Optimal Shape Design for 2D Radiative Enclosures Using NURBS

Subject Areas : Analytical and Numerical Methods in Mechanical Design

Farbod Fakhrabadi ¹ , Farshad Kowsary ²

1 - Department of Mechanical Engineering, Qazvin Branch, Islamic Azad University, Qazvin, Iran
2 -

Received: 2024-01-30 Accepted : 2024-04-05 Published : 2025-05-20

Keywords: Optimal shape design, Radiative enclosures, NURBS,

Abstract :

This article presents an optimal shape design methodology for 2D diffuse-walled radiant enclosures. In this study, the shape of the enclosure is parameterized by means of non-uniform rational B-spline (NURBS) surfaces, and their control points represent the design variables. The enclosure geometry is discretized by choosing the parameters of NURBS surfaces as generalized curvilinear coordinates, and the radiosity equation is solved using the infinitesimal-area analysis technique developed by Daun and Hollands [1]. The simplified conjugate-gradient method (SCGM) is used as the optimization method to obtain the optimal shape and adjust the design variables intelligently. The methodology is demonstrated by optimizing the shape profile of a cavity with the objective of enhancing the apparent emittance.

References:

[1] Daun, K. J., and Hollands, K. G. T., 2001, “Infinitesimal-Area Radiative Analysis Using Parametric Surface Representation, through NURBS,” J. Heat Transfer, 123, pp. 249-256.
[2] Fabbri, G., 1997, “A Genetic Algorithm for Fin Profile Optimization,” Int. J. Heat Mass Transfer, 40, pp. 2165-2172.
[3] Fabbri, G., 1998, “Heat Transfer Optimization in Internally Finned Tubes under Laminar Flow Conditions,” Int. J. Heat Mass Transfer, 41, pp. 1243-1253.
[4] Fabbri, G., 1999, “Optimum Profiles for Asymmetrical Longitudinal Fins in Cylindrical Ducts,” Int. J. Heat Mass Transfer, 42, pp. 511-523.
[5] Cheng, C. H., and Wu, C. Y., 2000, “An Approach Combining Body-Fitted Grid Generation and Conjugate Gradient Methods for Shape Design in Heat Conduction Problems,” Numerical Heat Transfer, Part B, 37, pp. 69-83.
[6] Lan, C. H., Cheng, C. H., and Wu, C. Y., 2001, “Shape Design for Heat Conduction Problems Using Curvilinear Grid Generation, Conjugate Gradient, and Redistribution Methods,” Numerical Heat Transfer, Part A, 39, pp. 487-510.
[7] Cheng, C. H., and Chang, M. H., 2003, “Shape Design for a Cylinder with Uniform Temperature Distribution on the Outer Surface by Inverse Heat Transfer Method,” Int. J. Heat Mass Transfer, 46, pp. 101-111.
[8] Cheng, C. H., Chan, C. K., and Lai, G. J., 2008, “Shape Design of Millimeter-Scale Air Channels for Enhancing Heat Transfer and Reducing Pressure Drop,” Int. J. Heat Mass Transfer, 51, pp. 2335-2345.
[9] Daun, K. J., Howell, J. R., and Morton, D. P., 2003, “Geometric Optimization of Radiative Enclosures through Nonlinear Programming,” Numerical Heat Transfer, Part B, 43, pp. 203-219.
[10] Hilbert, R., Janiga, G., Baron, R., and Thevenin, D., 2006, “Multi-Objective Shape Optimization of a Heat Exchanger Using Parallel Genetic Algorithms,” Int. J. Heat Mass Transfer, 49, pp. 2567-2577.
[11] Nobile, E., Pinto, F., and Rizetto, G., 2006, “Geometric Parameterization and Multiobjective Shape Optimization of Convective Periodic Channels,” Numerical Heat Transfer, Part B, 50, pp. 425-453.
[12] Balagangadhar, D., and Roy, S., 2001 “Design Sensitivity Analysis and Optimization of Steady Fluid-Thermal Systems” Comput. Methods Appl. Mech. Engrg., 190, 5465-5479.
[13] Piegl, L., and Tiller, W., 1997, The NURBS Book, 2nd Ed., Springer-Verlag, Berlin.
[14] Siegel, R., and Howell, J. R., 2002, Thermal Radiation Heat Transfer, 4th Ed., Taylor and Francis, NewYork.
[15] Cheng, C. H., and Chang, M. H., 2003, “A Simplified Conjugate-Gradient Method for Shape Identification Based on Thermal Data,” Numerical Heat Transfer, Part B, 43, pp. 489-507.