ME521_Lecture_20

ME521_Lecture_20 - ME 521 Fall 2007 Professor John M...

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Unformatted text preview: ME 521 Fall 2007 Professor John M. Cimbala Lecture 20 10/12/2007 Today, we will : • Discuss the production of vorticity at a wall, and the heat flux-vorticity analogy • Discuss how vorticity gets produced at a wall. • Do C a n d y Q u e s t i o n s f o r C a n d y F r i d a y Recall the statement we concluded from the previous lecture: A wall is the only place where vorticity can originate in a barotropic flow with conservative body forces. The Heat Flux-Vorticity Analogy Author: John M. Cimbala, Penn State University Latest revision: 10 October 2007 Note : For simplicity, consider two-dimensional incompressible, Newtonian flow in the x-y plane. 1. Heat Flux • Consider a wall that is parallel to the x-axis, and let q y be the y- component of the heat flux vector (rate of heat transfer per unit area to the fluid). From Fourier’s law of conduction , y T q k y ∂ = − ∂ . Right next to the wall, wall wall y T q k y ⎞ ∂ = − ⎟ ∂ ⎠ . • In words, Fourier’s law states that the heat flux at a wall is directly proportional to the negative of the temperature gradient at the wall . The actual value of T is not important, just its slope . • There are three cases of interest: 1. wall T y ⎞ ∂ < ⎟ ∂ ⎠ Here, q y at the wall is positive , and heat flows from the wall to the fluid . Since energy is being added to the fluid, we think of this as a source of internal energy (temperature) at the wall, or production of internal energy at the wall. 2. wall T y ⎞ ∂ > ⎟ ∂ ⎠ Here, q y at the wall is negative , and heat flows from the fluid to the wall . Since energy is being removed from the fluid, we think of this as a loss of internal energy (temperature) at the wall, or production of negative internal energy at the wall....
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This note was uploaded on 07/23/2008 for the course ME 521 taught by Professor Cimbala during the Fall '07 term at Penn State.

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ME521_Lecture_20 - ME 521 Fall 2007 Professor John M...

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