{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Stability lecture 13 - Lecture 13*Do HW Problems 6.1 6.2...

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
Lecture 13 *Do HW Problems 6.1 & 6.2 out of Drazin (pgs. 106-107) Rayleigh-Benard Convection: Continued… ( ) 3 2 2 Ra k k µ = − 2 For neutral solutions with assumed solution becomes ( ) 3 2 2 2 2 Ra n k π = − k Particular values of Ra for different values of . and n k ( ) 3 2 2 2 2 Ra n k k π = This is a neutral curve. ( ) is the horizontal wave number mode number 0 no motion at all 1, 2, ...... Mode 1 1 k n n n n n = = ± = ± ± = 1
Background image of page 1

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

View Full Document Right Arrow Icon
One cell of this type ( ) Mode 2 2 n = Seek minimum Ra, and corresponding k , gives minimum unstable flow point ( ) ( ) 3 2 2 1 2 2 2 1 2 2 1 0 no disturbances minimum is for 1 Ra to find minimum Ra 0 gives critical 2 Non-dimensional result 1 2 2 2 dimensional result : 2 2 depth 27 Ra 658 4 C C C C C n n k k d k dk k z h k h h π π π λ λ π = = + = = = = = = = = 2
Background image of page 2
Modes 2, 3 have slightly different . 's C k Note: The neutral condition (and critical point) are independent of Pr. But R σ depends on Pr.
Background image of page 3

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

View Full Document Right Arrow Icon
Image of page 4
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}