Statistics and Risk Management and Analysis - 18/2/2015

Wednesday, 18 February 2015, 1:30 p.m.

Lecturer: Carlos Dias, CENIMAT/I3N, DCM-FCT-UNL

Title: "A method of recursive images provides exact solutions for transient heat diffusion in a slab"

Local: Room 1.6, Edifício VII
Faculdade de Ciências e Tecnologia, Quinta da Torre, Caparica

Abstract: A simple yet powerful approach is presented to synthesize series solutions for the transient heat diffusion equation in a slab, using the superposition principle. The first term of the series is the solution for a semi-infinite medium satisfying the front face boundary condition which is known in a number of cases. A second term is then added to the solution which make the series satisfy the boundary condition at the back interface. After that, a third term is added, in order for the series to satisfy the boundary condition again at the front face and so on. As the magnitude of the added terms decrease exponentially, these series solutions converge very rapidly. This is an elegant method which can be traced back to the method of images applied to the diffusion equation, which nowadays is rarely used in university texts in the framework of diffusion phenomena. We illustrate its application in simple situations and also in a not so simple one. This generalized method of images has the potential to provide transient solutions to heat diffusion problems that normally are given at the graduate level but which, with the present approach, could be solved at the undergraduate level.