**Unformatted text preview: **show that . ) ( ) ( ∫∫∫ ∫∫ × ∇ = × R dV dS F F n r 4. (a) Show that . | | ) ( 2 2 T T T T T ∇ + ∇ = ∇ ⋅ ∇ (b) Suppose that at any time t , the temperature distribution ) , , , ( t z y x T over a domain D in 3 R satisfies the heat conduction equation T t T 2 ∇ = ∂ ∂ κ where the diffusivity κ is a constant. Suppose D is bounded by the surface σ . If either T = 0 or = ∂ ∂ = ⋅ ∇ n T T n on σ , show that ( 29 . | | 2 2 2 1 dV T dV T t D D ∫∫∫ ∫∫∫ ∇-= ∂ ∂...

View
Full Document

- Spring '10
- BLUMAN
- Derivative, Vector Calculus, Vector field, D. Suppose