wseas-12212-20261019073336-d008b4 20261019073336141 wseas/wseas wseas.group@gmail.com WSEAS WSEAS Transactions on Heat and Mass Transfer 1790-5044 2224-3461 05 25 2026 05 25 2026 21 Antonio Campo Coordinación de Ingeniería Mecánica Universidad Simón Bolívar Barruta, Caracas, Edo. Miranda, VENEZUELA The present study addresses unsteady heat conduction in a large wall with constant temperature at the surfaces and uniform temperature initially. The thermal diffusivity of the solid material is taken as nearly independent of temperature in the temperature interval of operation. A nonlinear interpolatin scheme is implemented with sole input from the Fourier one term series in the “large time” sub–domain t→∞. The goal of the study is to elaborate a center temperature asymptote, a mean temperature asymptote, as well as a heat transfer rate asymptote associated with the problematic “small time” sub–domain t→0. The obtained asymptotic thermal results exhibit excellent quality when compared against benchmark exact, analytical results that are available in the heat transfer literature. 10 19 2026 10 19 2026 176 15 https://creativecommons.org/licenses/by/4.0/ 10.37394/232012.2026.21.15 https://wseas.com/journals/articles.php?id=12212 J. B. J. Fourier, Théorie Analytique de la Chaleur, Firmin Didot, Paris, France, 1822. English translation: The Analytical Theory of Heat, Cambridge University Press, Cambridge, England, UK, 2009. https://archive.org/details/analyticaltheory00fourrich. H. S. Carslaw and J. C. Jaeger, Conduction of Heat in Solids, Oxford Press, Oxford, England, UK, 1959. V. Arpaci, Conduction Heat Transfer, Addision–Wesley, Reading, MA, 1966. A. V. Liukov, Analytical Heat Diffusion Theory, Academic Press, London, England, UK, 1968. G. E. Myers, Analytical Methods in Conduction Heat Transfer, Genium Publishing Corp., Amsterdam, NY,1987. M. N. Özişik, Heat Conduction, 2nd edition, John Wiley and Sons, Hoboken, NJ, 1993. D. Poulikakos, Conduction Heat Transfer, Prentice Hall, Englewood Cliffs, NJ, 1993. L. M. Jili, Heat Conduction, 3rd edition, Springer–Verlag, Berlin–Heidelberg, Germany, 2009. S. Kakaç, Y. Yener and C. Cotta, Heat Conduction, 5th edition, Taylor & Francis, CRC Press, Boca Raton, FL, 2018 J. von zur Gathen, Modern Computer Algebra, 3rd edition, Cambridge University Press, Cambridge, England, UK, 2013. Y. A. Cengel, M. A. Boles and M. Kanoglu, Thermodynamics: An Engineering Approach, 10th edition, McGraw Hill, New York, 2023. M. Al–Gwaiz, Sturm–Liouville Theory and Applications, Springer, Berlin/Heidelberg, Germany, 2008. U. Grigull, J. Bach and H. Sandner, Näherungslösungen der nichtstanionaren Wärmeleitung, Forsch. Ing. Wes., Vol. 32, No. 1, pp. 11–18, 1966. U. Grigull and H. Sandner, Heat Conduction, Hemisphere Publishing Com., New York, NY, 1984. C. Cortés, A. Campo and I. Arauzo, Reflections on lumped models for unsteady heat conduction in simple solid bodies, Intern. J. Therm. Sci., Vol. 42, No.10, pp. 921–930, 2003. https://doi.org/10.1016/S1290-0729(03)00070-X J. H. Lienhard V and J. H. Lienhard IV, A Heat Transfer Textbook, 6th edition. Version 6.00, Phlogiston Press, Cambridge MA, 2000–2024. https://ahtt.mit.edu. H. Suyama, Introduction to Modeling and Analysis of Complex Systems, Open SUNY Textbooks, The State University of New York, Albany, NY, 2015. G. Mastroianni and G. Milovanovic, Interpolation Processes: Basic Theory and Applications, Springer, Berlin/Heidelberg, Germany, 2008. F. S. Guzmán, Simple methods for initial value problems involving PDEs. In: Numerical Methods for Initial Value Problems in Physics, Springer, Berlin/Heidelberg, Germany, 2023. www.wolfram.com, Wolfram|One, Champaign, IL, 2026.