Thermodynamics HW Solutions 573

Thermodynamics HW Solutions 573 - Then, ( ) ) ( ) ( ) ( Re...

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Chapter 7 External Forced Convection 7-45 The flow of a fluid across an isothermal cylinder is considered. The change in the drag force and the rate of heat transfer when the free-stream velocity of the fluid is doubled is to be determined. Analysis The drag force on a cylinder is given by 2 2 1 = V ρ N D D A C F When the free-stream velocity of the fluid is doubled, the drag force becomes 2 ) 2 ( 2 2 = V N D D A C F Taking the ratio of them yields 4 = = 2 2 1 2 ) 2 ( V V D D F F The rate of heat transfer between the fluid and the cylinder is given by Newton's law of cooling. We assume the Nusselt number is proportional to the n th power of the Reynolds number with 0.33 < n < 0.805.
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Unformatted text preview: Then, ( ) ) ( ) ( ) ( Re ) ( ) ( 1 = = = = = T T A D D k T T A D D k T T A D k T T A Nu D k T T hA Q s s n n s s n s s n s s s s V V &amp; When the free-stream velocity of the fluid is doubled, the heat transfer rate becomes Pipe D T s Air V 2 V ) ( ) 2 ( 2 = T T A D D k Q s n n V &amp; Taking the ratio of them yields n 2 V V = = n n Q Q ) 2 ( 1 2 &amp; &amp; 7-28...
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