First Solution of Fractional Bioconvection with Power Law Kernel for a Vertical Surface

Asjad, Muhammad Imran; Rehman, Saif Ur; Ahmadian, Ali; Salahshour, Soheil; Salimi, Mehdi

doi:10.3390/math9121366

Cited by 18 publications

(7 citation statements)

References 66 publications

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“…e main objective, on the other hand, is to merge these two interesting subjects, fractional derivatives, and bioconvection. Recently, Asjad et al [55] presented fractional bioconvection properties for sticky fluid over an infinite perpendicular plate with Caputo fractional derivative. In the above-mentioned literature, there is not a single study on the subject of fractional bioconvection between two parallel plates with a Prabhakar fractional derivative.…”

Section: Introductionmentioning

confidence: 99%

Analysis of Fractional Bioconvection with Hybrid Nanoparticles in Channel Flow

Asjad

Ikram

Sarwar

et al. 2022

Mathematical Problems in Engineering

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In this paper, MHD Brinkman-type fluid flow containing titanium dioxide and silver nanoparticle hybrid nanoparticles with generalized Mittag–Leffler kernel-based fractional derivative is investigated in the presence of bioconvection. The governing equations with dimensional analysis and fractional approach are obtained by using the fractional Fourier’s law for heat flux and Fick’s law for diffusion. As a result, the bioconvection Rayleigh number, which is responsible for the declining in the fluid velocity and fractional parameters used to control the thermal and momentum boundary layers thickness of fluid properties. The obtained solutions can be beneficial for proper analysis of real data and provide a tool for testing possible approximate solutions where needed.

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Section: Introductionmentioning

confidence: 99%

Analysis of Fractional Bioconvection with Hybrid Nanoparticles in Channel Flow

Asjad

Ikram

Sarwar

et al. 2022

Mathematical Problems in Engineering

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“…The following equations may be used to derive the equations of momentum, energy, concentration, and free convection flow of second grade fluid over a vertically plate using the Boussinesq approximation [37]. Momentum equation:…”

Section: Mathematical Formulationmentioning

confidence: 99%

“…There is a gap in the existing literature with the fractional approach of bioconvection. Imran et al [37] released their study on the fractional bioconvection impact for viscous fluid over a vertical geometry and detailed how to use an integral transform technique to analyze how the fractional parameter and bioconvection number affect the fluid flow. Fourier and Ficks's Laws for Energy and Diffusion Equations were used in their research to develop the Caputo fractional model, and the results were promising.…”

Section: Introductionmentioning

confidence: 99%

Exploring the Impact of Prabhakar Fractional Derivatives on Bioconvection Flow of Nanofluids with Applications in Solar Energy

Shafique,

Ramzan,

Nazar

2024

Preprint

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The current research explores how entropy generation, heat, and mass transfer impact the motion of a second-grade fluid when exposed to solar radiation on a vertical plate. This study employs a base fluid composed of polyvinyl alcohol-water and considers the presence of copper nanoparticles and gyrotactic microorganisms. Given the increasing utilization of solar plates in various devices, there is a need to develop an effective numerical model for the flow and thermal characteristics of a parabolic trough solar collector (PTSC) mounted on a solar plate. Parabolic trough solar collectors (PTSCs) are solar energy systems that utilize curved mirrors, resembling parabolic troughs, to concentrate sunlight onto a single focal line. This focused sunlight heats the fluid flowing through a plate aligned along the focal line. The governing equations for heat, mass, and momentum, based on Fourier's and Fick's laws, have been established, and mathematical modeling is carried out. The Laplace transform method is applied to derive non-dimensional partial differential equations for the energy, mass, and velocity fields. The graphical analysis primarily focuses on the significant impact of key parameters, including the bioconvection Lewis number, magnetic field parameter, Prandtl number, electric field parameter, Grashof number, mass Grashof number, chemical reaction parameter, and Peclet number, related to the flow properties. Increasing the volume fraction and radiation parameter of nanoparticles is shown to enhance the temperature profile. Non-Newtonian nanofluids exhibit great potential for enhancing heat transfer processes and find diverse applications in solar energy systems, thermal energy systems, and microchip cooling. These nanofluids not only exhibit exceptional thermal properties but also unexpected thermal behavior. By incorporating nanoparticles into fluids, we can augment both solar energy storage and heat transfer capabilities.

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“…The fractional approach to bioconvection leaves a gap in the body of previous knowledge. In 2021, Imran et al [45] published their work on the fractional bioconvection impact for viscous fluid across a vertical geometry, and they provided explicit instructions on how to apply an integral transform approach to examine how a fractional parameter and the bioconvection number impact the fluid flow. The Caputo fractional model was developed in their study using Fourier's and Fick's law for energy and diffusion equations, and the outcomes were encouraging.…”

Section: Introductionmentioning

confidence: 99%

Bioconvection in Jeffrey nanofluid with gyrotactic organisms using CPC fractional derivative

Abbas,

Nazar,

Rahimzai

et al. 2023

Preprint

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The current research examines the effects of heat and mass transfer on the motion of the Jeffrey fluid in the presence of solar radiation over a vertical plate. The study considers the presence of copper nanoparticles and gyrotactic organisms in the polyvinyl alcohol-water base fluid. A useful mathematical model for the thermal and flow behaviors of a PTSC (Parabolic trough solar collector) fixed on a solar panel is currently being developed in light of the rise in the number of devices that use solar plates. Solar energy systems that employ curved mirrors in the form of a parabolic trough to focus sunlight onto a single focal line are known as PTSCs (Parabolic trough solar collectors). The fluid passing through a plate running along the focal line is then heated by this focused sunlight. Fourier's and Fick's laws are used in mathematical modeling to solve heat, mass, and momentum equations. The dimensionless partial differential equations for energy, mass, and velocity fields are computed using the Laplace transform method. The graphical analysis concentrates on the significant effects of significant parameters, such as Grashof number, mass Grashof number, bioconvection Lewis number, electric and magnetic parameters, Prandtl number, Peclet number, and chemical reaction parameter associated with the flow properties. The temperature profile is shown to be improved by raising the volume fraction and radiation parameters. Non-Newtonian nanofluids have shown tremendous promise for heat transfer processes and have a wide range of uses in solar energy systems, thermal energy systems, and cooling microchips.

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First Solution of Fractional Bioconvection with Power Law Kernel for a Vertical Surface

Cited by 18 publications

References 66 publications

Analysis of Fractional Bioconvection with Hybrid Nanoparticles in Channel Flow

Analysis of Fractional Bioconvection with Hybrid Nanoparticles in Channel Flow

Exploring the Impact of Prabhakar Fractional Derivatives on Bioconvection Flow of Nanofluids with Applications in Solar Energy

Bioconvection in Jeffrey nanofluid with gyrotactic organisms using CPC fractional derivative

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