Dynamic analysis of helical fin with fixed fin tip temperature boundary condition

Abstract

A dynamic analysis is performed on a traditional helical fin; but, with fixed fin tip temperature, rather than adiabatic fin tip boundary condition. A time dependent solution is provided. The final version of the solution is presented in an analytical and closed form equation. The problem is solved using Laplace transforms for partial differential equations. The complete governing equation is extensively in the form of the Bessel function. It is shown that the dynamic equation, when time reaches infinity, resolves to the steady state solution for the same problem.