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Double-diffusive convection in a magnetic nanofluid layer with cross diffusion effects

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Abstract

The present paper investigates the onset of double-diffusive convection in a layer of magnetic nanofluid with the Soret and Dufour effects. The impact of three important slip mechanisms, viz. Brownian motion, thermophoresis, and magnetophoresis are included in the model that is used for the magnetic nanofluids (MNFs). We performed a linear stability analysis to investigate the problem and derived the results for water-based and ester-based magnetic nanofluids. The results are presented simultaneously for both the gravity as well as the microgravity environment for Rigid–Rigid boundaries. A numerical technique is employed to examine the nature of the stability, and it is found that the stability of the considered problem is stationary. It is also observed that the effect of increase in the values of Dufour parameter \(N_{TC}\) and solutal Rayleigh number Rs is to delay, while increase in the values of Soret parameter \(N_{CT}\), concentration Rayleigh number \(R_n\), nonlinearity of fluid magnetization \(M_3\), Lewis number Le, and thermo-solutal Lewis number \(Le_s\) is to advance the onset of double-diffusive magnetic nanofluid convection in both the gravity and microgravity environment. In the gravity environment, value of the critical thermal Rayleigh number \(Ra_c\) first decreases as Langevin parameter \(\alpha _L\) increases from 1 to 2, and then it starts increasing with the further increase in the value of \(\alpha _L\). This behavior is found to be just opposite to that observed for the critical magnetic Rayleigh number \(Ng_c\) in the case of microgravity environment. Moreover, the values of \(Ra_c\) and \(Ng_c\) are found be higher in case of the ester-based MNFs compared with the water-based MNFs.

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Acknowledgements

The authors wish to thank the Council of Scientific and Industrial Research (CSIR), New Delhi for financial assistance to Dr. Amit Mahajan in the form of the Research and Development project [Ref. No. 25(0255)/16/EMR-II] and to Dr. Mahesh Kumar Sharma in the form of a Research Associate (RA).

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  1. Department of Applied Sciences, National Institute of Technology Delhi, Narela, Delhi, 110040, India

    Amit Mahajan & Mahesh Kumar Sharma

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  1. Amit Mahajan
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Correspondence to Mahesh Kumar Sharma.

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Mahajan, A., Sharma, M.K. Double-diffusive convection in a magnetic nanofluid layer with cross diffusion effects. J Eng Math 115, 67–87 (2019). https://doi.org/10.1007/s10665-019-09992-8

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