Liouville-Type Results for a Three-Dimensional Eyring-Powell Fluid with Globally Bounded Spatial Gradients in Initial Data

Palencia, José Luis Díaz; González, Julián Roa; Nouman, Muhammad

doi:10.3390/math10050741

Cited by 2 publications

(1 citation statement)

References 17 publications

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“…When the literature is reviewed carefully, the analytical solutions of these type models are missing, most studies consider numerical solutions (Ali et al ., 2018; Oke, 2021; Bilal and Ashbar, 2020; Diaz et al. , 2022a, b, c, d). First, using appropriate similarity transformation, the equations are reduced to dimensionless form (NODE).…”

Section: Introductionmentioning

confidence: 99%

Analytical studies of Eyring-Powell fluid models

Pınar

2022

MMMS

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PurposeWhen the literature is reviewed carefully, the analytical solutions of these types of models are missing. First using appropriate similarity transformation, the equations are reduced to dimensionless form (NODE). To solve the reduced models, ansatz-based methods are considered. Finally, the explicit form solutions are obtained and the effects of material parameters and Prandtl number on the velocity and temperature profiles are shown in figures by the exact solutions. This study aims to discuss the aforementioned solution.Design/methodology/approachOne of the non-Newtonian fluids is Eyring-Powell (EP) fluid which is derived from the kinetic theory of fluids. Two variations of EP model are considered to obtain the exact solutions that are missing in the literature. In order to obtain exact solutions, one of the ansatz-based methods is considered. The effects of material parameters and Prandtl number on the velocity and temperature profiles are shown in figures by the exact solutions. The results will guide to develop the model to predict the velocity profile and temperature profile when experimental data for dimensionless material parameters of EP fluid are available.FindingsFinally, the explicit form solutions are obtained and the effects of material parameters and Prandtl number are shown in the figures. The results will guide to develop of the model to predict the velocity profile and temperature profile when experimental data for dimensionless material parameters of EP fluid are available. For the modified EP models, only special cases are considered. The generalized form, i.e. the modified EP models, which include deformation parameters, will be considered in the authors’ future work.Originality/valueWhen the literature is reviewed carefully, the analytical solutions of these types of models are missing so by this work, the gap in the literature is filled. The explicit form solutions are obtained and the effects of material parameters and Prandtl number on the velocity and temperature profiles are shown in figures.

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Section: Introductionmentioning

confidence: 99%

Analytical studies of Eyring-Powell fluid models

Pınar

2022

MMMS

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Weak solution of a Neumann boundary value problem with 𝑝(𝑥)-Laplacian-like operator

2022

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In this paper, we study the existence of a weak solution for a class of Neumann boundary value problems for equations involving the p ⁢ ( x ) p(x) -Laplacian-like operator. Using a topological degree theory for a class of demicontinuous operators of generalized ( S + ) (S_{+}) -type and the theory of the variable exponent Sobolev spaces, we establish the existence of a weak solution of this problem. Our results extend and generalize several corresponding results from the existing literature.

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Liouville-Type Results for a Three-Dimensional Eyring-Powell Fluid with Globally Bounded Spatial Gradients in Initial Data

Cited by 2 publications

References 17 publications

Analytical studies of Eyring-Powell fluid models

Analytical studies of Eyring-Powell fluid models

Weak solution of a Neumann boundary value problem with 𝑝(𝑥)-Laplacian-like operator

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