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Ae104a10_problemset_2

Ae104a10_problemset_2 - Ae/APh 104a Homework Problem Set#2...

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Ae/APh 104a Homework Problem Set #2 ISSUED: Tuesday, October 12, 2010 DUE: Tuesday, October 19, 2010 (in class) 1/3 For a segment of an infinitely long wire placed normal to a flow of air that has mean velocity U and mean temperature T a , a simple heat transfer relationship between the electrical power dissipated in the segment and the forced convective heat transfer to the surroundings is given by: E 2 w R w = πhd w l ( T w - T a ) , (1) where h is the convective heat transfer coefficient, d w is the wire diameter and l is the length of the wire segment. The resistance of the wire segment, R w , is a function of the mean local temperature of the wire, T w , and the mean voltage across the wire is E w . Experiments have shown that a good empirical relationship between h and U is given by h = ( A + BU n ), where A and B are weak functions of temperature, usually approximated during calibration as constants for controlled experiments. (i) If the circuit that powers the wire is designed to maintain a (virtually) con- stant wire temperature, T w , and the output from the wire segment is the voltage across it, V w ( t ) = E w + e w ( t ), (a) write down the relationship between the mean voltage, E w , the mean fluid temperature T a and the mean flow velocity
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