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# practice2 - PROBLEM 7.25 KNOWN Plate dimensions and initial...

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PROBLEM 7.25 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 x,c Re 5 10 , (6) Constant properties. PROPERTIES: Table A-1 , AISI 1010 steel (573K): k p = 49.2 W/m K, c = 549 J/kg K, ρ = 7832 kg/m 3 . Table A-4 , Air (p = 1 atm, T f = 433K): ν = 30.4 × 10 -6 m 2 /s, k = 0.0361 W/m K, Pr = 0.688. ANALYSIS: The initial rate of heat transfer from a plate is () 2 si i q2 h ATT 2 h LTT ∞∞ =− With 62 5 L Re u L/ 10m/s 1m/30.4 10 m /s 3.29 10 , ν == × × = × flow is laminar over the entire surface and ( ) L 1/2 1/3 5 L Nu 0.664Re Pr 0.664 3.29 10 0.688 336 × = L 2 h k / L Nu 0.0361W / m K /1m 336 12.1W / m K = Hence, ( ) 2 2 q 2 12.1W / m K 1m 300 20 C 6780W − °= < Performing an energy balance at an instant of time for a control surface about the plate, out st EE , −= we obtain (Eq. 5.2), 22 i i dT Lc h2L T T dt ρδ ( ) 2 3 i 2 12.1W / m K 300 20 C dT 0.26 C/ s dt 7832 kg / m 0.006m 549J / kg K ⋅− ° ° ×× < COMMENTS: (1) With 4 p Bi h / 2 / k 7.4 10 , δ × use of the lumped capacitance method is appropriate. (2) Despite the large plate temperature and the small convection coefficient, if adjoining plates are in close proximity, radiation exchange with the surroundings will be small and the assumption of negligible radiation is justifiable.

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PROBLEM 7.31 KNOWN: Plate dimensions and freestream conditions. Maximum allowable plate temperature. FIND: (a) Maximum allowable power dissipation for electrical components attached to bottom of plate, (b) Effect of air velocity and fins on maximum allowable power dissipation. SCHEMATIC: ASSUMPTIONS: (1) Steady-state conditions, (2) Constant properties, (3) Negligible heat loss form sides and bottom, (4) Transition Reynolds number is 5 × 10 5 , (5) Isothermal plate. PROPERTIES: Table A.1 , Aluminum (T 350 K): k 240 W/m K; Table A.4 , Air (T f = 325 K, 1 atm): ν = 18.4 × 10 -6 m 2 /s, k = 0.028 W/m K, Pr = 0.70. ANALYSIS: (a) The heat transfer from the plate by convection is () elec s s Pq h A T T == . For u = 15 m/s, 5 Lx , c 62 u L 15m s 1.2m Re 9.78 10 Re 18.41 10 m s ν × = × > × . Hence, transition occurs on the plate and ( ) ( ) 4/5 1/3 5 L L Nu 0.037Re 871 Pr 0.037 9.78 10 871 0.70 1263  =− = × =   2 L k 0.028W m K h Nu 1263 29.7 W m K L 1.2m = The heat rate is ( ) 2 2 q 29.7 W m K 1.2m 350 300 K 2137 W =⋅ = .
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practice2 - PROBLEM 7.25 KNOWN Plate dimensions and initial...

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