Page 144 - Mechanical Engineers' Handbook (Volume 4)

9 Constructal Theory 133

Figure 10 Power plant with two finite-size heat Figure 11 Refrigerator model with two finite-
exchangers. 3 size heat exchangers. 3

exchangers (Fig. 11) subjected to the total UA constraint listed above, the refrigerator power
input is minimum when UA is divided equally among the two heat exchangers, (UA) H,opt
– 1 UA (UA) .
2 L,opt

9 CONSTRUCTAL THEORY

Flow systems are imperfect thermodynamically because of the resistances that their flows
must overcome. Depending on system purpose and complexity, the currents may carry fluids,
heat, electricity, and chemical species. The resistances are an integral and unavoidable pres-
ence because of the finite-size constraints that define the flow system. For example, the
resistance to the flow of heat between two streams in a balanced counterflow heat exchanger
can be made vanishingly small if the heat transfer surface can be made infinitely large. In
reality, the surface size is fixed, and this means that the heat current is destined to encounter
a thermal resistance. The current flows irreversibly, and this feature has a negative effect on
global thermodynamic performance. The flow system is destined to be imperfect.
When the flow system is complex, the currents and resistances are many and diverse.
The route to higher global performance consists of balancing each resistance against the rest.
The distributing and redistributing of imperfection through the complex flow system is ac-
complished by making changes in the flow architecture. A prerequisite then is for the flow
system to be free to change its configuration—free to morph. The morphing of structure is