Simulation of transient heat conduction using one-dimensional mapped infinite elements

Many engineering problems exist in physical domains that can be said to be infinitely large. A common problem in the simulation of these unbounded domains is that a balance must be met between a practically sized mesh and the accuracy of the solution. In transient applications, developing an appropriate mesh size becomes increasingly difficult as time marches forward. The concept of the infinite element was introduced and implemented for elliptic and for parabolic problems using exponential decay functions. This paper presents a different methodology for modeling transient heat conduction using a simplified mesh consisting of only two-node, one-dimensional infinite elements for diffusion into an unbounded domain and is shown to be applicable for multi-dimensional problems. A brief review of infinite elements applied to static and transient problems is presented. A transient infinite element is presented in which the element length is time-dependent such that it provides the optimal solution at each time step. The element is validated against the exact solution for constant surface heat flux into an infinite half-space and then applied to the problem of heat loss in thermal reservoirs. The methodology presented accurately models these phenomena and presents an alternative methodology for modeling heat loss in thermal reservoirs.