Effects of Wavy Profile on Heat Transfer Through a Fin

The effects of a wavy surface on a straight rectangular fin are studied numerically. The governing equation is formulated from the energy balance principle. Suitable dimensionless variables and parameters are defined by the dimensionless form of the governing equation. The Runge-Kutta shooting technique numerically solves the equation, yielding a dimensionless temperature distribution. A semi-analytical solution applying the collocation method is also generated. Results of this numerical method are compared with the existing exact analytical solutions for other space dependent profiles such as triangular fins, concave profile fins, and convex fins for verification of the numerical results. Further, results of the numerical technique are compared with those of the collocation method for small parameters and are found to be in close agreement. The influences of the dimensionless wave amplitude, wave number, dimensionless heat transfer coefficient, and Biot number on temperature distribution and efficiency are examined. Results reveal that for insulated tip approximation, when wave number rises from 0 to 2.5 for [Formula: see text], fin effectiveness enhances by nearly 6.12%. Fin efficiency, for insulated tip case may be increased by nearly 4.14% by using fin with periodic surface of dimensionless amplitude 0.25 and dimensionless wave number [Formula: see text].