (B)if the interior surface is maintained in this temperature, but polished so that emissivity is 0.15, what will be the radiant power emitted in the opening.
You are designing a chamber to contain the radiation emitted by nuclear decay during a
fusion reaction. The left face of the (plane) chamber wall (x = 0) is exposed to the radiation
and the right face of the wall (x = L) is perfectly insulated. To facilitate the fusion reaction,
the left face of the wall is maintained at fixed temperature To. The radiation penetrates the
wall causing uniform heat generation that varies with location inside the wall as
) = 40 (1 - 1)
g(x)
where qo [W/m^3 ] is a constant. Determine an expression for the temperature distribution
in the wall T(x) assuming the thermal conductivity of the wall (k) is constant.
An infrared camera is used to measure a temperature at a tissue location. The infrared
camera uses the same equation as that in the lecture notes. When the total hemispherical emissivity is
selected as &=1.0, the temperature reading on the camera is 45°C.
(a) Based on the equation given in the notes, please calculate the radiation heat flux received by the
camera qck. The Stefan-Boltzmann's constant ois 5.67*108 W/(m²K¹).
(b) However, you notice that the actual emissivity of the tissue surface should be 0.95. The room
temperature is 20°C. Use the equation again to calculate the temperature of the tissue location, note that
qck should be the same as in (a). What is the absolute error of the measurement if both the room
temperature and deviation from a perfect blackbody surface are not considered?
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