Prediction of temperature distribution in the two-dimensional bodies with heat source and radiation exchange present at the surface

Abstract

This paper is the outgrouth of the research to find theoretically the temperature distribution of metal workpiece placed in an ion-nitriding furnace. The problem is represented by heat conduction of two-dimensional bodies with radiation source present at the surface. Also there exists exchange of radiative energy between bodies or between differential areas in a self-seeing surface. The model problems considered in this paper are two solid cylinders of the same diameter and the same material placed at a distance, and single solid cylinder consisted by half of a hollow thick-walled circular cylinder. The first cylinder are assumed black bodys but the second is treated more generally by assuming a gray body. The difficulty of the problem lie in the boundary condition which is nonlinears and the integral form due to the presence of radiation source and exchange of radiative energy. The problem is solved numerically by the finite difference method followed by interative procedures. The converged steady state temperature distribution is given and the effect of radiation is parametrically outlined. Temperature measurement are made in several point with radiation pyrometer and it is found the comparison is satisfactory.