Open AccessExplicit Solution for Cylindrical Heat Conduction
Author(s) -
Kaitlyn Parsons,
Tyler Reichanadter,
Andi Vicksman,
Harvey Segur
Publication year - 2016
Publication title -
american journal of undergraduate research
Language(s) - English
Resource type - Journals
eISSN - 2375-8732
pISSN - 1536-4585
DOI - 10.33697/ajur.2016.020
Subject(s) - heat equation , partial differential equation , poincaré–steklov operator , mathematics , boundary value problem , heat kernel , mathematical analysis , first order partial differential equation , separation of variables , thermal conduction , free boundary problem , parabolic partial differential equation , robin boundary condition , thermodynamics , physics
The heat equation is a partial differential equation that elegantly describes heat conduction or other diffusive processes. Primary methods for solving this equation require time-independent boundary conditions. In reality this assumption rarely has any validity. Therefore it is necessary to construct an analytical method by which to handle the heat equation with time-variant boundary conditions. This paper analyzes a physical system in which a solid brass cylinder experiences heat flow from the central axis to a heat sink along its outer rim. In particular, the partial differential equation is transformed such that its boundary conditions are zero which creates a forcing function in the transform PDE. This transformation constructs a Green’s function, which admits the use of variation of parameters to find the explicit solution. Experimental results verify the success of this analytical method.KEYWORDS: Heat Equation; Bessel-Fourier Decomposition; Cylindrical; Time-dependent Boundary Conditions; Orthogonality; Partial Differential Equation; Separation of Variables; Green’s Functions