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Heat Chap09-094 - Chapter 9 Natural Convection Review...

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Chapter 9 Natural Convection Review Problems 9-94E A small cylindrical resistor mounted on the lower part of a vertical circuit board. The approximate surface temperature of the resistor is to be determined. Assumptions 1 Steady operating conditions exist. 2 Air is an ideal gas with constant properties. 3 The local atmospheric pressure is 1 atm. 4 Radiation effects are negligible. 5 Heat transfer through the connecting wires is negligible. Properties The properties of air at 1 atm and the anticipated film temperature of ( T s + T )/2 = (220+120)/2 = 170 F are (Table A-15E) 1 - 2 3 R 001587 . 0 R ) 460 170 ( 1 1 7161 . 0 Pr /s ft 10 222 . 0 F Btu/h.ft. 01692 . 0 f T k Analysis The solution of this problem requires a trial-and-error approach since the determination of the Rayleigh number and thus the Nusselt number depends on the surface temperature which is unknown. We start the solution process by “guessing” the surface temperature to be 220 F for the evaluation of the properties and h . We will check the accuracy of this guess later and repeat the calculations if necessary. The characteristic length in this case is the diameter of resistor, in. 2 . 0 D L c Then, 8 . 343 ) 7161 . 0 ( ) /s ft 10 222 . 0 ( ) ft 12 / 2 . 0 )( R 120 220 )( R 001587 . 0 )( ft/s 2 . 32 ( Pr ) ( 2 2 3 3 -1 2 2 3 D T T g Ra s 105 . 2 7161 . 0 / 559 . 0 1 ) 8 . 343 ( 387 . 0 6 . 0 Pr / 559 . 0 1 387 . 0 6 . 0 2 27 / 8 16 / 9 6 / 1 2 27 / 8 16 / 9 6 / 1 Ra Nu 2 2 2 2 ft 00175 . 0 4 / ft) 12 / 2 . 0 ( 2 ) ft 12 / 3 . 0 )( ft 12 / 2 . 0 ( 4 / 2 F . Btu/h.ft 138 . 2 ) 105 . 2 ( ft 12 / 2 . 0 F Btu/h.ft. 01692 . 0 D DL A Nu D k h s and F 211.5  ) ft 00175 . 0 )( F . Btu/h.ft 138 . 2 ( Btu/h ) 412 . 3 1 . 0 ( F 120 ) ( 2 2 s s s s hA Q T T T T hA Q which is sufficiently close to the assumed temperature for the evaluation of properties. Therefore, there is no need to repeat calculations. 9-84 Q Resistor 0.1 W D = 0.2 in Air T = 120 F
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Chapter 9 Natural Convection 9-95 An ice chest filled with ice at 0 C is exposed to ambient air. The time it will take for the ice in the chest to melt completely is to be determined for natural and forced convection cases. Assumptions 1 Steady operating conditions exist. 2 Air is an ideal gas with constant properties. 3 Heat transfer from the base of the ice chest is disregarded. 4 Radiation effects are negligible. 5 Heat transfer coefficient is the same for all surfaces considered. 6 The local atmospheric pressure is 1 atm. Properties The properties of air at 1 atm and the anticipated film temperature of ( T s + T )/2 = (15+20)/2 = 17.5 C are (Table A-15) 1 - 2 5 K 003442 . 0 K ) 273 5 . 17 ( 1 1 7316 . 0 Pr /s m 10 493 . 1 C W/m. 02495 . 0 f T k Analysis The solution of this problem requires a trial-and-error approach since the determination of the Rayleigh number and thus the Nusselt number depends on the surface temperature which is unknown. We start the solution process by “guessing” the surface temperature to be 15
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