PRABHAKAR FRACTIONAL DERIVATIVE AND ITS APPLICATIONS IN THE TRANSPORT PHENOMENA CONTAINING NANOPARTICLES

被引：37

作者：

Asjad, Muhammad Imran ^{[1
]}

Zahid, Muhammad ^{[1
]}

Chu, Yu-Ming ^{[2
,3
]}

Baleanu, Dumitru ^{[4
,5
,6
]}

机构：

[1] Univ Management & Technol, Dept Math, Lahore, Pakistan

[2] Huzhou Univ, Dept Math, Huzhou, Peoples R China

[3] Changsha Univ Sci & Technol, Hunan Prov Key Lab Math Modeling & Anal Engn, Changsha, Peoples R China

[4] Cankaya Univ, Dept Math, Ankara, Turkey

[5] Inst Space Sci, Magurele, Romania

[6] China Med Univ, Dept Med Res, Taichung, Taiwan

来源：

THERMAL SCIENCE | 2021年 / 25卷 / SpecialIssue 2期

关键词：

Prabhakar's fractional derivative; Mittag-Leffler kernel; heat transfer; Brinkman fluid; nanoparticles; FLUID; MODEL;

D O I：

10.2298/TSCI21S2411A

中图分类号：

O414.1 [热力学];

学科分类号：

摘要：

In this paper, a new approach of analytical solutions is carried out on the thermal transport phenomena of Brinkman fluid based on Prabhakar's fractional derivative with generalized Fourier's law. The governing equations are obtained through constitutive relations and analytical solutions obtained via Laplace transform technique. Solutions for temperature and velocity field were analyzed through graphical description by MathCad software. The fluid properties revealed various aspects for different flow parameters as well as fractional parameter values and found important results. As a result, it is found that fluid properties can be enhanced by increasing the values of fractional parameters and can be useful in some experimental data where suitable.

引用

页码：S411 / S416

页数：6

共 16 条

[1] Analysis of mathematical model of fractional viscous fluid through a vertical rectangular channel [J].

Aleem, Maryam ;

Asjad, Muhammad Imran ;

Chowdhury, Muhammad S. R. ;

Hussanan, Abid .

CHINESE JOURNAL OF PHYSICS, 2019, 61 :336-350

[2] Caputo-Fabrizio fractional derivatives modeling of transient MHD Brinkman nanoliquid: Applications in food technology [J].

Ali, Farhad ;

Ali, Farman ;

Sheikh, Nadeem Ahmad ;

Khan, Ilyas ;

Nisar, Kottakkaran Sooppy .

CHAOS SOLITONS & FRACTALS, 2020, 131

[3] New trends of fractional modeling and heat and mass transfer investigation of (SWCNTs and MWCNTs)-CMC based nanofluids flow over inclined plate with generalized boundary conditions [J].

Asjad, Muhammad Imran ;

Aleem, Maryam ;

Ahmadian, Ali ;

Salahshour, Soheil ;

Ferrara, Massimiliano .

CHINESE JOURNAL OF PHYSICS, 2020, 66 :497-516

[4] A novel Covid-19 model with fractional differential operators with singular and non-singular kernels: Analysis and numerical scheme based on Newton polynomial [J].

Atangana, Abdon ;

Araz, Seda IGret .

ALEXANDRIA ENGINEERING JOURNAL, 2021, 60 (04) :3781-3806

[5] On Fractional Operators and Their Classifications [J].

Baleanu, Dumitru ;

Fernandez, Arran .

MATHEMATICS, 2019, 7 (09)

[6]

Choi S. U. S., 1995, ASME Publ. Fed, V8, P99

[7] A new fractional mathematical model of extraction nanofluids using clay nanoparticles for different based fluids [J].

Danish Ikram, Muhammad ;

Imran Asjad, Muhammad ;

Ahmadian, Ali ;

Ferrara, Massimiliano .

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2020,

[8] Natural convection flows of carbon nanotubes nanofluids with Prabhakar-like thermal transport [J].

Elnaqeeb, Thanaa ;

Shah, Nehad Ali ;

Mirza, Itrat Abbas .

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2020,

[9]

Hristov J., 2019, Fractional derivatives with mittag-leffler kernel: trends and applications in science and engineering, V1st, P175, DOI [10.32604/iasc.2023.032883, DOI 10.32604/IASC.2023.032883]

[10] RESPONSE FUNCTIONS IN LINEAR VISCOELASTIC CONSTITUTIVE EQUATIONS AND RELATED FRACTIONAL OPERATORS [J].

Hristov, Jordan .

MATHEMATICAL MODELLING OF NATURAL PHENOMENA, 2019, 14 (03)

← 1 2 →