 #1
 48
 4
 Summary:

Hi
I got a condenser, which is using a refrigerant that will be condensed using water ( a water cooled plate condenser). I would really appreciate it if someone could peer review my calculations before submitting them for work.
A water cooled plate condenser, condensing refrigerant.
Heat exchanger (condenser with plates) characteristics:
Please note that I am using the C system which is basically the SI system using ° C instead of K.
For the refrigerant:
refrigerant mass flowrate mrf=0.06kg/s
For water:
water mass flowrate = mw=0.7kg/s
outlet water temperature Twoutlet=35°C
Calculations for the condenser:
1) Heat flux qc=h2−h3 = 448.8154408 kJ/kg  248.6436269 kJ/kg = 200.171814 kJ/kg
qc=200.171814kJ/kg
2) Heat Qc=mrf∗qc = 0.06 kg/s * 200.171814 kJ/kg = 12.01030884 kJ
Qc=12.01030884kJ
3) Inlet water temperature in the condenser twinlet=twateroutlet−Qc/(mw∗cpw) = 35 ° C  12.01030884 kJ / (0.7 kg/s*4.18 kJ/kg*K)
hence twinlet=30.89531482°C
4)mean water temperature twm=(twinlet+twoutlet)/2 = (35 ° C + 30.89531482 ° C) /2 = 32.94765741 ° C
twm=32.94765741°C
5)Water properties at mean temperature twm Calculations (calculated by ForTran Refprop)
a)Water thermal conductivity
λw = thermal conductivity (water, "PT", "C" 0.101325, twm; mean water temperature) / 1000 = 0.6187661 W/m*K
where: PT = as a function of pressure and temperature, pressure was used as atmospheric in MPa, and temperature was the mean water temp, divided by 1000 to get W from mW. Alternatively instead of PT I could have used TQ, such as mean water temperature twm and Q (quality, such as x = 0, liquid, but at 35 ° C we are far from saturation, so that's why I used PT, atmospheric pressure and mean water temperature).
λw=0.6187661W/(m∗K)
b)Water density
ρw = density(water, "PT", "C" 0.101325, mean water temperature) = 994.721891 kg/m^{3}
ρw=994.721891 kg/m^{3}
c)Water dynamic viscosity
μw = viscosity(water, "PT", "C" 0.101325, mean water temperature)*0.000001, so *10^{6} was used to convert μ Pa*s to kg/m*s
μw=0.000749615kg/(m∗s)
d)Water kinematic viscosity
νw=μw/ρw= (0.000749615kg/m*s) / (994.721891 kg/m3) = 7.53592E07 m^{2}/s
νw=7.53592E−07m^{2}/s
e) Prandtl
Pr = Prandtl (water, "PT", "C" 0.101325, mean water temperature)
Pr=5.063195386
f) Water flowing section
Scw=nwc∗w∗H0 = 14 * 0.07 m * 0.0022 m = 0.002156 m^{2}
Scw=0.002156 m^{2}
g) Water flowing velocity
uw=mw/(ρw∗Scw) = 0.7 kg/s / (994.721891 kg/m3*0.002156 m^{2})
uw=0.326398089m/s
h)Reynolds
Re=(uw∗dh)/νw = (0.326398089 m/s*0.0044 m)/7.53592E07 m^{2}/s
Re=1905.740592
i)Nusselt
Nu=0.212∗Re^{0.638}∗Pr^{0.33}
Nu = 0.212*1905.740592^{0.638}*5.063195386^{0.33}
Nu=44.82050053
j)Water convection coefficient
αw=(Nu∗λw)/dh = (44.82050053*0.6187661 W/m K)/0.0044 m
αw=6303.046887 [W/(m^{2}*K)]
I would really appreciate it if someone could peer review my calculations from 15 (aj), and let me know if they are correct.
Heat exchanger (condenser with plates) characteristics:
Description  symbol  value  value (converted) 
number of plates  np  28  
number of channels  nc  27  
number of water channels  nwc  14  
number of flowing channels for refrigerant  ncrf  13  
plates thickness  δp  0.8 mm  0.0008 m 
width of a plate  w  0.07 m  
length of a plate  L  0.2m  
height of flowing channel  H0  2.2mm  0.0022 m 
equivalent hydraulic diameter  dh = 2*H0  4.4 mm  0.0044 m 
thermal conductivity of the material of the plates (steel)  λp  20 W/m*K  
area of one plate  Sp = w*L  0.014 m2  
plates area  S = Sp*(np2)  0.364 m2  
Enthalpy at the inlet of condenser  h2  448.8154408 kJ/kg  
Enthalpy at the outlet of condenser  h3  248.6436269 kJ/kg 
Please note that I am using the C system which is basically the SI system using ° C instead of K.
For the refrigerant:
refrigerant mass flowrate mrf=0.06kg/s
For water:
water mass flowrate = mw=0.7kg/s
outlet water temperature Twoutlet=35°C
Calculations for the condenser:
1) Heat flux qc=h2−h3 = 448.8154408 kJ/kg  248.6436269 kJ/kg = 200.171814 kJ/kg
qc=200.171814kJ/kg
2) Heat Qc=mrf∗qc = 0.06 kg/s * 200.171814 kJ/kg = 12.01030884 kJ
Qc=12.01030884kJ
3) Inlet water temperature in the condenser twinlet=twateroutlet−Qc/(mw∗cpw) = 35 ° C  12.01030884 kJ / (0.7 kg/s*4.18 kJ/kg*K)
hence twinlet=30.89531482°C
4)mean water temperature twm=(twinlet+twoutlet)/2 = (35 ° C + 30.89531482 ° C) /2 = 32.94765741 ° C
twm=32.94765741°C
5)Water properties at mean temperature twm Calculations (calculated by ForTran Refprop)
a)Water thermal conductivity
λw = thermal conductivity (water, "PT", "C" 0.101325, twm; mean water temperature) / 1000 = 0.6187661 W/m*K
where: PT = as a function of pressure and temperature, pressure was used as atmospheric in MPa, and temperature was the mean water temp, divided by 1000 to get W from mW. Alternatively instead of PT I could have used TQ, such as mean water temperature twm and Q (quality, such as x = 0, liquid, but at 35 ° C we are far from saturation, so that's why I used PT, atmospheric pressure and mean water temperature).
λw=0.6187661W/(m∗K)
b)Water density
ρw = density(water, "PT", "C" 0.101325, mean water temperature) = 994.721891 kg/m^{3}
ρw=994.721891 kg/m^{3}
c)Water dynamic viscosity
μw = viscosity(water, "PT", "C" 0.101325, mean water temperature)*0.000001, so *10^{6} was used to convert μ Pa*s to kg/m*s
μw=0.000749615kg/(m∗s)
d)Water kinematic viscosity
νw=μw/ρw= (0.000749615kg/m*s) / (994.721891 kg/m3) = 7.53592E07 m^{2}/s
νw=7.53592E−07m^{2}/s
e) Prandtl
Pr = Prandtl (water, "PT", "C" 0.101325, mean water temperature)
Pr=5.063195386
f) Water flowing section
Scw=nwc∗w∗H0 = 14 * 0.07 m * 0.0022 m = 0.002156 m^{2}
Scw=0.002156 m^{2}
g) Water flowing velocity
uw=mw/(ρw∗Scw) = 0.7 kg/s / (994.721891 kg/m3*0.002156 m^{2})
uw=0.326398089m/s
h)Reynolds
Re=(uw∗dh)/νw = (0.326398089 m/s*0.0044 m)/7.53592E07 m^{2}/s
Re=1905.740592
i)Nusselt
Nu=0.212∗Re^{0.638}∗Pr^{0.33}
Nu = 0.212*1905.740592^{0.638}*5.063195386^{0.33}
Nu=44.82050053
j)Water convection coefficient
αw=(Nu∗λw)/dh = (44.82050053*0.6187661 W/m K)/0.0044 m
αw=6303.046887 [W/(m^{2}*K)]
I would really appreciate it if someone could peer review my calculations from 15 (aj), and let me know if they are correct.
Last edited: