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Bio-Marangoni convection flow of Casson nanoliquid through a porous medium in the presence of chemically reactive activation energy

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Abstract

Bioconvection research is primarily focused on the augmentation of energy and mass species, which has implications in the processes intensification, mechanical, civil, electronics, and chemical engineering branches. Advanced bioconvection technology sectors include cooling systems for electronic devices, building insulation, and geothermal nuclear waste disposal. Hence, the present investigation is mainly discoursing the impact of Marangoni convention Casson nanoliquid flow under gyrotactic microorganisms over the porous sheet. The partial differential equations (PDEs) are re-structured into ordinary differential equations (ODEs) via suitable similar variables. These ODEs are numerically solved with the help of the spectral relaxation method (SRM). The numerical outcomes are illustrated graphically for various parameters over velocity, temperature, concentration, and bioconvection profiles. Three-dimensional (3D) views of important engineering parameters are illustrated for various parameters. The velocity of the Casson nanoliquid increases with increasing the Marangoni parameter but decreases against higher porosity parameter. The surface drag force enhances for enhancement in the Marangoni number. The rate of mass transmission is higher for reaction rate constraint but diminishes for activation energy parameter. The higher radiative values augment the rate of heat transmission.

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Abbreviations

ψ (x, y):

stream function

\(\overline u ,\overline v \) :

velocity components

x, y :

coordinate axes

β :

casson parameter

ν :

kinematic viscosity

μ :

dynamic viscosity

ρ :

density

k :

thermal conductivity

c p :

specific heat

K* :

permeability of porous medium

\(\overline T \) :

temperature inside boundary layer

\({\overline T _{\rm{w}}}\) :

uniform constant temperature

\({\overline T _\infty }\) :

ambient temperature

\({\overline T _0}\) :

characteristic temperature

q r :

radiative heat flux

D B :

Brownian diffusion coefficient

l :

characteristic length

a :

stretching constant

\(K_{\rm{r}}^2\) :

reaction rate

E a :

activation energy

K :

Boltzmann’s constant

\(\overline C \) :

concentration

\({\overline C _{\rm{w}}}\) :

uniform constant concentration

\({\overline C _\infty }\) :

free stream concentration

\(\overline N \) :

concentration motile of microorganisms

σ :

surface tension

σ* :

Stephan-Boltzmann constant

k* :

mean absorption coefficient

D m :

microorganism diffusion coefficient

ρ c p :

heat capacitance

γT:

coefficient of temperature surface tension

C f :

skin friction coefficient

Nu :

Nusselt number

Sh :

Sherwood number

j w :

wall mass flux

τ w :

shear stress.

f:

base fluid

nf:

nanofluid

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Acknowledgements

The authors appreciate the editors and referees for the positive feedback and helpful suggestions, which improve the manuscript’s presentation.

Author information

Authors and Affiliations

  1. Department of Mathematics, Davangere University, Davangere, 577007, India

    J. K. Madhukesh & B. C. Prasannakumara

  2. Department of Mathematics, K. L. E. Society’s J. T. College, Gadag, 582101, India

    G. K. Ramesh

  3. Department of Mathematics, COMSATS University Islamabad, Sahiwal, 57000, Pakistan

    S. A. Shehzad

  4. Department of Mathematics, COMSATS University Islamabad, Islamabad, 44000, Pakistan

    F. M. Abbasi

Authors
  1. J. K. Madhukesh
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  2. G. K. Ramesh
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  3. B. C. Prasannakumara
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  4. S. A. Shehzad
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  5. F. M. Abbasi
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Correspondence to S. A. Shehzad.

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Citation: MADHUKESH, J. K., RAMESH, G. K., PRASANNAKUMARA, B. C., SHEHZAD, S. A., and ABBASI, F. M. Bio-Marangoni convection flow of Casson nanoliquid through a porous medium in the presence of chemically reactive activation energy. Applied Mathematics and Mechanics (English Edition), 42(8), 1191–1204 (2021) https://doi.org/10.1007/s10483-021-2753-7

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Madhukesh, J.K., Ramesh, G.K., Prasannakumara, B.C. et al. Bio-Marangoni convection flow of Casson nanoliquid through a porous medium in the presence of chemically reactive activation energy. Appl. Math. Mech.-Engl. Ed. 42, 1191–1204 (2021). https://doi.org/10.1007/s10483-021-2753-7

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