7.36 A long, cylindrical, electrical heating element of diameter D = 12 mm, thermal conductivity k = 240 W/m. K, den- sity p = 2700 kg/m³, and specific heat c, = 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 30°C and 8 m/s, respectively. (a) Neglecting radiation, estimate the steady-state sur- face temperature when, per unit length of the heater, electrical energy is being dissipated at a rate of 1000 W/m. (b) If the heater is activated from an initial temperature of 30°C, estimate the time required for the surface temperature to come within 10°C of its steady-state value.
7.36 A long, cylindrical, electrical heating element of diameter D = 12 mm, thermal conductivity k = 240 W/m. K, den- sity p = 2700 kg/m³, and specific heat c, = 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 30°C and 8 m/s, respectively. (a) Neglecting radiation, estimate the steady-state sur- face temperature when, per unit length of the heater, electrical energy is being dissipated at a rate of 1000 W/m. (b) If the heater is activated from an initial temperature of 30°C, estimate the time required for the surface temperature to come within 10°C of its steady-state value.
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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![7.36 A long, cylindrical, electrical heating element of diameter
D = 12 mm, thermal conductivity k = 240 W/mK, den-
sity p = 2700 kg/m³, and specific heat 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 30°C
and 8 m/s, respectively.
(a) Neglecting radiation, estimate the steady-state sur-
face temperature when, per unit length of the heater,
electrical energy is being dissipated at a rate of
1000 W/m.
(b) If the heater is activated from an initial temperature
of 30°C, estimate the time required for the surface
temperature to come within 10°C of its steady-state
value.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F53a2441e-c8b0-4860-bf8a-5f8d74e1cf79%2F66a28bcc-8d9c-4180-a556-15932f2c79ab%2Fhzc1pad_processed.png&w=3840&q=75)
Transcribed Image Text:7.36 A long, cylindrical, electrical heating element of diameter
D = 12 mm, thermal conductivity k = 240 W/mK, den-
sity p = 2700 kg/m³, and specific heat 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 30°C
and 8 m/s, respectively.
(a) Neglecting radiation, estimate the steady-state sur-
face temperature when, per unit length of the heater,
electrical energy is being dissipated at a rate of
1000 W/m.
(b) If the heater is activated from an initial temperature
of 30°C, estimate the time required for the surface
temperature to come within 10°C of its steady-state
value.
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