Meza-Castillo, Omar E.

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    Analysis of conduction heat transfer in semi-infinite slabs and infinite quadrants with discrete heat generation sources using green's function integral methods
    (2003) Meza-Castillo, Omar E.; Venkataraman, Nellore S.; College of Engineering; Coutín Rodicio, Sandra; González Cruz, Jorge E.; Department of Mechanical Engineering; Rinaldi Ramos, Carlos M.
    The problem of steady state heat conduction in semi-infinite plates and infinite quadrants of constant thermal conductivity, with discrete heat generating sources and Dirichlet boundary conditions (temperature specified on the boundary) was solved using the method of Green’s functions using the integral techniques. The Green’s functions for the geometries were found by the method of images. These functions were then employed for the solution of five cases for semi-infinite slabs with heat generation sources of different geometry. These were: a thin plate heating source, a hollow box heating source, a square prismatic heating source, finite line heating source and a thin cylindrical heating source. For infinite quadrants a heat generation source of the form of a thin current carrying wire in the form a square was considered. The heat sources were idealized as internal thermal energy generation. Solutions found with this method always yield closed form algebraic expressions or analytical solutions or “almost analytical” solutions (in the form of an integral). Results found in this work were validated and compared with the numerical method of finite elements in Ansys 6.0. It was concluded that, for the cases considered here, the method used in the present work is elegant and is superior in terms of computational requirements.