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Optimization and Computational Fluid Dynamics - Department of ...

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8 Multi-objective <strong>Optimization</strong> in Convective Heat Transfer 263<br />

though easier to optimize, cannot provide the same performances obtained by<br />

NURBS channels. It has been shown that, as in similar studies, very different<br />

channel shapes <strong>of</strong>fer almost the same flow <strong>and</strong> heat transfer performance,<br />

i.e., non-uniqueness <strong>of</strong> the shape optimization problem. The 3D channels have<br />

been obtained by extrusion at variable angles <strong>of</strong> linear piecewise <strong>and</strong> NURBS<br />

channels. The former has been optimized while for the latter, a parametric<br />

analysis has been done. In both cases, the presence <strong>of</strong> secondary motions,<br />

<strong>and</strong> in particular steady longitudinal vortices, leads to a significant increase<br />

<strong>of</strong> the heat transfer rate in comparison with the 2D channels.<br />

The optimization <strong>of</strong> the CC periodic module has been carried out considering<br />

both hot <strong>and</strong> cold fluid streams, without the necessity <strong>of</strong> imposing<br />

artificial constant-temperature or constant-flux boundary conditions. In this<br />

case, a major effort was the proper linking <strong>of</strong> the different s<strong>of</strong>tware packages<br />

<strong>and</strong> additional utilities. The first results are very encouraging since one <strong>of</strong><br />

the optimized geometries leads to almost the same heat transfer performance<br />

<strong>of</strong> the original design, but with a significant pressure drop reduction <strong>of</strong> about<br />

20% <strong>and</strong> without increase <strong>of</strong> the heat transfer surface.<br />

The procedure described has been proven robust <strong>and</strong> efficient, <strong>and</strong> in principle,<br />

could be applied to even more complex problems.<br />

Acknowledgements Financial support for this research is provided by MIUR, PRIN<br />

2004, Surface <strong>Optimization</strong> for Heat Transfer Problems, <strong>and</strong> PRIN 2005, Study <strong>and</strong> <strong>Optimization</strong><br />

<strong>of</strong> Buoyancy-controlled Thermal Systems, <strong>and</strong> is gratefully acknowledged.<br />

References<br />

1. ANSYS, Inc.: ANSYS-CFX, Release 10.0. Canonsburg, PA, USA (2005). See also<br />

URL http://www.ansys.com/products/cfx.asp<br />

2. ANSYS, Inc.: ANSYS ICEM-CFD Documentation. Canonsburg, PA, USA (2005). See<br />

also URL http://www.ansys.com/products/icemcfd.asp<br />

3. Bia̷lecki, R.A., Burczyński, T., D̷lugosz, A., Ku´s, W., Ostrowski, Z.: Evolutionary<br />

shape optimization <strong>of</strong> thermoelastic bodies exchanging heat by convection <strong>and</strong> radiation.<br />

Comp. Methods Appl. Mech. Engrg. 194(17), 1839–1859 (2005)<br />

4. Biethahan, J., Nissen, V. (eds.): Evolutionary Algorithms in Management Applications.<br />

Springer, Berlin (1995)<br />

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decision models with multiple criteria: Stepping stones for the analyst, 1st edn. International<br />

Series in Operations Research <strong>and</strong> Management Science, Volume 86. Springer,<br />

Boston (2006)<br />

6. Cheng, C.H., Wu, C.Y.: An approach combining body-fitted grid generation <strong>and</strong> conjugate<br />

gradient methods for shape design in heat conduction problems. Numerical<br />

Heat Transfer 37, part B, 69–83 (2000)<br />

7. Coello Coello, C.A.: Recent Trends in Evolutionary Multiobjective <strong>Optimization</strong>: Theoretical<br />

Advances <strong>and</strong> Applications, chap. Recent Trends in Evolutionary Multiobjective<br />

<strong>Optimization</strong>, pp. 7–32. Springer-Verlag, London (2005)<br />

8. Coello Coello, C.A., Van Veldhuizen, D.A., Lamont, G.B.: Evolutionary Algorithms<br />

for Solving Multi-Objective Problems. Kluwer Academic Publishers, New York (2002)

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