Energy flux vector field problem is the isotherms are circles

[doppelganger007]

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...

 

[HallsofIvy]

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?