14a
sigma = 5.67e-8
h = 15
R = 0.05
L = 20
cp = 2000
TL = 300 + 273
TH = 350 + 273
T_av = 0.5*(TH+TL)
Ta = 20+273
G = 1000
c = 40
IW_in = 2*R*L*c*G
IW_loss_conv = 2*pi*R*L*(h*(T_av-Ta))
IW_loss_rad = 2*pi*R*L*(sigma*(T_av^4-Ta^4))
IW_conv = cp*Im*(TH-TL)
2*R*L*c*G = cp*Im*(TH-TL) + 2*pi*R*L*(h*(T_av-Ta) + sigma*(T_av^4-Ta^4))
14b
sigma = 5.67e-8
taualpha = 1.0
h = 15
R = 0.05
| L = 100
cp = 2000
TL = 300 + 273
TH = 350 + 273
T_av = 0.5*(TH+TL)
Ta = 20+273
G = 1000
c = 40
IW_in = 2*R*L*taualpha*c*G
IW_loss_conv = 2*pi*R*L*(h*(T_p-Ta))
IW_loss_rad = 2*pi*R*L*(sigma*(T_p^4-Ta^4))
IW_trans_rad = 2*pi*R*L*sigma*(T_av^4-T_p^4)
IW_conv = cp*Im*(TH-TL)
IW_in = IW_conv + IW_trans_rad
IW_trans_rad = IW_loss_conv + IW_loss_rad
14c
Same equations as in 14b, plus equation(s) for endoreversible engine: P_engine = (1-sqrt(Ta/T_av))*IW_conv
The model equations can be solved with the help of programs such as EES.
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