Application of the Finite-Element Method to Heat-Transfer Problems. Part I. Finite-Element Method Applied to Heat-Conduction Solids with Nonlinear Boundary Conditions

摘要

The finite-element method was extended to solid heat conduction with a radiation-convection, nonlinear heat-flux, boundary condition. General finite-element models are developed that enable approximate solutions of transient heat in an arbitrary three-dimensional body subjected to the described initial conditions and nonlinear or linear heat flux across the surfaces of the body. Applications of the present approach involve: (a) heat in a semi-infinite solid with radiation taking place at the surface, (b) transient temperature in a slab subjected to radiation and convection boundary conditions at both surfaces, and (c) heat transfer of a small-caliber multilayer gun tube subjected to time-dependent heat convection and radiation boundary conditions under automatic firing situations. Numerical solutions to the first and the second problem are compared with the exact solution and with results obtained by use of the probability method. (Author)