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ISSN:2164-6376 (print)
ISSN:2164-6414 (online)
Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA

Email: dr.volchenkov@gmail.com

Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania

Email: dumitru.baleanu@gmail.com

The Effect of First-Order Chemical Reaction on Rotating Rayleigh-B'enard Convection in a Sparsely Packed Porous Layer

Discontinuity, Nonlinearity, and Complexity 13(3) (2024) 555--565 | DOI:10.5890/DNC.2024.09.013

Suman Shekhar$^1$, Ravi Ragoju$^2$, Dhananjay Yadav$^3$, P. Danumjaya$^4$

$^1$ Department of Humanities and Sciences, Malla Reddy University, Maisammaguda, Kompally, Hyderabad, 500100, India

$^2$ Department of Applied Sciences, National Institute of Technology Goa, Goa, 403401, India

$^3$ Department of Mathematical and Physical Sciences, University of Nizwa, Oman

$^4$ Department of Mathematics, BITS-Goa Campus, Goa 403726, India

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Abstract

The influence of first-order chemical reaction and rotation on the onset of convection in a sparsely packed porous layer heated continuously from the bottom is explored numerically using linear stability analysis. The boundaries of fluid are considered as either free or rigid. Eigenvalue problem for three different boundaries of the fluid are solved using bvp4c in MATLAB R2022a. Effects of Damk\"{o}hler number, Lewis number, solutal Rayleigh number, Taylor number and Darcy number are analyzed. The critical Rayleigh number $(Ra_c)$ and wavenumber $(a_c)$ are calculated and shown in tables for different boundary conditions. It is found that increasing the Taylor number inhibits the onset of convection. On the other hand Damk\"{o}hler number is observed to have destabilizing effect on the system. It is found that critical wave number does not depend on Lewis number, solutal Rayleigh number and Damk\"{o}hler number hence it has no impact on the size of convection cells. Critical wave number is an increasing function of Taylor number, so the size of convection cells decreases. The effect of Darcy number is to increase the size of convection cells because critical wave number decreases with Darcy number.

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