Bi-objective optimization of axial profile of pin fin with uniform base heat flux

Abstract

Cone shaped pin fin with curved profile and uniform base heat flux was investigated. The result from simultaneous optimization in regard of fin efficiency and total volume is presented. The profile is represented by the Non-Uniform Rational B-Spline (NURBS) for an additional degree of freedom to morph during the optimization process. An overall dominance was obtained from the present work, as compared to the classic concave parabolic profile, the practical constraint in fabrication taken into consideration. The profiles corresponding to the acquired Pareto solution sets tend to comply with the constructal law of design, in which freestream of heat flow is expected. Keywords pin fin; curved axial profile; NURBS; bi-objective optimization; constructal design Nomenclature T Temperature, K BiL Biot Number f Curve Function of the Axial Pin Fin Profile, m F Dimensionless Curve Function of the Axial Pin Fin Profile fr Reference Profile, see Eq. (4), m h Heat Transfer Coefficient, W/(m 2 ꞏK) i Indice for Control Points k Thermal Conductivity, W/(mꞏK), see Eq. (2) and Eq. (7); Indice for Breaking Points in a Knot Vector, see Eq. (10), Eq. (11) and Eq. (12); Order of the Basis Function for NURBS, see Eq. (10), Eq. (11) and Eq. (12)