Mechanical Engineering Exam > Mechanical Engineering Questions > The temperature distribution for a sphere for...
Start Learning for Free
The temperature distribution for a sphere for steady state heat flow and constant value of thermal conductivity is
- a)logarithmic
- b)parabolic
- c)hyperbolic
- d)exponential
Correct answer is option 'C'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
The temperature distribution for a sphere for steady state heat flow a...
Hence profile will be hyperbolic.
Most Upvoted Answer
The temperature distribution for a sphere for steady state heat flow a...
Understanding Steady State Heat Flow in a Sphere
In a sphere with steady-state heat conduction and constant thermal conductivity, the temperature distribution is derived from the principles of heat transfer.
Key Concepts
- Steady-State Condition: This implies that the temperature within the sphere does not change with time. The heat entering a volume equals the heat leaving it.
- Spherical Coordinates: The analysis is conducted in spherical coordinates (r, θ, φ), where 'r' represents the radial distance from the center of the sphere.
Mathematical Derivation
- Heat Equation: The heat conduction equation in spherical coordinates leads to a differential equation where the radial temperature distribution depends only on the radial distance 'r'.
- Boundary Conditions: By applying appropriate boundary conditions (such as temperatures at the surface or center), we can solve the differential equation to find the temperature profile.
Temperature Distribution
- Hyperbolic Nature: The solution to the differential equation results in a hyperbolic relationship, typically represented as:
- T(r) = A + B * ln(r), where A and B are constants determined by boundary conditions.
- Physical Interpretation: This hyperbolic behavior indicates that as one moves from the center to the surface of the sphere, the temperature decreases logarithmically, which is characteristic of heat conduction in spherical bodies.
Conclusion
The temperature distribution in a sphere under steady-state conditions and constant thermal conductivity indeed exhibits a hyperbolic nature, making option 'C' the correct answer. Understanding this concept is crucial for applications in thermal management and engineering designs involving spherical geometries.
In a sphere with steady-state heat conduction and constant thermal conductivity, the temperature distribution is derived from the principles of heat transfer.
Key Concepts
- Steady-State Condition: This implies that the temperature within the sphere does not change with time. The heat entering a volume equals the heat leaving it.
- Spherical Coordinates: The analysis is conducted in spherical coordinates (r, θ, φ), where 'r' represents the radial distance from the center of the sphere.
Mathematical Derivation
- Heat Equation: The heat conduction equation in spherical coordinates leads to a differential equation where the radial temperature distribution depends only on the radial distance 'r'.
- Boundary Conditions: By applying appropriate boundary conditions (such as temperatures at the surface or center), we can solve the differential equation to find the temperature profile.
Temperature Distribution
- Hyperbolic Nature: The solution to the differential equation results in a hyperbolic relationship, typically represented as:
- T(r) = A + B * ln(r), where A and B are constants determined by boundary conditions.
- Physical Interpretation: This hyperbolic behavior indicates that as one moves from the center to the surface of the sphere, the temperature decreases logarithmically, which is characteristic of heat conduction in spherical bodies.
Conclusion
The temperature distribution in a sphere under steady-state conditions and constant thermal conductivity indeed exhibits a hyperbolic nature, making option 'C' the correct answer. Understanding this concept is crucial for applications in thermal management and engineering designs involving spherical geometries.
Attention Mechanical Engineering Students!
To make sure you are not studying endlessly, EduRev has designed Mechanical Engineering study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Mechanical Engineering.
|
Explore Courses for Mechanical Engineering exam
|
|
Similar Mechanical Engineering Doubts
Top Courses for Mechanical EngineeringView all
The temperature distribution for a sphere for steady state heat flow and constant value of thermal conductivity isa)logarithmicb)parabolicc)hyperbolicd)exponentialCorrect answer is option 'C'. Can you explain this answer?
Question Description
The temperature distribution for a sphere for steady state heat flow and constant value of thermal conductivity isa)logarithmicb)parabolicc)hyperbolicd)exponentialCorrect answer is option 'C'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about The temperature distribution for a sphere for steady state heat flow and constant value of thermal conductivity isa)logarithmicb)parabolicc)hyperbolicd)exponentialCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The temperature distribution for a sphere for steady state heat flow and constant value of thermal conductivity isa)logarithmicb)parabolicc)hyperbolicd)exponentialCorrect answer is option 'C'. Can you explain this answer?.
The temperature distribution for a sphere for steady state heat flow and constant value of thermal conductivity isa)logarithmicb)parabolicc)hyperbolicd)exponentialCorrect answer is option 'C'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about The temperature distribution for a sphere for steady state heat flow and constant value of thermal conductivity isa)logarithmicb)parabolicc)hyperbolicd)exponentialCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The temperature distribution for a sphere for steady state heat flow and constant value of thermal conductivity isa)logarithmicb)parabolicc)hyperbolicd)exponentialCorrect answer is option 'C'. Can you explain this answer?.
Solutions for The temperature distribution for a sphere for steady state heat flow and constant value of thermal conductivity isa)logarithmicb)parabolicc)hyperbolicd)exponentialCorrect answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for Mechanical Engineering.
Download more important topics, notes, lectures and mock test series for Mechanical Engineering Exam by signing up for free.
Here you can find the meaning of The temperature distribution for a sphere for steady state heat flow and constant value of thermal conductivity isa)logarithmicb)parabolicc)hyperbolicd)exponentialCorrect answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
The temperature distribution for a sphere for steady state heat flow and constant value of thermal conductivity isa)logarithmicb)parabolicc)hyperbolicd)exponentialCorrect answer is option 'C'. Can you explain this answer?, a detailed solution for The temperature distribution for a sphere for steady state heat flow and constant value of thermal conductivity isa)logarithmicb)parabolicc)hyperbolicd)exponentialCorrect answer is option 'C'. Can you explain this answer? has been provided alongside types of The temperature distribution for a sphere for steady state heat flow and constant value of thermal conductivity isa)logarithmicb)parabolicc)hyperbolicd)exponentialCorrect answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice The temperature distribution for a sphere for steady state heat flow and constant value of thermal conductivity isa)logarithmicb)parabolicc)hyperbolicd)exponentialCorrect answer is option 'C'. Can you explain this answer? tests, examples and also practice Mechanical Engineering tests.
|
|
Explore Courses for Mechanical 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