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Numerical solutions are constructed and presented for the thermal distribution, the dimensionless heat flux rate, and fin efficiency for a two-dimensional orthotropic fin of cylindrical geometry formed by two media subject to a convection limit condition on the side surface and at the high fin base, and to a uniform temperature imposed on the other base of the fin. The results are presented and discussed according to the study parameters, radial thermal conductivity ratio, radial Biot number, and axial Biot number for each medium. Many specific cases are obtained from the global solution presented in this work, among others, the temperature distribution and the dimensionless heat flux rate at the base of a single orthotropic or isotropic fin as well as the case of a fin formed by an orthotropic and isotropic media. The findings of the present study demonstrate that the newly proposed fin design significantly improves the dimensionless heat flux rate of the fin compared to the conventional design. This improvement is particularly significant when the axial Biot number of the outer medium is high and the axial Biot number of the inner medium is low, regardless of the ratio of radial thermal conductivities. These results suggest that the proposed fin design is better suited for applications where heat transfer is critical, and the external environment has a high thermal resistance. In addition, the proposed design also provides a more compact geometry, which not only improves the mechanical performance of the fin but also reduces the cost of the material used in its fabrication.

Numerical study of the thermal behavior of a cylindrical fin formed by two orthotropic media