Ant_on_a_Heated_Plate

# Ant_on_a_Heated_Plate - Ant on a Heated Plate: A ant is...

This preview shows page 1. Sign up to view the full content.

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

Unformatted text preview: Ant on a Heated Plate: A ant is confined to walk in a circle of radius 5 about the origin on a heated plate with the following temp profile T ( x, y ) = 4 x 2 − kxy + y 2 . Determine the temperature extrema the ant will encounter for k = 4. 6 150 0.1 0.1 25 5 10 50 150 125 100 350 125 100 50 25 4 250 2 200 175 0.1 0.1 25 5 125 100 z 150 y 0 50 25 10 100 -2 50 175 50 0.1 0.1 -4 0 5 10 25 10 -50 6 4 2 0 y -2 -4 -10 -6 -5 0 x 5 10 -6 -6 -4 -2 0 x 50 25 5 5 10 2 4 k=4 Critical pt at origin leaves 2nd partials test inconclusive 6 175 150 125 10 0.1 -5 -1 0 -5 400 100 25 0-2 .1 10 5 4 350 -2 300 50 2 250 150 125 10 y 100 -2 50 50 10 0.1 25 0 10 -50 6 4 2 0 0 y -2 -4 -6 -10 x -4 -2 -5 -2 5 50 25 5 150 -6 -6 -4 -2 0 x 2 150 125 175 -5 0.1 10 25 100 5 4 150 125 0 100 25 200 z 0.1 5 0.1 10 100 50 25 5 6 k = 5 Critical pt at origin transitioned to a saddle pt. 125 100 50 300 10 5 6 -10 6 150 50 300 25 4 250 175 125 100 10 10 25 50 5 5 2 200 50 50 z 100 100 10 10 -2 125 25 150 25 0.1 y 0 100 10 50 50 50 -4 25 0 6 25 10 4 2 0 0 y -2 -4 -6 -10 x -6 -6 -4 -2 0 x 2 150 125 4 175 125 k = 3 Critical pt at origin is now a local minimum 100 5 6 ...
View Full Document

## This note was uploaded on 12/25/2009 for the course MATH 1920 taught by Professor Pantano during the Spring '06 term at Cornell University (Engineering School).

Ask a homework question - tutors are online