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Entropy generation analysis in error estimation of an approximate solution: A constant surface temperature semi-infinite conductive problem

Esfahani Abolfazli Javad (Mechanical Engineering Department, Ferdowsi University of Mashhad, Mashhad, Iran)
Koohi-Fayegh Seama (Mechanical Engineering Department, Ferdowsi University of Mashhad, Mashhad, Iran)

The integral solution of one-dimensional heat conduction in a semi-infinite wall with constant temperature at its surface has been reviewed and compared with the exact solution for three temperature profiles. Then, an entropy generation analysis has been carried out for all solutions. Introducing an average normalized entropy generation, the error of the integral solution is found to show values in the same order as the values calculated for the normalized entropy generation. Therefore, it can be concluded that when no exact solution is available for a similar problem, one can verify the error of the available approximate solutions simply by applying an entropy generation analysis on the problem.

Keywords: heat conduction, semi-infinite, constant surface temperature, approximate solution, entropy generation, estimation error