Diffusion of thermal disturbances in two-dimensional Cartesian transient heat conduction

This paper analyzes the diffusion of thermal disturbances in heat-conducting two-dimensional rectangular bodies through characteristic times, such as penetration and deviation times, denoting their effects within a certain order of magnitude. A single basic criterion governing the above diffusion is derived thanks to the similarity of the findings. It allows very accurate solutions to be obtained considering in advance only the physical region of interest in place of considering the complete body. Therefore, it is efficient in terms of modeling and computational effort in numerically based methods as well as analytical techniques. In the former case, the grid domain can considerably be reduced. In the latter case, the number of terms needed to obtain long-time solutions when time-partitioning is applied can significantly be limited. Also, complex 1D and 2D semi-infinite problems are solved explicitly in the paper and evaluated numerically as part of the analysis.