Analytical and numerical modeling of steady periodic heat transfer in extended surfaces

Abstract

This paper deals with the analytical and numerical approaches that have been used to study periodic or oscillatory heat transfer processes occurring in extended surfaces. The details pertain to harmonic oscillations but many of the methods can be applied to more general periodic functions. For linear problems, the techniques include complex combination, Laplace transforms, finite differences, and boundary elements. For the nonlinear situations, approaches such as finite differences, finite elments, and different combinations of complex temperature, perturbation, series expansions, straightline, and finite differences have proved effective. Following a brief introduction, the applications of each approach are discussed in detail. Both straight and annular fin configurations are covered and the profile shapes include rectangular, trapezoidal, triangular, and convex parabolic. The periodic conditions involve oscillating base temperature, oscillating base heat flux, oscillating environment temperature, convection at the fin's base through a fluid with oscillating temperature, and some combinations of these conditions. The nonlinear problems discussed cover radiating and convecting-radiating fins, fins with variable thermal conductivity and coordinate dependent heat transfer coefficients, and systems with fin-to-fin, fin-to-base, and fin-to-environment radiative interactions