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Advances in Mathematical Methods and High Performance Computing pp 429–448Cite as

Linear and Nonlinear Double Diffusive Convection in a Couple Stress Fluid Saturated Anisotropic Porous Layer with Soret Effect and Internal Heat Source

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Part of the book series: Advances in Mechanics and Mathematics ((AMMA,volume 41))

Abstract

In this paper, we analyze the effect of internal heating and the Soret effect on linear and nonlinear double diffusive convection in a couple stress fluid saturated anisotropic porous layer, heated and salted from below. Linear stability analysis has been performed by using normal mode technique and nonlinear analysis is carried out using a truncated Fourier series. The modified Darcy model, which includes the time-derivative term, has been employed in the momentum equation. The effects of the Vadasz number, the anisotropic parameter, the Soret parameter, the couple stress parameter, the solute Rayleigh number, the internal heat source parameter, the Lewis number, the Darcy–Prandtl number, and normalized porosity on the stationary and oscillatory are shown graphically. Also, heat and mass transports are calculated in terms of the Nusselt number and the Sherwood number and shown graphically.

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Acknowledgements

The author Kanchan Shakya gratefully acknowledges the financial assistance from Babasaheb Bhimrao Ambedkar University, Lucknow, India as UGC research fellowships.

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Authors and Affiliations

  1. Department of Applied Mathematics, School for Physical Sciences, Babasaheb Bhimrao Ambedkar University, Lucknow, 226025, India

    Kanchan Shakya

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  1. Kanchan Shakya
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Correspondence to Kanchan Shakya .

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Editors and Affiliations

  1. Department of Applied Science and Humanities, Inderprastha Engineering College, Ghaziabad, Uttar Pradesh, India

    Vinai K. Singh

  2. School of Science and Technology, Federation University Australia, Mt. Helen, VIC, Australia

    David Gao

  3. Institute of Numerical Mathematics, Technische Universität Dresden, Dresden, Germany

    Andreas Fischer

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Shakya, K. (2019). Linear and Nonlinear Double Diffusive Convection in a Couple Stress Fluid Saturated Anisotropic Porous Layer with Soret Effect and Internal Heat Source. In: Singh, V., Gao, D., Fischer, A. (eds) Advances in Mathematical Methods and High Performance Computing. Advances in Mechanics and Mathematics, vol 41. Springer, Cham. https://doi.org/10.1007/978-3-030-02487-1_27

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