Accession Number : AD0430798


Title :   AN INTEGRAL EQUATION APPROACH TO HEAT CONDUCTION PROBLEMS WITH NON-LINEAR BOUNDARY CONDITIONS,


Corporate Author : WEST VIRGINIA UNIV MORGANTOWN


Personal Author(s) : Brant,Darius Nelson


Report Date : Jan 1943


Pagination or Media Count : 78


Abstract : A numerical method is developed for solving heat conduction problems with nonlinear boundary conditions by step-wise integration of a singular, Volterra integral equation of the second kind. This equation is formulated by use of Laplace transforms and the convolution theorem. The method is developed and tested by solving for the surface temperature (over a large time range) of an infinite slab radiating to a zero sink. The finite slab solution is also demonstrated and the application to other boundary conditions is discussed. The numerical integration is performed by dividing the integrand into three regions which exhibit different behaviors. By using special devices in two of these regions the difficulties due to the singular nature of the integral were circumvented without resorting to iteration procedures. (Author)


Descriptors :   HEAT TRANSFER , INTEGRALS , SURFACES , THERMAL RADIATION , THERMAL CONDUCTIVITY


Distribution Statement : APPROVED FOR PUBLIC RELEASE