One dimensional transient heat conduction in segmented fin-like geometries with distinct discrete peripheral convection

This study presents the solution of transient heat conduction in a composite extended surface whose periphery is exposed to convection and whose thermophysical properties experience discontinuities along the longitudinal direction. The solution development uses the natural analytic approach and formats the description so that the constants of integration of each of the composite segments are expressed in terms of the previous segment's eigenfunctions. This allows the solution to be “built” in a very systematic and sequential manner. A three-segment case study is also provided to show the simplicity and applicability of the implementation of this solution.