A copper sphere initially at a uniform temperature To is immersed in a fluid. Electric heaters are placed in the fluid and controlled so that the temperature of the fluid follows a periodic variation given by Too - Tm = A sin wt where Tm = time-average mean fluid temperature A = amplitude of temperature wave @= = frequency Derive an expression for the temperature of the sphere as a function of time and the heat-transfer coefficient from the fluid to the sphere. Assume that the tempres of the sphere and fluid are uniform at any instant so that the lumped-capacity method of analysis may be used.
A copper sphere initially at a uniform temperature To is immersed in a fluid. Electric heaters are placed in the fluid and controlled so that the temperature of the fluid follows a periodic variation given by Too - Tm = A sin wt where Tm = time-average mean fluid temperature A = amplitude of temperature wave @= = frequency Derive an expression for the temperature of the sphere as a function of time and the heat-transfer coefficient from the fluid to the sphere. Assume that the tempres of the sphere and fluid are uniform at any instant so that the lumped-capacity method of analysis may be used.
Introduction to Chemical Engineering Thermodynamics
8th Edition
ISBN:9781259696527
Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Chapter1: Introduction
Section: Chapter Questions
Problem 1.1P
Related questions
Question
![A copper sphere initially at a uniform temperature To is immersed in a fluid. Electric
heaters are placed in the fluid and controlled so that the temperature of the fluid
follows a periodic variation given by
Too - Tm A sin wt
where
Tm = time-average mean fluid temperature
A = amplitude of temperature wave
@= frequency
Derive an expression for the temperature of the sphere as a function of time and the
heat-transfer coefficient from the fluid to the sphere. Assume that the temperares
of the sphere and fluid are uniform at any instant so that the lumped-capacity method
of analysis may be used.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcc8f37f3-92d8-410c-ac96-c718ecb99213%2Fa19903ca-0bab-4797-8f8a-c2353bf6ac50%2Fgqqewtm_processed.jpeg&w=3840&q=75)
Transcribed Image Text:A copper sphere initially at a uniform temperature To is immersed in a fluid. Electric
heaters are placed in the fluid and controlled so that the temperature of the fluid
follows a periodic variation given by
Too - Tm A sin wt
where
Tm = time-average mean fluid temperature
A = amplitude of temperature wave
@= frequency
Derive an expression for the temperature of the sphere as a function of time and the
heat-transfer coefficient from the fluid to the sphere. Assume that the temperares
of the sphere and fluid are uniform at any instant so that the lumped-capacity method
of analysis may be used.
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 9 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Recommended textbooks for you
![Introduction to Chemical Engineering Thermodynami…](https://www.bartleby.com/isbn_cover_images/9781259696527/9781259696527_smallCoverImage.gif)
Introduction to Chemical Engineering Thermodynami…
Chemical Engineering
ISBN:
9781259696527
Author:
J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:
McGraw-Hill Education
![Elementary Principles of Chemical Processes, Bind…](https://www.bartleby.com/isbn_cover_images/9781118431221/9781118431221_smallCoverImage.gif)
Elementary Principles of Chemical Processes, Bind…
Chemical Engineering
ISBN:
9781118431221
Author:
Richard M. Felder, Ronald W. Rousseau, Lisa G. Bullard
Publisher:
WILEY
![Elements of Chemical Reaction Engineering (5th Ed…](https://www.bartleby.com/isbn_cover_images/9780133887518/9780133887518_smallCoverImage.gif)
Elements of Chemical Reaction Engineering (5th Ed…
Chemical Engineering
ISBN:
9780133887518
Author:
H. Scott Fogler
Publisher:
Prentice Hall
![Introduction to Chemical Engineering Thermodynami…](https://www.bartleby.com/isbn_cover_images/9781259696527/9781259696527_smallCoverImage.gif)
Introduction to Chemical Engineering Thermodynami…
Chemical Engineering
ISBN:
9781259696527
Author:
J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:
McGraw-Hill Education
![Elementary Principles of Chemical Processes, Bind…](https://www.bartleby.com/isbn_cover_images/9781118431221/9781118431221_smallCoverImage.gif)
Elementary Principles of Chemical Processes, Bind…
Chemical Engineering
ISBN:
9781118431221
Author:
Richard M. Felder, Ronald W. Rousseau, Lisa G. Bullard
Publisher:
WILEY
![Elements of Chemical Reaction Engineering (5th Ed…](https://www.bartleby.com/isbn_cover_images/9780133887518/9780133887518_smallCoverImage.gif)
Elements of Chemical Reaction Engineering (5th Ed…
Chemical Engineering
ISBN:
9780133887518
Author:
H. Scott Fogler
Publisher:
Prentice Hall
![Process Dynamics and Control, 4e](https://www.bartleby.com/isbn_cover_images/9781119285915/9781119285915_smallCoverImage.gif)
![Industrial Plastics: Theory and Applications](https://www.bartleby.com/isbn_cover_images/9781285061238/9781285061238_smallCoverImage.gif)
Industrial Plastics: Theory and Applications
Chemical Engineering
ISBN:
9781285061238
Author:
Lokensgard, Erik
Publisher:
Delmar Cengage Learning
![Unit Operations of Chemical Engineering](https://www.bartleby.com/isbn_cover_images/9780072848236/9780072848236_smallCoverImage.gif)
Unit Operations of Chemical Engineering
Chemical Engineering
ISBN:
9780072848236
Author:
Warren McCabe, Julian C. Smith, Peter Harriott
Publisher:
McGraw-Hill Companies, The