Coated fins constitute a new concept in heat transfer enhancement. This type of fin is made from a primary material (the substrate) that usually possesses a low-to-moderate thermal conductivity. To augment the transfer of heat from the primary material to a surrounding fluid, a viable avenue is to coat the substrate with a thin layer of a high conductivity material (the coating). Undoubtedly, the formal model for a two-material fin is complicated because it involves a conjugate system of two heat conduction equations in two space variables. As a simpler alternative, Campo (2001) proposed a simplified quasi one-dimensional model that engages an ordinary differential equation with embedded spatial means of the thermal conductivities of the substrate and the coating. The objective of the present study is to extend the statistically-based ideas for a one material fin to two-material fins of variable thickness. To this end, a system of two heat conduction equations, coupled with the applicable boundary conditions, is solved with the Finite Element Method (FEM). The adequacy of the approximate algebraic route for the estimation of fin efficiencies is tested against the numerically-determined fin efficiencies supplied by the FEM.

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