Stability lecture 13

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

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Lecture 13 *Do HW Problems 6.1 & 6.2 out of Drazin (pgs. 106-107) Rayleigh-Benard Convection: Continued… () 3 22 Ra kk µ −= 2 For neutral solutions with assumed solution becomes ( ) 3 2 2 Ra nk π −−= k Particular values of Ra for different values of . and 3 2 2 Ra k −− = 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 nn n =− ± = 1
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One cell of this type () Mode 2 2 n = Seek minimum Ra, and corresponding k , gives minimum unstable flow point 3 22 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 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 λ =− = + = =→ =    == = 2
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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. is found by solution of Eigenvalue problem.
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This note was uploaded on 06/07/2011 for the course EOC 6934 taught by Professor Staff during the Fall '08 term at University of Florida.

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

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