Chemical Engineering Exam > Chemical Engineering Questions > A metal wire of 0.01 m dia and thermal conduc...
Start Learning for Free
A metal wire of 0.01 m dia and thermal conductivity 200 W/m.K is exposed to a fluid stream with a convective heat transfer coefficient of 100 W/m2.K. The Biot number is
- a)5.6
- b)0.025
- c)3.5
- d)0.0035
Correct answer is option 'B'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
A metal wire of 0.01 m dia and thermal conductivity 200 W/m.K is expos...
The Biot number is
0.025Most Upvoted Answer
A metal wire of 0.01 m dia and thermal conductivity 200 W/m.K is expos...
To calculate the Biot number, we need to compare the resistance to heat transfer inside the wire (due to conduction) with the resistance to heat transfer at the surface of the wire (due to convection). The Biot number is defined as the ratio of the internal resistance to the external resistance.
Given data:
- Diameter of the wire (D): 0.01 m
- Thermal conductivity of the wire (k): 200 W/m.K
- Convective heat transfer coefficient (h): 100 W/m2.K
Let's calculate the Biot number step by step:
1. Calculate the characteristic length:
The characteristic length for a wire is its diameter. In this case, the characteristic length (L) is equal to the diameter of the wire, which is 0.01 m.
2. Calculate the internal resistance (Ri):
The internal resistance is due to conduction inside the wire. For a cylindrical shape, the resistance is given by the formula:
Ri = ln(r2/r1)/(2πkL), where r1 and r2 are the inner and outer radii of the wire.
In this case, the wire is solid, so r1 = 0 and r2 = D/2 = 0.01/2 = 0.005 m.
Ri = ln(0.005/0)/(2π(200)(0.01)) = ln(0.005)/(2π(200)(0.01))
3. Calculate the external resistance (Re):
The external resistance is due to convection at the surface of the wire. For a cylindrical shape, the resistance is given by the formula:
Re = 1/(h2πDL), where D is the diameter of the wire and L is the characteristic length.
Re = 1/(100(2π)(0.01)(0.01))
4. Calculate the Biot number (Bi):
Bi = Ri/Re = (ln(0.005)/(2π(200)(0.01))) / (1/(100(2π)(0.01)(0.01)))
Simplifying the expression:
Bi = (100(2π)(0.01)(0.01)ln(0.005)) / (2π(200)(0.01))
Bi = 100ln(0.005)/200
Calculating the value:
Bi = 0.025
Therefore, the Biot number is 0.025.
Given data:
- Diameter of the wire (D): 0.01 m
- Thermal conductivity of the wire (k): 200 W/m.K
- Convective heat transfer coefficient (h): 100 W/m2.K
Let's calculate the Biot number step by step:
1. Calculate the characteristic length:
The characteristic length for a wire is its diameter. In this case, the characteristic length (L) is equal to the diameter of the wire, which is 0.01 m.
2. Calculate the internal resistance (Ri):
The internal resistance is due to conduction inside the wire. For a cylindrical shape, the resistance is given by the formula:
Ri = ln(r2/r1)/(2πkL), where r1 and r2 are the inner and outer radii of the wire.
In this case, the wire is solid, so r1 = 0 and r2 = D/2 = 0.01/2 = 0.005 m.
Ri = ln(0.005/0)/(2π(200)(0.01)) = ln(0.005)/(2π(200)(0.01))
3. Calculate the external resistance (Re):
The external resistance is due to convection at the surface of the wire. For a cylindrical shape, the resistance is given by the formula:
Re = 1/(h2πDL), where D is the diameter of the wire and L is the characteristic length.
Re = 1/(100(2π)(0.01)(0.01))
4. Calculate the Biot number (Bi):
Bi = Ri/Re = (ln(0.005)/(2π(200)(0.01))) / (1/(100(2π)(0.01)(0.01)))
Simplifying the expression:
Bi = (100(2π)(0.01)(0.01)ln(0.005)) / (2π(200)(0.01))
Bi = 100ln(0.005)/200
Calculating the value:
Bi = 0.025
Therefore, the Biot number is 0.025.
|
Explore Courses for Chemical Engineering exam
|
|
Similar Chemical Engineering Doubts
A metal wire of 0.01 m dia and thermal conductivity 200 W/m.K is exposed to a fluid stream with a convective heat transfer coefficient of 100 W/m2.K. The Biot number isa)5.6b)0.025c)3.5d)0.0035Correct answer is option 'B'. Can you explain this answer?
Question Description
A metal wire of 0.01 m dia and thermal conductivity 200 W/m.K is exposed to a fluid stream with a convective heat transfer coefficient of 100 W/m2.K. The Biot number isa)5.6b)0.025c)3.5d)0.0035Correct answer is option 'B'. Can you explain this answer? for Chemical Engineering 2024 is part of Chemical Engineering preparation. The Question and answers have been prepared according to the Chemical Engineering exam syllabus. Information about A metal wire of 0.01 m dia and thermal conductivity 200 W/m.K is exposed to a fluid stream with a convective heat transfer coefficient of 100 W/m2.K. The Biot number isa)5.6b)0.025c)3.5d)0.0035Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Chemical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A metal wire of 0.01 m dia and thermal conductivity 200 W/m.K is exposed to a fluid stream with a convective heat transfer coefficient of 100 W/m2.K. The Biot number isa)5.6b)0.025c)3.5d)0.0035Correct answer is option 'B'. Can you explain this answer?.
A metal wire of 0.01 m dia and thermal conductivity 200 W/m.K is exposed to a fluid stream with a convective heat transfer coefficient of 100 W/m2.K. The Biot number isa)5.6b)0.025c)3.5d)0.0035Correct answer is option 'B'. Can you explain this answer? for Chemical Engineering 2024 is part of Chemical Engineering preparation. The Question and answers have been prepared according to the Chemical Engineering exam syllabus. Information about A metal wire of 0.01 m dia and thermal conductivity 200 W/m.K is exposed to a fluid stream with a convective heat transfer coefficient of 100 W/m2.K. The Biot number isa)5.6b)0.025c)3.5d)0.0035Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Chemical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A metal wire of 0.01 m dia and thermal conductivity 200 W/m.K is exposed to a fluid stream with a convective heat transfer coefficient of 100 W/m2.K. The Biot number isa)5.6b)0.025c)3.5d)0.0035Correct answer is option 'B'. Can you explain this answer?.
Solutions for A metal wire of 0.01 m dia and thermal conductivity 200 W/m.K is exposed to a fluid stream with a convective heat transfer coefficient of 100 W/m2.K. The Biot number isa)5.6b)0.025c)3.5d)0.0035Correct answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for Chemical Engineering.
Download more important topics, notes, lectures and mock test series for Chemical Engineering Exam by signing up for free.
Here you can find the meaning of A metal wire of 0.01 m dia and thermal conductivity 200 W/m.K is exposed to a fluid stream with a convective heat transfer coefficient of 100 W/m2.K. The Biot number isa)5.6b)0.025c)3.5d)0.0035Correct answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
A metal wire of 0.01 m dia and thermal conductivity 200 W/m.K is exposed to a fluid stream with a convective heat transfer coefficient of 100 W/m2.K. The Biot number isa)5.6b)0.025c)3.5d)0.0035Correct answer is option 'B'. Can you explain this answer?, a detailed solution for A metal wire of 0.01 m dia and thermal conductivity 200 W/m.K is exposed to a fluid stream with a convective heat transfer coefficient of 100 W/m2.K. The Biot number isa)5.6b)0.025c)3.5d)0.0035Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of A metal wire of 0.01 m dia and thermal conductivity 200 W/m.K is exposed to a fluid stream with a convective heat transfer coefficient of 100 W/m2.K. The Biot number isa)5.6b)0.025c)3.5d)0.0035Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A metal wire of 0.01 m dia and thermal conductivity 200 W/m.K is exposed to a fluid stream with a convective heat transfer coefficient of 100 W/m2.K. The Biot number isa)5.6b)0.025c)3.5d)0.0035Correct answer is option 'B'. Can you explain this answer? tests, examples and also practice Chemical Engineering tests.
|
|
Explore Courses for Chemical Engineering exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup