Energy flux vector field problem is the isotherms are circles

In summary, the isotherms in a region are all concentric spheres centered at the origin. This means that at any point on the sphere, the line from the origin to that point is perpendicular to the surface. Using the equation J = - k (del)T, we can see that the energy flux vector field, represented by -(del)T, will always point either towards or away from the origin, since the line from the origin to any point on the sphere will always be perpendicular to the surface and therefore parallel to the energy flux vector field.
  • #1
doppelganger007
18
0

Homework Statement


Suppose that the isotherms in a region are all concentric spheres centered at the origin. Prove that the energy flux vector field points either toward or away from the origin.


Homework Equations


J = - k (del)T


The Attempt at a Solution


so I know that -(del)T is perpendicular to the surface T, which is constant, but I'm not really sure how to finish off the proof from there...
 
Physics news on Phys.org
  • #2
You are given that " isotherms in a region are all concentric spheres centered at the origin." Suppose you are at a point (x,y,z) on such a sphere. At what angle does the line from (0,0,0) through (x,y,z) cross the sphere?
 

Related to Energy flux vector field problem is the isotherms are circles

What is an energy flux vector field?

An energy flux vector field is a mathematical representation of the flow of energy through a system. It is often used to study the transfer of heat or other forms of energy in various physical systems.

What is the significance of isotherms being circles in the energy flux vector field problem?

The circles formed by isotherms in an energy flux vector field represent regions of equal temperature. This can provide valuable information about the distribution and transfer of heat within a system.

How does the shape of isotherms affect the energy flux in a vector field?

The shape of isotherms can have a significant impact on the energy flux in a vector field. In the case of circles, the energy flux will be more evenly distributed throughout the system compared to other shapes, resulting in a more uniform temperature distribution.

What are some real-world applications of studying the energy flux vector field problem?

Studying the energy flux vector field has many practical applications, including understanding weather patterns, thermal management in engineering systems, and optimizing energy efficiency in buildings and other structures.

What are some methods used to solve the energy flux vector field problem?

There are various mathematical and computational methods used to solve the energy flux vector field problem, such as finite difference methods, finite element methods, and computational fluid dynamics. These methods involve breaking down the system into smaller elements and solving for the energy flux at each point.

Similar threads

  • Calculus and Beyond Homework Help
Replies
5
Views
813
  • Calculus and Beyond Homework Help
Replies
6
Views
1K
  • Calculus and Beyond Homework Help
Replies
4
Views
2K
  • Calculus and Beyond Homework Help
Replies
2
Views
2K
  • Calculus and Beyond Homework Help
Replies
7
Views
2K
  • Calculus and Beyond Homework Help
Replies
3
Views
995
Replies
8
Views
870
  • Classical Physics
7
Replies
236
Views
8K
  • Calculus and Beyond Homework Help
Replies
11
Views
2K
Replies
16
Views
1K
Back
Top