Stretching/shrinking longitudinal fins of rectangular profile and heat transfer

• The stretching/shrinking parameter enhances the fin temperature.
• The temperature is reduced by increasing the Biot number.
• Higher fin efficiencies occur for shrinking fin profiles.
• A shrinking fin surface performs better fin efficiency and heat transfer rate.

The present study deals with the heat transfer enhancement and efficiency of longitudinal rectangular fin profiles when a stretching or shrinking mechanism is mounted on the surface of the fin. Exact analytic solutions are sought from which the combined effects of some physical parameters like the convection sink temperature parameter, the Peclet number, the stretching/shrinking parameter and the convection–conduction parameter (Biot number) on the efficiency of longitudinal rectangular fins against non stretched straight rectangular fins can be comparatively analyzed. It is shown that stretching degrades the efficiency, whereas shrinking provides better fin efficiency pointing to significant advantages in terms of fin design purposes. Moreover, the presented neat formulae serve a verification tool for the researchers actively working in the field, particularly when numerical methods are employed to investigate more complex phenomena.