- #1
NoOne0507
- 16
- 0
Homework Statement
A cannonball is heated with with temperature distribution T(x,y,z)=60(y2+z2-x2).
The cannonball is a sphere of 1 ft with it's center at the origin
a) Where are the max and min temperatures in the cannonball, and where do they occur?
Homework Equations
[itex]\nabla[/itex]f=λ[itex]\nabla[/itex]g
Where g is the the constraint and λ is the common ratio.
[itex]\nabla[/itex]= fx i + fy j + fz k
The Attempt at a Solution
The cannonball is the restraint so
λ[itex]\nabla[/itex]f = 2xλ i + 2yλ j + 2zλ k
[itex]\nabla[/itex]T = -120x i + 120y j + 120z k
2xλ = -120x, λ= -60
2yλ = 120y, λ = 60
2zλ = 120z, λ = 60
I don't know where to go from here. All the variables canceled so I can't relate them to each other, and the λs are different.
Last edited: