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New solutions of generalized MHD viscous fluid flow with thermal memory and bioconvection

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Abstract

In this paper, the fractional model of the bioconvection flow of a MHD viscous fluid for vertical surface has been investigated. Introducing dimensionless variables, the governing equations are solved by Laplace transform technique. Classical governing model is drawn out to fractional order technique with non-singular kernel which can be used to explain the memory for natural phenomena. Since this operator describes the rate of change at each point of the measured interval, so we use this operator. To see the behavior of related parameters physically, some graphs have been plotted in conclusion section. In the end, some useful conclusions have been attained. It is resulted that constant proportional Caputo fractional derivative measures the memory strong in comparison with Caputo and Caputo–Fabrizio fractional approaches. Further, on comparison between different kinds of viscous fluid (Water, Air, Kerosene) and found that temperature and velocity of air are higher than water and kerosene, respectively. The impacts of dimensionless numbers on velocity field have been discussed graphically and concluded that velocity increased by increasing \(\text {Gr}\) and showed opposite behavior for \(\text {M}\) and \(\text {Ra}\).

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Abbreviations

\(\rho\) :

Fluid density

g :

Gravitational acceleration

T :

Fluid temperature

\(\Theta\) :

Dimensionless temperature

\(T_\mathrm{w}\) :

Temperature at the wall

\(T_{\infty }\) :

Ambient temperature of the fluid

v :

Velocity

k :

Thermal conductivity

\(D_\mathrm{N}\) :

Diffusivity of microorganisms

Ra:

Bioconvection Rayleigh number

q :

Laplace transform

C :

Caputo

M :

magnetic field parameter

\(\mu\) :

Viscosity

\(\beta _\mathrm{T}\) :

Volumetric coefficient of thermal expansion

N :

Concentration of microorganisms

\(\eta\) :

Dimensionless concentration of microorganisms

\(N_\mathrm{w}\) :

Concentration of microorganisms at the wall

\(N_{\infty }\) :

The density of motile microorganisms

\(\Omega\) :

Dimensionless velocity

\(C_\mathrm{p}\) :

Specific heat at constant pressure

\(\phi\) :

The dimensionless nanoparticle volume fraction

Gr:

Grashof number

CPC:

Constant proportional Caputo

CF:

Caputo–Fabrizio

H(t):

Unit step function

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Acknowledgments

The authors are greatly obliged and thankful to the University of Management and Technology Lahore, Pakistan for facilitating and supporting the research work.

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Authors and Affiliations

  1. Department of Mathematics, University of Management and Technology Lahore, Lahore, 54770, Pakistan

    Muhammad Imran Asjad & Muhammad Danish Ikram

  2. Decision Lab, Mediterranea University of Reggio Calabria, Reggio Calabria, Italy

    Ali Ahmadian

  3. Faculty of Engineering and Natural Sciences, Bahcesehir University, Istanbul, Turkey

    Soheil Salahshour

  4. Department of Mathematics and Statistics, St. Francis Xavier University, Antigonish, NS, Canada

    Mehdi Salimi

  5. Department of Mathematics, Near East University, Nicosia, TRNC, Mersin 10, Turkey

    Ali Ahmadian

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  1. Muhammad Imran Asjad
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Correspondence to Ali Ahmadian or Mehdi Salimi.

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Asjad, M.I., Ikram, M.D., Ahmadian, A. et al. New solutions of generalized MHD viscous fluid flow with thermal memory and bioconvection. J Therm Anal Calorim 147, 14019–14029 (2022). https://doi.org/10.1007/s10973-022-11609-9

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