Homework Help is Here – Start Your Trial Now!
Engineering
Mechanical Engineering
spherical container, with an inner radius r1= 1.4 m and an outer radius r2 = 1.45 m has its inner surface subjected to a uniform heat flux of q1= 7 kW/m2. The outer surface of the container has a temperature T2 = 25°C, and the container wall thermal conductivity is k = 1.5 W/m∙K. Determine the inner surface temperature of the container. (Round your answer to the nearest whole number.) The inner surface temperature is ____°C.

spherical container, with an inner radius r1= 1.4 m and an outer radius r2 = 1.45 m has its inner surface subjected to a uniform heat flux of q1= 7 kW/m2. The outer surface of the container has a temperature T2 = 25°C, and the container wall thermal conductivity is k = 1.5 W/m∙K. Determine the inner surface temperature of the container. (Round your answer to the nearest whole number.) The inner surface temperature is ____°C.

Elements Of Electromagnetics
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
See similar textbooks
icon
Related questions
Question

A spherical container, with an inner radius r1= 1.4 m and an outer radius r2 = 1.45 m has its inner surface subjected to a uniform heat flux of q1= 7 kW/m2. The outer surface of the container has a temperature T2 = 25°C, and the container wall thermal conductivity is k = 1.5 W/m∙K.

Determine the inner surface temperature of the container. (Round your answer to the nearest whole number.)

The inner surface temperature is ____°C.

 

 

 

### Heat Transfer in Spherical Coordinates In studying heat transfer in spherical coordinates, consider the diagram below which represents the cross-section of a spherical container. #### Diagram Explanation: - The diagram shows a spherical container composed of two concentric spheres. The inner sphere has a radius \( r_1 \), and the outer sphere has a radius \( r_2 \). - The region between these radii is the material of the container. - The inner sphere is filled with a substance at a higher temperature, denoted as \( T_1 \), and the heat flux \( \dot{q}_1 \) is directed radially outward towards the outer sphere. - The outer sphere is in contact with another substance at a lower temperature, denoted as \( T_2 \), facilitating the heat transfer across the spherical container. #### Key Variables: - \( r \): General radial distance from the center. - \( r_1 \): Radius of the inner sphere. - \( r_2 \): Radius of the outer sphere. - \( T_1 \): Temperature of the substance within the inner sphere. - \( T_2 \): Temperature of the substance surrounding the outer sphere. - \( \dot{q}_1 \): Heat flux from the inner sphere to the outer surface. This setup simplifies understanding heat flow through spherical coordinates. Heat transfer would be analyzed considering the thermal conductivity of the material between \( r_1 \) and \( r_2 \), the temperature gradient, and other properties pertinent to the specific application.
Transcribed Image Text:### Heat Transfer in Spherical Coordinates In studying heat transfer in spherical coordinates, consider the diagram below which represents the cross-section of a spherical container. #### Diagram Explanation: - The diagram shows a spherical container composed of two concentric spheres. The inner sphere has a radius \( r_1 \), and the outer sphere has a radius \( r_2 \). - The region between these radii is the material of the container. - The inner sphere is filled with a substance at a higher temperature, denoted as \( T_1 \), and the heat flux \( \dot{q}_1 \) is directed radially outward towards the outer sphere. - The outer sphere is in contact with another substance at a lower temperature, denoted as \( T_2 \), facilitating the heat transfer across the spherical container. #### Key Variables: - \( r \): General radial distance from the center. - \( r_1 \): Radius of the inner sphere. - \( r_2 \): Radius of the outer sphere. - \( T_1 \): Temperature of the substance within the inner sphere. - \( T_2 \): Temperature of the substance surrounding the outer sphere. - \( \dot{q}_1 \): Heat flux from the inner sphere to the outer surface. This setup simplifies understanding heat flow through spherical coordinates. Heat transfer would be analyzed considering the thermal conductivity of the material between \( r_1 \) and \( r_2 \), the temperature gradient, and other properties pertinent to the specific application.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Conduction
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Elements Of Electromagnetics
Elements Of Electromagnetics
Mechanical Engineering
ISBN:
9780190698614
Author:
Sadiku, Matthew N. O.
Publisher:
Oxford University Press
Mechanics of Materials (10th Edition)
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:
9780134319650
Author:
Russell C. Hibbeler
Publisher:
PEARSON
Thermodynamics: An Engineering Approach
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:
9781259822674
Author:
Yunus A. Cengel Dr., Michael A. Boles
Publisher:
McGraw-Hill Education
Control Systems Engineering
Control Systems Engineering
Mechanical Engineering
ISBN:
9781118170519
Author:
Norman S. Nise
Publisher:
WILEY
Mechanics of Materials (MindTap Course List)
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:
9781337093347
Author:
Barry J. Goodno, James M. Gere
Publisher:
Cengage Learning
Engineering Mechanics: Statics
Engineering Mechanics: Statics
Mechanical Engineering
ISBN:
9781118807330
Author:
James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:
WILEY
SEE MORE TEXTBOOKS