Numerical Analysis of Heat Transfer through a Pin Fin using RK5 and Euler Methods under the Tip Condition of Convective Heat Transfer

Numerical determination of the temperature distribution along a circular pin fin and the fin heat transfer rate to the medium is presented. Both an Euler method and Butcher’s fifth-order Runge- Kutta method (RK5) were used to solve the second-order governing differential equation for the temperature distribution. A shooting method was employed to convert the boundary value problem into an initial value problem. Computer code on SciLab package was written to perform the numerical iterations until the solution converges to the given convective heat transfer condition at the tip of the pin fin. Numerical results approximated the analytical solution well, while those from the RK5 method were almost identical to the exact solution. RK5 is thus by far more accurate than the Euler method. Parameters such as length, diameter and material of the pin fin were varied to improve the effectiveness of the pin fin for the heat transfer.