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Convective stability of a permeable nanofluid inside a horizontal conduit: Fast chemical reactions

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  • Umavathi, Jawali C.
  • Chamkha, Ali J.

Abstract

This problem considers the instabilities, which can occur when a horizontal sparsely filled nanofluid porous layer is saturated with a binary mixture with fast chemical reaction. The upper and lower plates are heated isothermally. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. The modified Darcy equation that includes the time derivative term is used to model the momentum equation. The energy equation includes cross and regular diffusion conditions. In conjunction with the Brownian motion, the nanoparticle fraction becomes stratified; hence the viscosity and the conductivity are stratified. The nanofluid is assumed to be diluted and this enables the porous medium to be treated as a weakly heterogeneous medium with variation, in the vertical direction, of conductivity and viscosity. The oscillatory and stationary convection are evaluated analytically. The reaction rate is supposed to be greater than the diffusion rate. We find that both a stationary instability and an oscillatory instability can occur as the first bifurcation, depending on the sign and the value of the heat of reaction. The execution of the porous parameter, Prandtl number, Soret parameter, Dufour parameter, Lewis number, solutal Rayleigh number, chemical reaction and the modified diffusivity ratio parameters is implemented pictorially. It is found that the presence of nanoparticles the critical Rayleigh number is increased and helps to stabilize the system. The presence of chemical reaction parameter destabilizes the system. The results of previously-published work are also obtained as special cases of the general solution.

Suggested Citation

  • Umavathi, Jawali C. & Chamkha, Ali J., 2021. "Convective stability of a permeable nanofluid inside a horizontal conduit: Fast chemical reactions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 187(C), pages 155-170.
    • Handle: RePEc:eee:matcom:v:187:y:2021:i:c:p:155-170
    DOI: 10.1016/j.matcom.2021.02.016
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    References listed on IDEAS

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    1. Hayat, Tasawar & Riaz, Rubina & Aziz, Arsalan & Alsaedi, Ahmed, 2020. "Influence of Arrhenius activation energy in MHD flow of third grade nanofluid over a nonlinear stretching surface with convective heat and mass conditions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 549(C).
    2. Brand, H. & Steinberg, V., 1983. "Convective instabilities in binary mixtures in a porous medium," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 119(1), pages 327-338.
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