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Three-Component Convection in a Vertically Oscillating Oldroyd-B Fluid With Cross Effects

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Abstract

This paper sheds light on the impact of vertical oscillations (or gravity modulation) on triple-diffusive convection in a viscoelastic fluid using the Oldroyd-B model, in the presence of cross effects. Cross effects can significantly impact three-component convective systems, despite having small magnitudes. When the cross terms, indicating coupled molecular cross-diffusion of the mixture components, are included in the equations governing heat and species transport, then a deviation from the usual three-component convection process is observed. An analytical solution has been found using linear and nonlinear analysis. The conditions for the onset of convection have been obtained using the linear analysis, which is based on the perturbation technique and the Venezian method. In nonlinear analysis, the expressions for Nusselt and Sherwood numbers, which quantify the rate of heat and mass transport respectively, are obtained by deriving the Lorenz model. It has been found that the onset of convection and heat and mass transport can be controlled by choosing the appropriate values of the parameters.

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Acknowledgements

The authors wish to thank their institution for support and encouragement in the completion of this paper. The authors are grateful to the reviewers for their helpful comments that improved our understanding of the problem and thereby, improved the paper.

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  1. Centre for Mathematical Needs, Department of Mathematics, CHRIST (Deemed to be University), Karnataka, Bangalore, 560029, India

    S. Pranesh & Richa Saha

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Pranesh, S., Saha, R. Three-Component Convection in a Vertically Oscillating Oldroyd-B Fluid With Cross Effects. Microgravity Sci. Technol. 34, 21 (2022). https://doi.org/10.1007/s12217-022-09935-6

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