09 02 15

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ST&M 09-02-15 Problem 1 Room lightning is provided by a 25W halogen light sensor consisting of a nearly spherical quartz bulb with a surface of 5cm2. The filament operates at a steady state temperature of Tf =3250K. Air and walls are at a temperature T∞ = 17°C. Assume that: A)The filament has negligible surface area and radiates as a black body B)Quartz: τλ =1 for λ < 4μm and τλ =0 for λ < 4μm ; ρ =0 on all spectrum C)The heat loss from the bulb to the external ambient due to free convection is equal to the one due to radiation. Determine : 1) Heat flow absorbed by the bulb 2) The bulb temperature (hint: make a suitable assumption for the bulb ε) 3) If assumption C is acceptable under the constraint that the error on the overall heat loss is less then 15% Thermal property air: ρ =1,218 kg/m3 , Cp=1003 J/(Kg*K) , K =0,025 W/(m*K) , μ =1,78*10-5 Kg/(m*s) -NuLc = 0,15 * RaLc1/3 -NuLc = 2+ ( 0,589 * RaLc1/3 ) / ( 1 + ( 0,469 / Pr )9/16 )4/9 -NuLc = 0,360 + ( 0,518 * RaLc1/4 ) / ( 1+( 0,559 / Pr )9/16 )4/9 Problem 1 Electronic device shaped as a square parallelepiped of side L= 40mm and thickness H =2mm ( ρ =2350 kg/m3 , Cp=700 J/(Kg*K) , K =80 W/(m*K) ) is cooled by air stream parallel to the square sides through a heat transfer advective coefficient h =40 W/(m2*K). Radiation is neglected in this analysis. Device operates by a sequence of cycles, each encompassing tho models: -ON MODE: the device σ = 3*106 W/m3 (evenly distributed) -OFF MODE: σ = 0 Referring to the first cycle, the device is initially in thermal equilibrium with the surroundings at T∞ = 25°C. Then is operated the ON MODE dusting a time interval [0, t1] & an OFF MODE till the end of the cycle at t2. Determine: 1) t1 e t2 so that the maximum device temperature doesn’t exceed Tmax = 75°C 2) the velocity of the air…