Consider a spherical aluminum tank used to store ice at 0oC with an internal radius of 0.6 m, wall 10 cm thick and k=15.1 W/(m.oC). The exposed surface of the container exchanges heat by convection with ambient air at 30oC and h=20 W/(m2.oC). Ask: (a) Write the differential equation that describes heat conduction through the wall; (b) Solve the equation to obtain the wall temperature profile of the tank as a function of the radial position, using as conditions boundary the temperatures of the surfaces T1 (at r=r1) and T2 (at r=r2); (c) Apply an energy balance on the surface r=r2 to estimate the temperature T2 (d) Obtain the heat gain rate (in W)
Consider a spherical aluminum tank used to store ice at 0oC with an internal radius of 0.6 m, wall 10 cm thick and k=15.1 W/(m.oC). The exposed surface of the container exchanges heat by convection with ambient air at 30oC and h=20 W/(m2.oC). Ask: (a) Write the differential equation that describes heat conduction through the wall; (b) Solve the equation to obtain the wall temperature profile of the tank as a function of the radial position, using as conditions boundary the temperatures of the surfaces T1 (at r=r1) and T2 (at r=r2); (c) Apply an energy balance on the surface r=r2 to estimate the temperature T2 (d) Obtain the heat gain rate (in W)
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
Related questions
Question
100%
Consider a spherical aluminum tank used to store
ice at 0oC with an internal radius of 0.6 m, wall 10 cm thick and k=15.1 W/(m.oC). The exposed surface of the container exchanges heat by convection with ambient air at 30oC and h=20 W/(m2.oC). Ask:
(a) Write the differential equation that describes heat conduction
through the wall;
(b) Solve the equation to obtain the wall temperature profile
of the tank as a function of the radial position, using as conditions
boundary the temperatures of the surfaces T1 (at r=r1) and T2 (at
r=r2);
(c) Apply an energy balance on the surface r=r2 to estimate the
temperature T2
(d) Obtain the heat gain rate (in W).
Expert Solution
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 2 steps with 2 images
Recommended textbooks for you
Elements Of Electromagnetics
Mechanical Engineering
ISBN:
9780190698614
Author:
Sadiku, Matthew N. O.
Publisher:
Oxford University Press
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:
9780134319650
Author:
Russell C. Hibbeler
Publisher:
PEARSON
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:
9781259822674
Author:
Yunus A. Cengel Dr., Michael A. Boles
Publisher:
McGraw-Hill Education
Elements Of Electromagnetics
Mechanical Engineering
ISBN:
9780190698614
Author:
Sadiku, Matthew N. O.
Publisher:
Oxford University Press
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:
9780134319650
Author:
Russell C. Hibbeler
Publisher:
PEARSON
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:
9781259822674
Author:
Yunus A. Cengel Dr., Michael A. Boles
Publisher:
McGraw-Hill Education
Control Systems Engineering
Mechanical Engineering
ISBN:
9781118170519
Author:
Norman S. Nise
Publisher:
WILEY
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:
9781337093347
Author:
Barry J. Goodno, James M. Gere
Publisher:
Cengage Learning
Engineering Mechanics: Statics
Mechanical Engineering
ISBN:
9781118807330
Author:
James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:
WILEY