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Enhanced heat transportation for bioconvective motion of Maxwell nanofluids over a stretching sheet with Cattaneo–Christov flux

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Abstract

The main aim of this work is to study the thermal conductivity of base fluid with mild inclusion of nanoparticles. We perform numerical study for transportation of Maxwell nanofluids with activation energy and Cattaneo–Christov flux over an extending sheet along with mass transpiration. Further, bioconvection of microorganisms may support avoiding the possible settling of nanoentities. We formulate the theoretical study as a nonlinear coupled boundary value problem involving partial derivatives. Then ordinary differential equations are obtained from the leading partial differential equations with the help of appropriate similarity transformations. We obtain numerical results by using the Runge–Kutta fourth-order method with shooting technique. The effects of various physical parameters such as mixed convection, buoyancy ratio, Raleigh number, Lewis number, Prandtl number, magnetic parameter, mass transpiration on bulk flow, temperature, concentration, and distributions of microorganisms are presented in graphical form. Also, the skin friction coefficient, Nusselt number, Sherwood number, and motile density number are calculated and presented in the form of tables. The validation of numerical procedure is confirmed through its comparison with the existing results. The computation is carried out for suitable inputs of the controlling parameters.

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Data Availability

All date generated or analyzed during this study are included in this paper.

Abbreviations

\(u_{1}, u_{2}\) :

velocity components (m/s)

\(x,y\) :

Cartesian coordinates (m)

\(U_{w}\) :

stretching velocity of plate (m/s)

\(B_{0}\) :

magnetic field strength (T)

\(C\) :

concentration of nanoparticles

\(T\) :

temperature of nanoparticles (K)

\(N\) :

Microorganism distribution

\(g\) :

gravity (m/s2)

\(k_{1}\) :

vortex viscosity

\(\rho _{p}\) :

liquid density

\(C_{p}\) :

volume friction constant

\(\rho _{m}\) :

motile microorganism density

\(D_{B}\) :

Brownian motion coefficient (m2/s)

\(D_{T}\) :

thermophoresis constant (m2/s)

\(D_{n}\) :

diffusion constant of microorganisms (m2/s)

\(T_{\infty }\) :

ambient temperature (K)

\(C_{\infty }\) :

ambient concentration of nanoparticles

\(N_{\infty }\) :

ambient motile microorganisms

\(\tau _{1}\) :

relaxation time of heat flux

\(m\) :

fitted rate parameter

\(E_{a}\) :

activation energy (J/mol)

\(b_{1}\) :

chemotaxis constant (m)

\(b\) :

thermal relaxation constant

\(W_{c}\) :

maximum swimming cell speed (m/s)

\(n\) :

rotation of microorganisms (1/s)

\(q_{w}\) :

heat transfer rate (W/m2)

\(M\) :

magnetic parameter

\(Kp\) :

porosity parameter

\(Nr\) :

buoyancy ratio parameter

\(Rb\) :

Rayleigh number

\(Pr\) :

Prandtl number

\(Nbt\) :

diffusivity ratio

\(Nc\) :

ratio of heat capacities

\(Le\) :

Lewis number

\(Sc\) :

Schmidt number

\(E\) :

activation energy coefficient

\(Lb\) :

bioconvection Lewis number

\(Pe\) :

Peclet number

\(H\) :

suction/injection parameter

\(A\) :

chemical reaction rate

\(\alpha \) :

thermal diffusivity (m2/s)

\(\beta \) :

Deborah number

\(\nu _{nf}\) :

kinematic viscosity (m2/s)

\(\lambda \) :

fluid relaxation time

\(\sigma \) :

electrical conductivity (S/m)

\(\rho \) :

density (kg/m3)

\(\gamma \) :

average volume of microorganisms

\(\omega \) :

mixed convection

\(\eta \) :

similarity variable

\(\theta \) :

similarity temperature

\(\phi \) :

similarity concentration of nanoparticles

\(\chi \) :

similarity density of micro-organisms

\(\delta \) :

temperature difference

\(\Omega \) :

microorganism concentration difference

\(p\) :

nanoparticles

\(w\) :

on the sheet surface

\(\infty \) :

Ambient

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Authors and Affiliations

  1. School of Mathematics, Northwest University, No.229 North Taibai Avenue, Xi’an, 7100069, China

    Sohaib Abdal

  2. Department of Mathematics, University of Management and Technology, Lahore, Pakistan

    Imran Siddique

  3. Decision Lab, Mediterranea University of Reggio Calabria, 89124, Reggio Calabria, Italy

    Ali Ahmadian

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

    Soheil Salahshour

  5. Department of Mathematics, Statistics, and Computer Science, St. Francis Xavier University, Antigonish, Canada

    Mehdi Salimi

  6. Department of Mathematics, Near East University, Nicosia, Turkey

    Ali Ahmadian

  7. Center for Dynamics, Faculty of Mathematics, Technische Universität Dresden, 01062, Dresden, Germany

    Mehdi Salimi

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  1. Sohaib Abdal
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  2. Imran Siddique
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Each of the authors contributed equally to each part of this work. All authors read and approved the final manuscript.

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Correspondence to Ali Ahmadian or Mehdi Salimi.

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Abdal, S., Siddique, I., Ahmadian, A. et al. Enhanced heat transportation for bioconvective motion of Maxwell nanofluids over a stretching sheet with Cattaneo–Christov flux. Mech Time-Depend Mater 27, 1257–1272 (2023). https://doi.org/10.1007/s11043-022-09551-2

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