Heat and Mass Transfer Problem

  • Thread starter Yr11Kid
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Hi everyone i've got a problem about the convective heat loss from a spa
any help or pointers would be greatly appreciated

A person installed a circular outdoor spa bath in the open area. In a typical operating condition, when the spa water is maintained at 37°C, and when the ambient air has a temperature of 17°C with a relative humidity of 30%, he has to top up the water at a rate of 0.002 kg/s so as to maintain a fixed water level in the bath. The tub is well insulated on all sides and its bottom, and the makeup water enters at 17°C.

a) Determine the value of hmA that commensurate with the makeup water flow rate. The symbols have their usual meaning.

b) Determine the extent of convective heat loss from the spa bath.

c) Determine the electrical power needed to maintain the spa bath temperature at 37°C.


At 300K, rhoair = 1.161 kg/m3, cp,air = 1.007 kJ/kgK, alpha = 22.5X 10-6 m2/s.
At 310K, rhowater vapour,sat = 0.0436 kg/m3, hfg = 2414 kJ/kg.
At 290K, rhowater vapour,sat = 0.0143 kg/m3.
DAB = 26X 10-6 m2/s, cp,water = 4.2 kJ/kgK



For part a i found hmA by using the evaporative cooling rate, the humidity and the density of saturated water vapor at 310k.

part b i don't quite understand, do i simply use q=hmA(Ts-Tambient) or do i need to find the temperature gradient between both mediums utilising the heat and mass transfer coefficients. This would make sense as i would have to use more of the given information like the diffusivity etc

for part c am i just doing a simple energy balance on the system???

Thanks
 

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