Approximate Solutions of the Model Describing Fluid Flow Using Generalized ρ-Laplace Transform Method and Heat Balance Integral Method

Axioms

Mehmet Yavuz¹  Ndolane Sene² 

[1] Department of Mathematics and Computer Sciences, Faculty of Science, Necmettin Erbakan University, 42090 Konya, Turkey;Laboratoire Lmdan, Département de Mathématiques de la Décision, Faculté des Sciences Economiques et Gestion, Université Cheikh Anta Diop de Dakar, BP 5683 Dakar Fann, Senegal;

关键词: generalized fractional derivative;    second-grade fluid;    ρ-Laplace homotopy perturbation transform method;    heat integral balance method;   

DOI  :  10.3390/axioms9040123

来源: DOAJ

【 摘 要 】

This paper addresses the solution of the incompressible second-grade fluid models. Fundamental qualitative properties of the solution are primarily studied for proving the adequacy of the physical interpretations of the proposed model. We use the Liouville-Caputo fractional derivative with its generalized version that gives more comprehensive physical results in the analysis and investigations. In this work, both the $\rho$-Laplace homotopy transform method ($\rho$-LHTM) and the heat balance integral method (HBIM) are successfully combined to solve the fractional incompressible second-grade fluid differential equations. Numerical simulations and their physical interpretations of the mentioned incompressible second-grade fluid model are ensured to illustrate the main findings. It is also proposed that one can recognize the differences in physical analysis of diffusions such as ballistic diffusion, super diffusion, and subdiffusion cases by considering the impact of the orders $\rho$ and $\phi$.

【 授权许可】

Unknown