Open AccessTime limit for using the semi-infinite heat transfer solutions: a novel approach
Author(s) -
Mahesh Kumar Yadav,
Vinod Yadav
Publication year - 2020
Publication title -
iop scinotes
Language(s) - English
Resource type - Journals
ISSN - 2633-1357
DOI - 10.1088/2633-1357/abaf67
Subject(s) - limit (mathematics) , thermal conduction , heat transfer , time limit , mathematics , boundary value problem , boundary (topology) , mathematical analysis , mechanics , thermodynamics , physics , engineering , systems engineering
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.