HomeworkSolutions_C11 - Problem: Recall from the lecture...

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Problem: Recall from the lecture note the empirical relation for approximation of the wall heat flux for turbulent flow in a circular tube for large Pr, using Reynolds analogy. Based on the following approximation () 00 33 ** 1 Pr 14.5 1 Pr 14.5 R dy dy qq yu yu ν ++ ∫∫ ± Show that 1/3 0 * 0 RePr 2 14.5 z R qD u u kT T π ⎛⎞ = ⎜⎟ ⎝⎠ Answer: The difference between the temperature at the wall (T 0 ) and the time-averaged temperature at the tube axis ( R T ) is expressed as 3 0 * (1) 1P r 1 4 . 5 R dy qk T yu =− + T The integral in Eq. (1) can be evaluated by making a change of variable. Let Pr . / * 13 14 5 yv v x ⎟ = Then Eq. (1) becomes 1 * 0 3 0 Pr 14.5 1 oR vd x x + T T The integral may be found in a table of integrals, where we find
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This note was uploaded on 09/01/2011 for the course PGE 312 taught by Professor Peters during the Fall '08 term at University of Texas at Austin.

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HomeworkSolutions_C11 - Problem: Recall from the lecture...

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