Consider an air-conditioning system composed of abank of

Chapter 7, Problem 7.148

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Consider an air-conditioning system composed of abank of tubes arranged normal to air flowing in a ductat a mass rate of (kg/s). A coolant flowing throughthe tubes is able to maintain the surface temperatureof the tubes at a constant value of Ts?Ta,i, where Ta,iis the inlet air temperature (upstream of the tubebank). It has been suggested that air cooling may beenhanced if a thin, uniform film of water is main-tained on the outer surface of each of the tubes.(a) Assuming the water film to be at the temperatureTs, develop an expression for the ratio of theamount of cooling that occurs with the water filmto the amount of cooling that occurs without thefilm. The amount of cooling may be defined asTa,i?Ta,o, where Ta,ois the outlet air temperature(downstream of the tube bank). The upstream air may be assumed to be dry, and the driving poten-tials for convection heat and mass transfer may beapproximated as (Ta,i?Ts) and ?A,sat(Ts), respec-tively. Note:The total rate of heat loss from theair may be expressed as (Ta,i?Ta,o).Estimate the value of this ratio under conditionsfor which Ta,i?35?C and Ts?10?C.(b) Consider a tube bank that is 5 rows deep, with 12tubes in a row. Each tube is 0.5 m long, with anoutside diameter of 8 mm, and a staggered arrange-ment is used for which ST?SL?24 mm. Underconditions for which m.a?0.5 kg/s,V?3 m/s,Ta,i?35?C, and Ts?10?C, what is the value of Ta,oif the tubes are wetted? What is the specifichumidity of the air leaving the tube bank?