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HomeworkSolutions_C11

# 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 ( ) ( ) 0 0 3 3 0 0 * * 1 Pr 14.5 1 Pr 14.5 R dy dy q q yu yu ν ν + + ± Show that ( ) ( ) 1/3 0 * 0 3 3 RePr 2 14.5 z R q D u u k T 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 ( ) ( ) 0 0 3 0 * (1) 1 Pr 14.5 R dy q k T yu ν = + T The integral in Eq. (1) can be evaluated by making a change of variable. Let Pr . / * 1 3 145 yv v x ⎟ = Then Eq. (1) becomes 1 1/3 * 0 3 0 Pr 14.5 1 o R v dx q k x ν = + T T The integral may be found in a table of integrals, where we find

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