A long, cylindrical, electrical heating element of diameter D=D= 10 mm, thermal conductivity k=k= 240 W/m·K, density ρ=ρ
Posted: Tue Apr 26, 2022 5:00 pm
A long, cylindrical, electrical heating element of
diameter D=D= 10 mm, thermal
conductivity k=k= 240 W/m·K, density ρ=ρ= 2700
kg/m3, and specific heat cp=cp= 900 J/kg·K is
installed in a duct for which air moves in cross flow over the
heater at a temperature and velocity of 27°C and 20 m/s,
respectively.
(a) Neglecting radiation, estimate the steady-state surface
temperature when, per unit length of the heater, electrical energy
is being dissipated at a rate of 2000 W/m.
(b) If the heater is activated from an initial temperature of 27°C,
estimate the time required for the surface temperature to come
within 10°C of its steady-state value.
Evaluate the properties of air at 450 K.
Step 1
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What is the value of the Reynolds number?
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What is the value of the average Nusselt number?
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Step 3
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What is the steady state temperature, in K?
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Step 4
What is the value of the Biot number?
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Step 5
How long does it take for the element to come within 10°C of the
steady state temperature, in s?
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Step 6
Knowing the steady state temperature, what is the actual value
of the film temperature that should be used to find the air
properties, in K? (Do not redo the problem.)
diameter D=D= 10 mm, thermal
conductivity k=k= 240 W/m·K, density ρ=ρ= 2700
kg/m3, and specific heat cp=cp= 900 J/kg·K is
installed in a duct for which air moves in cross flow over the
heater at a temperature and velocity of 27°C and 20 m/s,
respectively.
(a) Neglecting radiation, estimate the steady-state surface
temperature when, per unit length of the heater, electrical energy
is being dissipated at a rate of 2000 W/m.
(b) If the heater is activated from an initial temperature of 27°C,
estimate the time required for the surface temperature to come
within 10°C of its steady-state value.
Evaluate the properties of air at 450 K.
Step 1
Correct answer icon
Your answer is correct.
What is the value of the Reynolds number?
Attempts: unlimited
Question Part Score
2/2
Step 2
New attempt is in progress. Some of the new entries may impact
the last attempt grading.
Your answer is incorrect.
What is the value of the average Nusselt number?
Save for Later
Attempts: unlimited
Submit Answer
Question Part Score
0/2
Step 3
Incorrect answer icon
Your answer is incorrect.
What is the steady state temperature, in K?
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Attempts: unlimited
Submit Answer
Question Part Score
0/2
Step 4
What is the value of the Biot number?
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Attempts: unlimited
Submit Answer
Question Part Score
--/2
Step 5
How long does it take for the element to come within 10°C of the
steady state temperature, in s?
Save for Later
Attempts: unlimited
Submit Answer
Question Part Score
--/2
Step 6
Knowing the steady state temperature, what is the actual value
of the film temperature that should be used to find the air
properties, in K? (Do not redo the problem.)