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.
First monthly exam
Gas dynamics
Third stage
Q1/Water at 15° C flow through a 300 mm diameter riveted steel pipe, E-3 mm with a head loss of 6 m in
300 m length. Determine the flow rate in pipe. Use moody chart.
Q2/ Assume a car's exhaust system can be approximated as 14 ft long and 0.125 ft-diameter cast-iron pipe (
= 0.00085 ft) with the equivalent of (6) regular 90° flanged elbows (KL = 0.3) and a muffler. The
muffler acts as a resistor with a loss coefficient of KL= 8.5. Determine the pressure at the beginning of the
exhaust system (pl) if the flowrate is 0.10 cfs, and the exhaust has the same properties as air.(p = 1.74 ×
10-3 slug/ft³, u= 4.7 x 10-7 lb.s/ft²) Use moody chart
(1)
MIDAS
Kel=0.3
Q3/Liquid ammonia at -20°C is flowing through a 30 m long section of a 5 mm diameter copper tube(e =
1.5 × 10-6 m) at a rate of 0.15 kg/s. Determine the pressure drop and the head losses.
.μ= 2.36 × 10-4 kg/m.s)p = 665.1 kg/m³
2/Y
Y+1
2Cp
Q1/ Show that
Cda
Az x
P1
mactual
Cdf
Af
R/T₁
2pf(P1-P2-zxgxpf)
Q2/ A simple jet carburetor has to supply 5 Kg of air per minute. The air is at a pressure of 1.013 bar
and a temperature of 27 °C. Calculate the throat diameter of the choke for air flow velocity of 90 m/sec.
Take velocity coefficient to be 0.8. Assume isentropic flow and the flow to be compressible.
Quiz/ Determine the air-fuel ratio supplied at 5000 m altitude by a carburetor which is adjusted to give
an air-fuel ratio of 14:1 at sea level where air temperature is 27 °C and pressure is 1.013 bar. The
temperature of air decreases with altitude as given by the expression
The air pressure decreases with altitude as per relation h = 19200 log10 (1.013), where P is in bar. State
any assumptions made.
t = ts
P
0.0065h
36
2) Use the method of MEMBERS to determine the true magnitude and
direction of the forces in members1 and 2 of the frame shown below
in Fig 3.2.
300lbs/ft
member-1
member-2
30°
Fig 3.2.
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