On the use of fractional calculus in a heat flow problem in a circular plate

• Grant number: 24/23322-8
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: June 01, 2025
• End date: May 31, 2026
• Field of knowledge: Interdisciplinary Subjects
• Principal Investigator: Sergio Adriani David
• Grantee: Gabriel Antonio Felipe
• Host Institution: Faculdade de Zootecnia e Engenharia de Alimentos (FZEA). Universidade de São Paulo (USP). Pirassununga , SP, Brazil

Abstract

The extension of mathematical operators of differentiation and integration of integer order to operators of fractional order has allowed greater flexibility and generalization in the mathematical modeling of complex problems. The application of Fractional Calculus (FC) in problems modeled by Partial Differential Equations (PDEs) has proven to be of extreme importance in the description of various phenomena, among which we seek to include the one involving the problem of steady-state heat flux in a circular plate. The main objective of this project is to employ FC to analytically model the aforementioned physical phenomenon, using the method of separation of variables and power series in order to obtain analytical solutions for both integer and arbitrary (fractional) order cases. It is expected that the results will contribute to advancing the understanding of the advantages and disadvantages of applying FC to a problem involving heat flux in circular plates or the study of how heat propagates through a material with a circular geometry, such as a flat plate or disk. Furthermore, the goal is to improve learning in this area, as well as to expand the understanding and discussion on the potential use of FC as a mathematical tool applied to classical problems, exploring its implications.