CSU MECH 344 - HW7 - Solutions (8 pages)

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PROBLEM 7 17 KNOWN Temperature pressure and Reynolds number for air flow over a flat plate of uniform surface temperature FIND a Rate of heat transfer from the plate b Rate of heat transfer if air velocity is doubled and pressure is increased to 10 atm SCHEMATIC ASSUMPTIONS 1 Steady state conditions 2 Uniform surface temperature 3 Negligible radiation 4 Re x 5 105 c PROPERTIES Table A 4 Air Tf 348K 1 atm k 0 0299 W m K Pr 0 70 ANALYSIS a The heat rate is q h L w L Ts T 4 Since the flow is laminar over the entire plate for ReL 4 10 it follows that h L 1 2 1 3 Nu L L 0 664 Re1 2 Pr1 3 0 664 40 000 0 70 117 9 L k k 0 0299 W m K Hence h L 117 9 117 9 17 6 W m2 K L 0 2m and q 17 6 W m2 K 0 1m 0 2m 100 50 o C 17 6 W b With p2 10 p1 it follows that 2 10 1 and 2 1 10 Hence u L u L ReL 2 2 10 20 ReL 1 8 105 2 1 and mixed boundary layer conditions exist on the plate Hence h L 1 3 0 037 8 105 4 5 871 0 70 1 3 Nu L L 0 037 Re4 5 871 Pr L k Nu L 961 Hence h L 961 q 143 6 W m2 K 0 0299 W m K 143 6 W m2 K 0 2m 0 1m 0 2m 100 50 o C 143 6 W COMMENTS Note that in calculating ReL 2 ideal gas behavior has been assumed It has also been assumed that k and Pr are independent of pressure over the range considered PROBLEM 7 24 KNOWN Plate dimensions and initial temperature Velocity and temperature of air in parallel flow over plates FIND Initial rate of heat transfer from plate Rate of change of plate temperature SCHEMATIC ASSUMPTIONS 1 Negligible radiation 2 Negligible effect of conveyor velocity on boundary layer development 3 Plates are isothermal 4 Negligible heat transfer from sides of plate 5 5 Re x c 5 10 6 Constant properties PROPERTIES Table A 1 AISI 1010 steel 573K kp 49 2 W m K c 549 J kg K 7832 3 6 2 kg m Table A 4 Air p 1 atm Tf 433K 30 4 10 m s k 0 0361 W m K Pr 0 688 ANALYSIS The initial rate of heat transfer from a plate is q 2 h As Ti T 2 h L2 Ti T With Re L u L 10 m s 1m 30 4 10 6 m 2 s 3 29 105 flow is laminar over the entire surface and 2 1 3 0 664 3 29 105 Nu L 0 664 Re1 L Pr 1 2 0 688 1 3 336 h