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# Comparative study of heat and mass transfer of generalized MHD Oldroyd-B bio-nano fluid in a permeable medium with ramped conditions

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Scientific Reports
Nature Publishing Group UK

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### Abstract

This article aims to investigate the heat and mass transfer of MHD Oldroyd-B fluid with ramped conditions. The Oldroyd-B fluid is taken as a base fluid (Blood) with a suspension of gold nano-particles, to make the solution of non-Newtonian bio-magnetic nanofluid. The surface medium is taken porous. The well-known equation of Oldroyd-B nano-fluid of integer order derivative has been generalized to a non-integer order derivative. Three different types of definitions of fractional differential operators, like Caputo, Caputo-Fabrizio, Atangana-Baleanu (will be called later as \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C,CF,AB$$\end{document} ) are used to develop the resulting fractional nano-fluid model. The solution for temperature, concentration, and velocity profiles is obtained via Laplace transform and for inverse two different numerical algorithms like Zakian’s, Stehfest’s are utilized. The solutions are also shown in tabular form. To see the physical meaning of various parameters like thermal Grashof number, Radiation factor, mass Grashof number, Schmidt number, Prandtl number etc. are explained graphically and theoretically. The velocity and temperature of nanofluid decrease with increasing the value of gold nanoparticles, while increase with increasing the value of both thermal Grashof number and mass Grashof number. The Prandtl number shows opposite behavior for both temperature and velocity field. It will decelerate both the profile. Also, a comparative analysis is also presented between ours and the existing findings.

### Most cited references50

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### Linear Models of Dissipation whose Q is almost Frequency Independent--II

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### Algorithm 368: Numerical inversion of Laplace transforms [D5]

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### A new definition of fractional derivative without singular kernel

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### Author and article information

###### Contributors
aamirf88@yahoo.com
###### Journal
Sci Rep
Sci Rep
Scientific Reports
Nature Publishing Group UK (London )
2045-2322
6 December 2021
6 December 2021
2021
: 11
###### Affiliations
[1 ]GRID grid.410729.9, ISNI 0000 0004 1759 3199, Nanchang Institute of Technology, ; Nanchang, 30044 China
[2 ]GRID grid.464484.e, ISNI 0000 0001 0077 475X, School of Mathematics and Statistics, , Xuzhou University of Technology, ; Xuzhou, 221018 China
[3 ]GRID grid.467118.d, ISNI 0000 0004 4660 5283, Department of Pure and Applied Mathematics, , University of Haripur, ; Haripur, KPK, Pakistan
[4 ]GRID grid.412895.3, ISNI 0000 0004 0419 5255, Department of Physics, Faculty of Science, , Taif University, ; P.O. Box 888, Taif, 21944 Saudi Arabia
[5 ]GRID grid.418920.6, ISNI 0000 0004 0607 0704, Department of Mathematics, , COMSATS University Islamabad, ; Vehari Campus, Vehari, 61100 Pakistan
[6 ]GRID grid.418920.6, ISNI 0000 0004 0607 0704, Department of Mathematics, , COMSATS University Islamabad, ; Wah Campus, Islamabad, 47040 Pakistan
[7 ]GRID grid.412895.3, ISNI 0000 0004 0419 5255, Department of Physics, College of Science, , Taif University, ; P. O. Pox 11099, Taif, 21944 Saudi Arabia
[8 ]GRID grid.444992.6, ISNI 0000 0004 0609 495X, Department of Basic Sciences, , University of Engineering Technology, ; Peshawar, Pakistan
[9 ]Section of Mathematics, International Telematic University Uninettanu, Corso Vittorio Emanuele II, 39, 00186 Roma, Italy
[10 ]GRID grid.494514.9, ISNI 0000 0004 5935 783X, Department of Mathematics, , Abbottabad University of Science and Technology, ; Abbottabad, Pakistan
###### Article
2326
10.1038/s41598-021-02326-8
8648785
d415132b-8df3-43b6-b926-1318c5a86a8b

###### Funding
Funded by: FundRef http://dx.doi.org/10.13039/501100006261, Taif University;
Award ID: TURSP-2020/319
Award ID: TURSP-2020/319
###### Categories
Article