Two-dimensional Cartesian heat conduction for short times

This paper is intended to provide very accurate analytical solutions modelling transient heat conduction processes in 2D Cartesian finite bodies for small values of the time. The analysis of the diffusion of two-dimensional and boundary effects indicates that, when the space and time coordinates satisfy a certain criterion, the simple transient 1D semi-infinite solutions may be “used” for generating extremely accurate values for temperature and heat flux at any point of a finite rectangle. Also, they may be “used” with excellent accuracy as short-time solutions when the time-partitioning method is applied (so avoiding the usually difficult integration of the short-cotime Green‟s functions). A complex 2D semi-infinite problem is solved explicitly and evaluated numerically as part of the analysis. The proposed criterion is based on an accuracy of one part in 1010 but can be made more or less accurate if desired.