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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?
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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.
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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?
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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?.
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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
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