MULTIDIMENSIONAL FINITE-ELEMENT CODE FOR TRANSIENT HEAT TRANSFER CALCULATIONS

Abstract

A transient, multidimensional, finite-element code has been developed for predicting the time-dependent thermal field within solid geometries exposed to spatially varying, time-dependent boundary conditions. First, validation of the code is performed using both two- and three-dimensional finite-element meshes exposed to either step change or harmonically varying boundary conditions. Numerical predictions from the simulation are in very good agreement with analytical solutions for all types of elements and boundary conditions considered. Subsequently, the effects of time step, sampling frequency of harmonic boundary conditions, and grid density on solution accuracy and convergence are explored. The results suggest appropriate time stepping strategies for the time derivative of temperature, and optimum sampling rates for harmonic boundary conditions. Guidelines for mesh refinement near boundary surfaces are also furnished.

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Dennis N. Assanis

Address correspondence to Professor Dennis N. Assanis, Department of Mechanical and Industrial Engineering, University of Illinois ac Urbana-Champaign, 1206 West Green Street, Urbana, IL 61801, USA