Thermal analysis of orthotropic annular fins with contact resistance: A closed-form analytical solution

Light weight polymeric composite fins are being considered to tackle thermal management problems for many microelectronic components covering both industrial and commercial applications. These composite fins cannot be handled by a traditional one-dimensional approach because of inherently anisotropic; however, these materials can be designed to provide high thermal conductivity values in the desired direction to handle application-specific demands. In this paper, we present analytical solutions for temperature distribution and heat transfer rate for orthotropic two-dimensional, annular fins subject to convective-tip boundary condition and the contact resistance at the fin base. The generalized results are presented in terms of one geometric parameter (β/α) and three dimensionless fin parameters that relate the internal conductive resistance to three convective resistances discussed in terms of dimensionless variables such as contact, tip and axial Biot numbers (Bicr,Bier,Biz), in addition to the axial-to-radial conductivity ratio, K. Several special cases including the insulated tip boundary condition are presented. It is demonstrated that the temperature distribution and heat transfer rate from the two-dimensional isotropic annular fin introduced earlier in the literature, can easily be recovered from the benchmark solutions presented in this paper. Furthermore, dimensionless heat transfer rates are presented for the annular fins that can help to solve design and optimization problems of many natural-to-forced convection composite fins that are typically encountered in many applications.