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Gravitactic Bio-Thermal Convection Oscillates Vertically in a Porous Layer

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Proceedings of the 1st International Conference on Fluid, Thermal and Energy Systems (ICFTES 2022)

Part of the book series: Lecture Notes in Mechanical Engineering ((LNME))

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Abstract

The onset of stationary convection is examined in a homogeneous suspension of gravitactic micro-swimmers in a thermally stratified porous layer subject to vertical oscillation. For the situation of high-frequency and low-amplitude vertical oscillation, the governed model-averaged differential equations are presented. The monotonic stability boundary for stationary convection was obtained using the Galerkin method. The influence of the altered thermal Rayleigh-Darcy number, \(R_{a}\), on the modified bioconvection Rayleigh-Darcy number, \(R_{b}\), is numerically examined. Due to porous media, the bioconvection strength is less in results than its non-existence.

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Abbreviations

\({\tilde{\text{b}}}\):

Vibration amplitude [s]

\(c_{a}\):

Measure of acceleration [–]

\(c_{p}\):

Specific heat at constant pressure [J/kg.K]

\(D_{a}\):

Darcy number [–]

\(\overline{D}_{c}\):

Mean Diffusivity of gravitactic swimmers [m2/s]

\({\mathbf{g}}\):

Gravity [m/s2]

\(h\):

Depth of the layer [m]

\(\overline{n}\):

Mean concentration of the swimmers [mol/m3]

\(\overline{p}\):

Averaged pressure [kg/m.s2]

\(Pe\):

Péclet number [–]

\(\overline{q}\):

The mean fluid velocity [m/s]

\({\text{q}}_{c}\):

Swimming velocity of the microorganism [m/s]

\(R_{a}\):

Thermal Rayleigh-Darcy number [–]

\(R_{b}\):

Bioconvection Rayleigh-Darcy number [–]

\(R_{t}\):

Thermal vibrational-Darcy parameter [–]

\(\Re\):

The medium permeability [m2]

\(t\):

Time [s]

\(\overline{T}\):

The mean temperature [K]

\(\rho_{f}\):

Density of fluid [kg/m3]

\(\rho_{c}\):

Density of cell [kg/m3]

\(\Delta \rho\):

Density difference [kg/m3]

\(\theta\):

The average volume a gravitactic particle [m3]

\(\mu\):

The dynamic viscosity [kg/m.s]

\(\beta\):

The measure of volume expansion [1/K]

\(\kappa\):

The conductivity of thermal convection [W/m.K]

\(\varphi\):

The porosity of the layer [–]

ω:

Frequency of vibration [1/s]

\(\alpha\):

Wave number [1/m]

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Authors and Affiliations

  1. Department of Mathematics, School of Mathematics and Computer Sciences, Central University of Tamilnadu, Thiruvarur, 610005, India

    Srikanth Kummari & Virendra Kumar

  2. Department of Mathematics, Rajiv Gandhi National Institute of Youth Development, Sriperumbudur, Tamilnadu, 602105, India

    Srikanth Kummari

Authors
  1. Srikanth Kummari
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  2. Virendra Kumar
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Correspondence to Srikanth Kummari .

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Editors and Affiliations

  1. Department of Chemical Engineering, National Institute of Technology Calicut, Calicut, Kerala, India

    Sudev Das

  2. Department of Chemical Engineering, Indian Institute of Technology Hyderabad, Hyderabad, Telangana, India

    Narasimha Mangadoddy

  3. Department of Mechanical Engineering, Stellenbosch University, Stellenbosch, Western Cape, South Africa

    Jaap Hoffmann

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Kummari, S., Kumar, V. (2024). Gravitactic Bio-Thermal Convection Oscillates Vertically in a Porous Layer. In: Das, S., Mangadoddy, N., Hoffmann, J. (eds) Proceedings of the 1st International Conference on Fluid, Thermal and Energy Systems . ICFTES 2022. Lecture Notes in Mechanical Engineering. Springer, Singapore. https://doi.org/10.1007/978-981-99-5990-7_60

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  • DOI: https://doi.org/10.1007/978-981-99-5990-7_60

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  • Online ISBN: 978-981-99-5990-7

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