UPSC Exam > UPSC Questions > A stainless steel tube (k_{s} = 19W / m * K) ...
Start Learning for Free
A stainless steel tube (k_{s} = 19W / m * K) of 2 cm ID and 5 cm OD is insulated with 3 cm thick asbestos (k = 0.2 W/mK). If the temperature difference between the innermost and outermost surfaces is 600 deg * C the heat transfer rate per unit length is: (a) 0.94W / m (b) 9.44W / m (c) 944.72W / m (d) 9447.21W / m?
Most Upvoted Answer
A stainless steel tube (k_{s} = 19W / m * K) of 2 cm ID and 5 cm OD is...
Given Data:
Inner diameter (ID) of stainless steel tube = 2 cm = 0.02 m
Outer diameter (OD) of stainless steel tube = 5 cm = 0.05 m
Insulation thickness = 3 cm = 0.03 m
Temperature difference = 600°C = 600 K
Thermal conductivity of stainless steel (ks) = 19 W/m*K
Thermal conductivity of asbestos (k) = 0.2 W/m*K
Calculations:
1. Calculate the outer radius of the stainless steel tube:
Outer radius (Ro) = OD / 2 = 0.05 / 2 = 0.025 m
2. Calculate the inner radius of the stainless steel tube:
Inner radius (Ri) = ID / 2 = 0.02 / 2 = 0.01 m
3. Calculate the radius of the insulation layer:
Radius of insulation (Rins) = Ro + Insulation thickness = 0.025 + 0.03 = 0.055 m
4. Calculate the thermal resistance of the stainless steel tube:
Resistance of stainless steel (Rss) = ln(Ro / Ri) / (2 * π * ks * length)
= ln(0.025 / 0.01) / (2 * π * 19 * length)
= 0.549 / (119.38 * length)
= 0.0046 / length
5. Calculate the thermal resistance of the insulation layer:
Resistance of insulation (Rins) = ln(Rins / Ro) / (2 * π * k * length)
= ln(0.055 / 0.025) / (2 * π * 0.2 * length)
= 0.641 / (3.14 * 0.4 * length)
= 0.512 / length
6. Total thermal resistance (Rtotal) = Rss + Rins
= 0.0046 / length + 0.512 / length
= 0.5166 / length
7. Calculate the heat transfer rate per unit length:
Heat transfer rate = Temperature difference / Rtotal
= 600 / 0.5166
≈ 1161.73 W/m
Answer:
The heat transfer rate per unit length is approximately 1161.73 W/m. Therefore, the closest option provided is (c) 944.72 W/m.
Inner diameter (ID) of stainless steel tube = 2 cm = 0.02 m
Outer diameter (OD) of stainless steel tube = 5 cm = 0.05 m
Insulation thickness = 3 cm = 0.03 m
Temperature difference = 600°C = 600 K
Thermal conductivity of stainless steel (ks) = 19 W/m*K
Thermal conductivity of asbestos (k) = 0.2 W/m*K
Calculations:
1. Calculate the outer radius of the stainless steel tube:
Outer radius (Ro) = OD / 2 = 0.05 / 2 = 0.025 m
2. Calculate the inner radius of the stainless steel tube:
Inner radius (Ri) = ID / 2 = 0.02 / 2 = 0.01 m
3. Calculate the radius of the insulation layer:
Radius of insulation (Rins) = Ro + Insulation thickness = 0.025 + 0.03 = 0.055 m
4. Calculate the thermal resistance of the stainless steel tube:
Resistance of stainless steel (Rss) = ln(Ro / Ri) / (2 * π * ks * length)
= ln(0.025 / 0.01) / (2 * π * 19 * length)
= 0.549 / (119.38 * length)
= 0.0046 / length
5. Calculate the thermal resistance of the insulation layer:
Resistance of insulation (Rins) = ln(Rins / Ro) / (2 * π * k * length)
= ln(0.055 / 0.025) / (2 * π * 0.2 * length)
= 0.641 / (3.14 * 0.4 * length)
= 0.512 / length
6. Total thermal resistance (Rtotal) = Rss + Rins
= 0.0046 / length + 0.512 / length
= 0.5166 / length
7. Calculate the heat transfer rate per unit length:
Heat transfer rate = Temperature difference / Rtotal
= 600 / 0.5166
≈ 1161.73 W/m
Answer:
The heat transfer rate per unit length is approximately 1161.73 W/m. Therefore, the closest option provided is (c) 944.72 W/m.
Attention UPSC Students!
To make sure you are not studying endlessly, EduRev has designed UPSC study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in UPSC.
|
Explore Courses for UPSC exam
|
|
Top Courses for UPSCView all
A stainless steel tube (k_{s} = 19W / m * K) of 2 cm ID and 5 cm OD is insulated with 3 cm thick asbestos (k = 0.2 W/mK). If the temperature difference between the innermost and outermost surfaces is 600 deg * C the heat transfer rate per unit length is: (a) 0.94W / m (b) 9.44W / m (c) 944.72W / m (d) 9447.21W / m?
Question Description
A stainless steel tube (k_{s} = 19W / m * K) of 2 cm ID and 5 cm OD is insulated with 3 cm thick asbestos (k = 0.2 W/mK). If the temperature difference between the innermost and outermost surfaces is 600 deg * C the heat transfer rate per unit length is: (a) 0.94W / m (b) 9.44W / m (c) 944.72W / m (d) 9447.21W / m? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A stainless steel tube (k_{s} = 19W / m * K) of 2 cm ID and 5 cm OD is insulated with 3 cm thick asbestos (k = 0.2 W/mK). If the temperature difference between the innermost and outermost surfaces is 600 deg * C the heat transfer rate per unit length is: (a) 0.94W / m (b) 9.44W / m (c) 944.72W / m (d) 9447.21W / m? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A stainless steel tube (k_{s} = 19W / m * K) of 2 cm ID and 5 cm OD is insulated with 3 cm thick asbestos (k = 0.2 W/mK). If the temperature difference between the innermost and outermost surfaces is 600 deg * C the heat transfer rate per unit length is: (a) 0.94W / m (b) 9.44W / m (c) 944.72W / m (d) 9447.21W / m?.
A stainless steel tube (k_{s} = 19W / m * K) of 2 cm ID and 5 cm OD is insulated with 3 cm thick asbestos (k = 0.2 W/mK). If the temperature difference between the innermost and outermost surfaces is 600 deg * C the heat transfer rate per unit length is: (a) 0.94W / m (b) 9.44W / m (c) 944.72W / m (d) 9447.21W / m? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A stainless steel tube (k_{s} = 19W / m * K) of 2 cm ID and 5 cm OD is insulated with 3 cm thick asbestos (k = 0.2 W/mK). If the temperature difference between the innermost and outermost surfaces is 600 deg * C the heat transfer rate per unit length is: (a) 0.94W / m (b) 9.44W / m (c) 944.72W / m (d) 9447.21W / m? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A stainless steel tube (k_{s} = 19W / m * K) of 2 cm ID and 5 cm OD is insulated with 3 cm thick asbestos (k = 0.2 W/mK). If the temperature difference between the innermost and outermost surfaces is 600 deg * C the heat transfer rate per unit length is: (a) 0.94W / m (b) 9.44W / m (c) 944.72W / m (d) 9447.21W / m?.
Solutions for A stainless steel tube (k_{s} = 19W / m * K) of 2 cm ID and 5 cm OD is insulated with 3 cm thick asbestos (k = 0.2 W/mK). If the temperature difference between the innermost and outermost surfaces is 600 deg * C the heat transfer rate per unit length is: (a) 0.94W / m (b) 9.44W / m (c) 944.72W / m (d) 9447.21W / m? in English & in Hindi are available as part of our courses for UPSC.
Download more important topics, notes, lectures and mock test series for UPSC Exam by signing up for free.
Here you can find the meaning of A stainless steel tube (k_{s} = 19W / m * K) of 2 cm ID and 5 cm OD is insulated with 3 cm thick asbestos (k = 0.2 W/mK). If the temperature difference between the innermost and outermost surfaces is 600 deg * C the heat transfer rate per unit length is: (a) 0.94W / m (b) 9.44W / m (c) 944.72W / m (d) 9447.21W / m? defined & explained in the simplest way possible. Besides giving the explanation of
A stainless steel tube (k_{s} = 19W / m * K) of 2 cm ID and 5 cm OD is insulated with 3 cm thick asbestos (k = 0.2 W/mK). If the temperature difference between the innermost and outermost surfaces is 600 deg * C the heat transfer rate per unit length is: (a) 0.94W / m (b) 9.44W / m (c) 944.72W / m (d) 9447.21W / m?, a detailed solution for A stainless steel tube (k_{s} = 19W / m * K) of 2 cm ID and 5 cm OD is insulated with 3 cm thick asbestos (k = 0.2 W/mK). If the temperature difference between the innermost and outermost surfaces is 600 deg * C the heat transfer rate per unit length is: (a) 0.94W / m (b) 9.44W / m (c) 944.72W / m (d) 9447.21W / m? has been provided alongside types of A stainless steel tube (k_{s} = 19W / m * K) of 2 cm ID and 5 cm OD is insulated with 3 cm thick asbestos (k = 0.2 W/mK). If the temperature difference between the innermost and outermost surfaces is 600 deg * C the heat transfer rate per unit length is: (a) 0.94W / m (b) 9.44W / m (c) 944.72W / m (d) 9447.21W / m? theory, EduRev gives you an
ample number of questions to practice A stainless steel tube (k_{s} = 19W / m * K) of 2 cm ID and 5 cm OD is insulated with 3 cm thick asbestos (k = 0.2 W/mK). If the temperature difference between the innermost and outermost surfaces is 600 deg * C the heat transfer rate per unit length is: (a) 0.94W / m (b) 9.44W / m (c) 944.72W / m (d) 9447.21W / m? tests, examples and also practice UPSC tests.
|
|
Explore Courses for UPSC exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup