A Prabhakar Fractional Approach for the Convection Flow of Casson Fluid across an Oscillating Surface Based on the Generalized Fourier Law

In the present work, an unsteady convection flow of Casson fluid, together with an oscillating vertical plate, is examined. The governing PDEs corresponding to velocity and temperature profile are transformed into linear ODEs with the help of the Laplace transform method. The ordinary derivative mod...

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Autores principales:	Noman Sarwar, Muhammad Imran Asjad, Thanin Sitthiwirattham, Nichaphat Patanarapeelert, Taseer Muhammad
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	Casson fluid oscillating vertical plate Prabhakar fractional approach Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/2fa0a435509147418d93b09af6949ee1
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spelling	oai:doaj.org-article:2fa0a435509147418d93b09af6949ee12021-11-25T19:06:14ZA Prabhakar Fractional Approach for the Convection Flow of Casson Fluid across an Oscillating Surface Based on the Generalized Fourier Law10.3390/sym131120392073-8994https://doaj.org/article/2fa0a435509147418d93b09af6949ee12021-10-01T00:00:00Zhttps://www.mdpi.com/2073-8994/13/11/2039https://doaj.org/toc/2073-8994In the present work, an unsteady convection flow of Casson fluid, together with an oscillating vertical plate, is examined. The governing PDEs corresponding to velocity and temperature profile are transformed into linear ODEs with the help of the Laplace transform method. The ordinary derivative model generalized to fractional model is based on a generalized Fourier law. The solutions for energy and velocity equations are obtained after making the equations dimensionless. To check the insight of the physical parameters, especially the symmetric behavior of fractional parameters, it is found that for small and large values of time, fluid properties show dual behavior. Since the fractional derivative exhibits the memory of the function at the chosen value of time, therefore the present fractional model is more suitable in exhibiting memory than the classical model. Such results can be useful in the fitting of real data where needed. In the limiting case when fractional parameters are taken <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>β</mi><mo>=</mo><mi>γ</mi></mrow></semantics></math></inline-formula> = 0 and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula> = 1 for both velocity and temperature, we get the solutions obtained with ordinary derivatives from the existing literature.Noman SarwarMuhammad Imran AsjadThanin SitthiwiratthamNichaphat PatanarapeelertTaseer MuhammadMDPI AGarticleCasson fluidoscillating vertical platePrabhakar fractional approachMathematicsQA1-939ENSymmetry, Vol 13, Iss 2039, p 2039 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Casson fluid oscillating vertical plate Prabhakar fractional approach Mathematics QA1-939
spellingShingle	Casson fluid oscillating vertical plate Prabhakar fractional approach Mathematics QA1-939 Noman Sarwar Muhammad Imran Asjad Thanin Sitthiwirattham Nichaphat Patanarapeelert Taseer Muhammad A Prabhakar Fractional Approach for the Convection Flow of Casson Fluid across an Oscillating Surface Based on the Generalized Fourier Law
description	In the present work, an unsteady convection flow of Casson fluid, together with an oscillating vertical plate, is examined. The governing PDEs corresponding to velocity and temperature profile are transformed into linear ODEs with the help of the Laplace transform method. The ordinary derivative model generalized to fractional model is based on a generalized Fourier law. The solutions for energy and velocity equations are obtained after making the equations dimensionless. To check the insight of the physical parameters, especially the symmetric behavior of fractional parameters, it is found that for small and large values of time, fluid properties show dual behavior. Since the fractional derivative exhibits the memory of the function at the chosen value of time, therefore the present fractional model is more suitable in exhibiting memory than the classical model. Such results can be useful in the fitting of real data where needed. In the limiting case when fractional parameters are taken <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>β</mi><mo>=</mo><mi>γ</mi></mrow></semantics></math></inline-formula> = 0 and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula> = 1 for both velocity and temperature, we get the solutions obtained with ordinary derivatives from the existing literature.
format	article
author	Noman Sarwar Muhammad Imran Asjad Thanin Sitthiwirattham Nichaphat Patanarapeelert Taseer Muhammad
author_facet	Noman Sarwar Muhammad Imran Asjad Thanin Sitthiwirattham Nichaphat Patanarapeelert Taseer Muhammad
author_sort	Noman Sarwar
title	A Prabhakar Fractional Approach for the Convection Flow of Casson Fluid across an Oscillating Surface Based on the Generalized Fourier Law
title_short	A Prabhakar Fractional Approach for the Convection Flow of Casson Fluid across an Oscillating Surface Based on the Generalized Fourier Law
title_full	A Prabhakar Fractional Approach for the Convection Flow of Casson Fluid across an Oscillating Surface Based on the Generalized Fourier Law
title_fullStr	A Prabhakar Fractional Approach for the Convection Flow of Casson Fluid across an Oscillating Surface Based on the Generalized Fourier Law
title_full_unstemmed	A Prabhakar Fractional Approach for the Convection Flow of Casson Fluid across an Oscillating Surface Based on the Generalized Fourier Law
title_sort	prabhakar fractional approach for the convection flow of casson fluid across an oscillating surface based on the generalized fourier law
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/2fa0a435509147418d93b09af6949ee1
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A Prabhakar Fractional Approach for the Convection Flow of Casson Fluid across an Oscillating Surface Based on the Generalized Fourier Law

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