Page 142 - Mechanical Engineers' Handbook (Volume 4)

8 Power Plants 131

Another type of optimum is discovered when the overall size of the installation is fixed.
For example, in an extraterrestrial power plant with collector area A and radiator area A ,
L
H
if the total area is constrained 1
A A A (constant)
L
H
then the optimal way to allocate the area is A 0.35A and A 0.65A. Other examples
H,opt L,opt
of optimal allocation of hardware between various components subject to overall size con-
straints are given in Ref. 4.

8 POWER PLANTS

There are several EGM models and optima of power plants that have fundamental impli-
cations. The loss of heat from the hot end of a power plant can be modeled by using a
thermal resistance in parallel with an irreversibility-free compartment that accounts for the
˙
power output W of the actual power plant (Fig. 8). The hot-end temperature of the working
˙
fluid cycle T can vary. The heat input Q H is fixed. The bypass heat leak is proportional to
H
˙
the temperature difference, Q C C(T T ), where C is the thermal conductance of the
H
L
power plant insulation. The power output is maximum (and S ˙ gen is minimum) when the hot-
end temperature reaches the optimal level 3,9
T 1 1/2
˙
Q
T H,opt L H
CT L
˙
˙
The corresponding efficiency (W max /Q H ) is
(1 r) 1/2 1

(1 r) 1/2 1
˙
where r Q H /(CT ) is a dimensionless way of expressing the size (thermal resistance) of
L
the power plant. An optimal T value exists because when T T H,opt , the Carnot efficiency
H
H

Figure 8 Power plant model with bypass heat leak. 3,9