Analysis of polygonal fins using the boundary element method

In this paper, polygonal fins on square and hexagonal (equilateral–triangular) pitches are analysed and compared with the equivalent radial rectangular fin based on the same surface area of the fins. Semi-analytical solutions for the aforementioned fins are obtained using the boundary element method and, in addition, the convergence, stability and consistency of the numerical method employed are checked. The heat flows corresponding to the polygonal fins analysed in this study are compared in the normal energy procedure taking the radial fin with an adiabatic boundary condition on the extreme radius. The isotherms for the geometries investigated in this paper are also presented. The numerical analysis developed for the polygonal fins is based on typical geometries and operating conditions used in evaporators and condensers in an industrial 5 kW refrigeration system employing vapour–recompression cycles.