Triangular Shell Heat Transfer Element for the Thermal Analysis of Nonuniformly Heated Structures

Abstract

This paper presents a triangular shell heat transfer element that is used to simulate the thermal response of nonuniformly heated structures. The formulation uses a combination of finite-element and control volume techniques to arrive at a layered shell element that is used to solve the 3D conduction heat transfer problem in a highly efficient manner. This paper considers a 3-node linear element and a 6-node quadratic element. The element formulation is verified against a converged continuum heat transfer model for a thick steel plate exposed to a concentrated heat flux, a thick steel pipe exposed to a concentrated heat flux, and a concrete slab exposed to a localized fire. The verification studies demonstrate that the linear and quadratic elements consistently converge to the continuum model and require a fraction of the computational cost. The verification study involving the concrete slab exposed to a localized fire demonstrates that the formulation can readily handle steep temperature gradients as well as temperature-dependent material properties.