Analysis of heat transfer through Bi-convection fins

Heat transfer through fins subject to two different convective media is modeled and analyzed analytically in this work. The terminology “Bi-convection fin” is used to refer to this kind of fins. Five different cases are analyzed: Case A: Bi-convection thickness-wise Bi-metallic fins; Case B: Bi-convection span-wise rectangular fins; Case C: Bi-convection longitudinal-wise fins; Case D: Bi-convection perimeter-wise fins with uniform cross-section; and Case E: Bi-convection perimeter-wise permeable fins. Closed form solutions for the fin temperature and heat transfer rate are obtained. It is found that Heat transfer through Bi-convection fins may be minimized for certain designs such as those belonging to cases A, B, D and E. On the other hand, it may be maximized as for those belonging to case C at specific values of fin indices and convection heat transfer coefficients ratio. Finally, the heat transfer through Bi-convection fins is found to increase as their effective thermal conductivity, cross-sectional area, fin indices and the difference between the base and the effective free stream temperatures increase.