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Bioconvection in oxytactic microorganism-saturated porous square enclosure with thermal radiation impact

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Abstract

This investigation addresses bioconvection of oxytactic microorganisms in a porous square enclosure by thermal radiation impact. The bioconvection flow and heat transfer in porous media are formulated based on Darcy model of Boussinesq approximation. Appropriate transformations lead to the non-dimensionalized governing partial differential equations. Galerkin finite element method for the resulting equations is computed. The role of relevant parameters on the streamlines, isotherms, isoconcentrations of oxygen and microorganisms and average Nusselt number is analysed in the outputs. It is revealed that the flow intensity of bioconvection is pronounced with larger Rayleigh number and reduced with radiation parameter. Furthermore, the temperature distribution is affected significantly with Rayleigh number. Radiation parameter serves to fasten the heat transfer in the enclosure. Oxygen density is enhanced with Rayleigh number and radiation parameter. The profile of motile isoconcentrations is boosted with Rayleigh number. The stability of microorganisms is improved with the radiation parameter.

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Abbreviations

b :

Chemotaxis constant, \(m\)

C :

Concentration of oxygen

\(C_{{{\rm{min}}}}\) :

Minimum concentration of oxygen required for microorganisms to be active

\(C_{0}\) :

Concentration at free surface

\(C_{\text{P}}\) :

Specific heat at constant pressure

\(D_{\text{C}}\) :

Diffusivity of oxygen, m2 s−1

\(D_{\text{n}}\) :

Diffusivity of microorganisms, m2 s−1

\(g\) :

Acceleration due to gravity, m s−2

K :

Permeability of the porous medium

\(k^{*}\) :

Mean absorption coefficient

L :

Length of porous cavity, \(m\)

Le:

Lewis number

n :

Number density of motile microorganisms

\(n_{0}\) :

Average density of the microorganism

N :

Dimensionless number density of microorganisms

\({\text{Nu}}_{\text{Y}}\) :

Local Nusselt number

\({\text{Nu}}_{\text{avg}}\) :

Average Nusselt number

\({\text{Nn}}_{\text{Y}}\) :

Local Sherwood number of microorganisms

\({\text{Nn}}_{\text{avg}}\) :

Average Sherwood number of microorganisms

p :

Excess pressure above hydrostatic

Pe:

Peclet number

\(q_{\text{r}}\) :

Radiative heat flux

Ra:

Rayleigh number of porous medium

Rb:

Bioconvection Rayleigh number

Rd:

Radiation parameter

\({\text{Sh}}_{\text{Y}}\) :

Local Sherwood number of oxygen concentration

\({\text{Sh}}_{\text{avg}}\) :

Average Sherwood number of oxygen concentration

T :

Temperature, \({\text{K}}\)

\(T_{\text{H}}\) :

Temperature at hot wall, \({\text{K}}\)

\(T_{\text{C}}\) :

Temperature at cold wall, \({\text{K}}\)

\(T_{\infty }\) :

Ambient temperature, \({\text{K}}\)

u, v :

Velocity components in \(x,y\)-directions, m s−1

\(W_{\text{C}}\) :

Maximum cell swimming speed

\(x,y\) :

Cartesian coordinates, \(m\)

\(X,Y\) :

Dimensionless coordinates

\(\alpha_{\text{m}}\) :

Effective thermal diffusivity of the porous medium, m2 s−1

\(\beta\) :

Volumetric thermal expansion coefficient of water at constant pressure, \({\text{K}}^{ - 1}\)

\(\gamma\) :

Average volume of a microorganism

\(\mu\) :

Dynamic viscosity of the suspension (N s) m−2

\(\nu\) :

Kinematic viscosity, m2 s−1

\(\phi\) :

Dimensionless oxygen concentration

\(\rho\) :

Density of cell, kg m−3

\(\rho_{\text{f}}\) :

Fluid density, kg m−3

\(\psi\) :

Stream function, m2 s−1

\(\Psi\) :

Dimensionless stream function

\(\sigma\) :

Electric conductivity, S m−1

\(\sigma^{*}\) :

Stefan–Boltzmann constant

\(\theta\) :

Dimensionless temperature

\(\chi\) :

Constant

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Authors and Affiliations

  1. Department of Mathematics, Koneru Lakshmaiah Education Foundation, Hyderabad, Telangana, 500075, India

    Chandra Shekar Balla

  2. Department of Mathematics, Geethanjali College of Engineering and Technology, Hyderabad, Telangana, India

    Alluguvelli Ramesh

  3. Department of Mathematics, Osmania University, Hyderabad, India

    Naikoti Kishan

  4. Department of Mathematics, Faculty of Science, Aswan University, Aswân, 81528, Egypt

    A. M. Rashad

  5. Basic and Applied Sciences Department, College of Engineering and Technology, Arab Academy for Science and Technology and Maritime Transport (AASTMT), Aswan Branch, Aswân, Egypt

    Z. M. A. Abdelrahman

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  1. Chandra Shekar Balla
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Correspondence to Chandra Shekar Balla.

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Balla, C.S., Ramesh, A., Kishan, N. et al. Bioconvection in oxytactic microorganism-saturated porous square enclosure with thermal radiation impact. J Therm Anal Calorim 140, 2387–2395 (2020). https://doi.org/10.1007/s10973-019-09009-7

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