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Unformatted text preview: 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 ⎞ ∂ = − ⎟ ∂ ⎠ . q y Wall x 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 . q y > 0 Wall x , T y T • 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 ....
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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 Pennsylvania State University, University Park.
- Fall '07