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ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

Anomalous Heat Diffusion in a Boundary Layer: A Fractionary Blasius's System

Journal of Applied Nonlinear Dynamics 12(2) (2023) 245--256 | DOI:10.5890/JAND.2023.06.004

Thiago Bissiatte Monteiro, Alexandre C. L. Almeida, Ad\'{e}lcio C. Oliveira

Departamento de Estatística, F'{i}sica e Matem'{a}tica, Universidade Federal de S~{a}o Jo~{a}o del Rei, Ouro Branco, C.P. 131, MG, Brazil

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Abstract

A model of an anomalous boundary layer over a flat plate was presented through fractional calculus. It is a generalization of Blasius's system, including a fractional derivative order in the heat equation. A nonlinear differential system with contour condition is usually difficult to solve, in this case, the system has a fractional differential term, therefore a semi-analytical approximation method was used combined with the initial value problem approximation by sequential parameter optimization method. Besides, it was shown that the derivative order has a significant influence on the boundary layer thermal shape and causes a bigger change in the temperature gradient curve.

Acknowledgments

The authors acknowledge José Eloy Ottoni for the helpful comments and suggestions. The authors gratefully acknowledge the support of Brazilian agency Fundação de Amparo a Pesquisa do Estado de Minas Gerais (FAPEMIG) through grant No. APQ-01366-16. This study was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Brasil (CAPES) - Finance Code 001 and by National Council for Scientific and Technological Development – CNPq.

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