{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# hw3 - Homework 3 PHZ 5156 Due Tuesday 1 Consider the...

This preview shows pages 1–2. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Homework 3 PHZ 5156 Due Tuesday, September 22, 2009 1. Consider the diffusion or heat flow equation in two spatial dimensions ∂ 2 ∂x 2 + ∂ 2 ∂y 2 u = 1 α 2 ∂u ∂t a) Use the method of separation of variables and take u ( x,y,t ) = F ( x,y ) T ( t )to show that this equation can be reduced to two ordinary differential equations ∂ 2 ∂x 2 + ∂ 2 ∂y 2 F ( x,y ) + k 2 F ( x,y ) = 0 and dT dt =- k 2 α 2 T b) Find the general set of solutions subject to the boundary conditions u ( x = ,y,t ) = 0, u ( x = L,y,t ) = 0, u ( x,y = 0 ,t ) = 0, u ( x,y = L,t ) = 0 (Hint: You might want to start by first applying separation of variables to the spatial equation, taking F ( x,y ) = X ( x ) Y ( y )). 2. The gravitational potential Φ (potential energy per unit mass) at a distance r away from the center of the Earth is given by, Φ( r ) =- GM r where r = ( x 2 + y 2 + z 2 ) 1 2 , and G = 6 . 67 × 10- 11 Nm 2 kg 2 , and the mass of the Earth is M = 5 . 97 × 10 24 kg ....
View Full Document

{[ snackBarMessage ]}

### Page1 / 2

hw3 - Homework 3 PHZ 5156 Due Tuesday 1 Consider the...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online