Time limit for using the semi-infinite heat transfer solutions: a novel approach

In the present study, authors are conceptually showing that the classically considered time limit to use the semi-infinite approximate solutions is highly conservative, particularly at the internal location(s) inside the finite heat conduction medium. Accordingly, a new length scale, which accounts the heat propagation from the far-field boundary condition as well, is proposed to ascertain the prolonged time limit. The proposed time limit is obtained by comparing the temperature distribution in a finite heat conduction problem with its equivalent semi-infinite model. Overall, three standard one-dimensional heat conduction problems are analysed and the proposed time limit is found to be valid in all three problems. The new time limit will certainly boost the utility of the semi-infinite solutions and rejuvenate the interest of the scientific community in such solutions.