Homework 6 - it HOWELL/ka #5122 DL/tfi MWMLL 53501-...

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Unformatted text preview: it HOWELL/ka #5122 DL/tfi MWMLL 53501- laminar flow over a flat plate, the local heat ' ansfer coefficient hx is known to vary as if“, here :c is the distance from the leading edge (x = ,0) of the plate. What is the ratio of the average coef- ficient between the leading edge and some location I x on the plate to. the local coefficient at x? In flow over a surface, velocity and temperature profiles are of the forms u(y) = Ay + By“- — Cy3 and TO) = D + Ey + F312 - Gy3 , where the coefficients A through G are constants. Obtain expressions for the friction coefficient Cf - and the convection coefficient h in terms of Lt”, To; and'appropriate profile coefficients and fluid proper; ties. ' A fan that can provide air speeds up to 50 m/S i5 be used in a low-speed wind tunnel with atm0§a pheric air at 25°C. If one Wishes to use the Wig-5 tunnel to study flat-plate boundaiy layer behavigr up to Reynolds numbers of Rex = 105, what is the minimum plate length that should be used? At what distance from the leading edge would transi- tion occur if the Critical Reynolds number were "Raw = 5 X 10°? Assuming a transition Reynolds number of 5 X 105, determine the distance from the leading edge of a @ , 'flat plate at which transition will occur for each of the following fluids when it, = 1 m/s: atmospheric A air, water, engine oil, and mercury. In each case the fluid temperature is 27°C. Experimental results for heat transfer over a flat plate with an extremely rough surface were found to be correlated by an expression of the form N “x = 0.0412339 Prl/a Where Mix is the local value of the Nusselt number at a position x measured from the leading edge of the plate. Obtain an expression for the ratio of the average heat transfer coefficient/3x to the local coef- ficient hx. ‘ ExPerimentai measurements of the convection heat transfer coefficient for a square bar in cross flow yielded the following values: 131 = 50 W/m2 - K when VI = 20 m/s 122 = 40 W/m1 - K when V2 = 15 m/s l“ o.L5=m "l Assume__ that the functional form of the Nusselt num- ber 15 Nu = C Re'" Pr", Where C, m, and n are con- stants. - (a) What will be the convection heat transfer coeffi- cient for a similar bar with L = 1 In when V = 15 m/s? (b) What Will be the convection heat transfer coeffi- cient for a similar bar with L =, 1 111 when V = 30 m/s? (c) Would your results be the same if the side of the I bar, rather than its diagonal, were used as the I characteristic length? A thin, flat plate that is 0.2 m by 0.2 m on a side is oriented parallel to an atmospheric airstream having a velocity of 40 m/s. The air is at a temperature of Tm = 20°C. While the plate is maintained at ’1} = 120°C. The air flows over the top and bottom sur- faces of the plate, and measurement of the drag force reveals a value of 0.075 N. What is the rate of heat transfer from-both sides of the plate to the air? ...
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Homework 6 - it HOWELL/ka #5122 DL/tfi MWMLL 53501-...

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