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Inspection of modified Fourier’s and Fick’s laws in magnetized transport of Oldroyd-B nanofluid with swimming motile microorganisms: a theoretical model

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Abstract

In modern technology, the cooling mechanisms are important for energy storage devices that have been performed with both active and passive heat transfer enhancement techniques. Engineers and scientists have produced various strategies for improving heat transport within thermal process. Nanofluids are the developing consequence of the improvement in heat transfer which has been continuously analyzed. This article discusses the 2D flow of Oldroyd-B nanofluid including swimming gyrotactic motile microorganisms through stretched cylinder. Aspects of Arrhenius activation energy, Cattaneo–Christov heat and mass fluxes and heat source/sink are also considered. The significance of Brownian motion and thermophoresis diffusions is also described to analyze the nanoparticles. Oldroyd-B nanofluid is auspicious for depicting many forms of problems, because this fluid system has the potential to show the features of several rate-type liquids like fluids under the short-chain suspended tiny particles, fluid particles, cleaning products as well as blood in humans. Appropriate similarity variables are used to attain a non-dimensional appearance of problem, and then embedded coupled ODEs have been solved mathematically by using bvp4c solver in the computational software MATLAB. Significance of involved pertinent parameters on flow field like temperature profile, volumetric nanoparticle concentration and microorganism field is also analyzed through graphs. It has been found that the increment in Prandtl number reduces temperature. It is also interesting to observe that temperature field is enhanced for larger temperature ratio and thermophoresis parameters. The outcomes indicate that concentration of nanoparticles is decreasing functions of concentration relaxation parameter and Lewis number. Furthermore, the microorganism field is reduced for larger bioconvection Lewis number while upgraded for bioconvection Rayleigh number.

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Data availability statement

This manuscript has associated data in a data repository. [Authors’ comment: The data used to support the findings of this study are included within the article.]

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Acknowledgement

The authors extend their appreciation to the Deanship of Scientific Research at King Khalid University, Abha, Saudi Arabia for funding this work through research groups program under grant number R.G.P-2/76/42.

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Authors and Affiliations

  1. Department of Mathematics, Government College University Faisalabad, Layyah Campus, Layyah, 31200, Pakistan

    Hassan Waqas, Shan Ali Khan & Sumeira Yasmin

  2. Department of Mathematics, College of Sciences, King Khalid University, Abha, 61413, Saudi Arabia

    Taseer Muhammad

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  1. Hassan Waqas
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Correspondence to Hassan Waqas.

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Waqas, H., Muhammad, T., Khan, S.A. et al. Inspection of modified Fourier’s and Fick’s laws in magnetized transport of Oldroyd-B nanofluid with swimming motile microorganisms: a theoretical model. Eur. Phys. J. Plus 136, 860 (2021). https://doi.org/10.1140/epjp/s13360-021-01843-9

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