Page 139 - Mechanical Engineers' Handbook (Volume 4)

128 Exergy Analysis, Entropy Generation Minimization, and Constructal Theory

Figure 5 The optimal size of a plate, cylinder and sphere for minimum entropy generation. (From A.
Bejan, G. Tsatsaronis, and M. Moran, Thermal Design and Optimization. 1996 John Wiley & Sons,
Inc. Reprinted by permission.)

˙
Q /W
B B
)
U (k T Pr 1/3 1 /2

and W is the plate dimension perpendicular to the figure. The same figure shows the cor-
responding results for the optimal diameter of a cylinder in cross-flow, where Re
D,opt
U D / , and B is given by the same expression as for the plate. The optimal diameter of

opt
the sphere is referenced to the sphere duty parameter defined by
˙
Q
B B
s
(k T Pr 1/3 1 /2
)

The fins built on the surfaces of heat exchanges act as bodies with heat transfer in
external flow. The size of a fin of given shape can be optimized by accounting for the internal
heat-transfer characteristics (longitudinal conduction) of the fin, in addition to the two terms
(convective heat and fluid flow) shown in the last S ˙ gen formula. The EGM method has also
been applied to complete heat exchangers and heat exchanger networks. This vast literature
is reviewed in Ref. 4. One technological benefit of EGM is that it shows how to select certain
dimensions of a device so that the device destroys minimum power while performing its
assigned heat and fluid flow duty.
Several computational heat and fluid flow studies recommended that future commercial
CFD packages have the capability of displaying entropy generation rate fields (maps) for
8
both laminar and turbulent flows. For example, Paoletti et al. recommend the plotting of
˙
˙
contour lines for constant values of the dimensionless group Be S gen, T /(S
gen, T