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8 Multi-objective Optimization in Convective Heat Transfer 255
Table 8.5 Control points for the selected NURBS-based channels
ID a ID b ID c
(x1,y1) (0, 0) (0, 0) (0, 0)
(x2,y2) (0.160, 0) (0.354, 0) (0.179, 0)
(x3,y3) (0.207, 0) (0.457, 0) (0.252, 0)
(x4,y4) (0.190, 0.220) (1.183, 0.251) (0.409, 0.161)
(x5,y5) (0.410, 0.199) (0.196, 0.267) (0.612, 0.207)
(x6,y6) (1.348, 0.198) (0.893, −0.234 (0.965, 0.224)
(x7,y7) (0.768, 0) (1.830, 0) (0.580, 0)
(x8,y8) (0.554, 0) (1.950, 0) (0.843, 0)
(x9,y9) (0.870, 0) (2.304, 0) (1.023, 0)
transl 0.290 −1.039 −0.204
ID d ID e ID f
(x1,y1) (0, 0) (0, 0) (0, 0)
(x2,y2) (0.341, 0) (0.113, 0) (0.347, 0)
(x3,y3) (0.487, 0) (0.171, 0) (0.480, 0)
(x4,y4) (1.149, 0.248) (−0.105, 0.249) (1.068, 0.209)
(x5,y5) (1.152, 0.268) (0.208, 0.279) (1.111, 0.262)
(x6,y6) (0.827, −0.362) (0.551, −0436) (0.696, −0.440)
(x7,y7) (1.853, 0) (0.685, 0) (1.890, 0)
(x8,y8) (1.880, 0) (0.909, 0) (1.916, 0)
(x9,y9) (2.221, 0) (1.023, 0) (2.263, 0)
transl −0.920 −0.268 −0.994
values of control points and of upper wall translation for the six channels are
listed.
8.8.3 Linear Piecewise versus NURBS
In Fig. 8.20, the results sets obtained by the linear piecewise and NURBS
optimization are compared. The ones marked by stars, represent channels
with linear piecewise wall profile. The others marked by squares, represent
channels with smooth NURBS wall profile. The higher geometrical complexity
and computational costs of NURBS channels is well counterbalanced by
the significant performance improvement over the simpler channels with linear
piecewise walls. The greater number of variables makes the convergence
slower and an asymptotic limit of the front was not reached during the optimization
of NURBS profile channel.