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Soret and Dufour effects in the flow of Casson nanofluid in a vertical channel with thermal radiation: entropy analysis

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Abstract

In this article, we have investigated the Soret and Dofour effects on Casson nanofluid flowing in a vertical channel with the impact of thermal radiation. Entropy generation in the system is also analysed for the considered flow. Channel walls are assumed to satisfy the convective constraints of heat transfer. The governing equations are modelled using Buongiorno’s model by incorporating the effects of Brownian motion and thermophoresis. The equations are non-dimensionalised by defining suitable dimensionless parameters. The resulting equations are nonlinear and coupled. These are tackled by employing differential transform method and MATLAB bvp4c code based on finite difference method. Velocity, temperature and entropy generation are plotted for various physical parameters which affects the flow and are analysed graphically. Both the methods are observed to give the results with good agreement. Casson fluid parameter intensifies both velocity field and thermal field. Dufour parameter enhances both velocity and thermal field. Soret parameter also positively accelerates both velocity and temperature. Casson parameter, Dufour parameter, Soret parameter minimise the entropy generation in the system.

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Abbreviations

\({\text{Br}}\) :

Brinkman number

\({\text{Bi}}\) :

Biot number

\(C\) :

Nanoparticle concentration (\({\text{mol}}/{\text{m}}^{3}\))

\(c_{{\text{p}}}\) :

Specific heat capacity (\({\text{Jkg}}^{ - 1} {\text{K}}^{ - 1}\))

\(D_{{\text{T}}}\) :

Thermophoresis coefficient

\(D_{{\text{B}}}\) :

Brownian motion coefficient

\({\text{Du}}\) :

Dufour parameter

\(g\) :

Gravity acceleration (\({\text{ms}}^{ - 2}\))

\({\text{Gr}}\) :

Grashof number

\(k\) :

Heat conductivity (\({\text{Wm}}^{ - 1} {\text{K}}^{ - 1}\))

\(L\) :

Wall separation (\({\text{m}}\))

\({\text{Le}}\) :

Lewis number

\({\text{Nb}}\) :

Brownian movement parameter

\({\text{Nr}}\) :

Buoyancy parameter

\({\text{Nt}}\) :

Thermophoresis parameter

\({\text{Pr}}\) :

Prandtl number

\({\text{Sr}}\) :

Soret parameter

\(T\) :

Thermal field (\({\text{K}}\))

\(u\) :

Velocity (\({\text{ms}}^{ - 1}\))

\(\rho\) :

Density of the fluid (\({\text{kg}}\,{\text{m}}^{ - 3}\))

\(\theta\) :

Dimensionless temperature

\(\mu\) :

Viscosity (\({\text{Pas}}^{ - 1}\))

\(\phi\) :

Dimensionless nanoparticle concentration

\(\beta\) :

Casson fluid parameter

λ :

Concentration difference parameter

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Acknowledgements

The authors acknowledged the financial support received for the research project entitled “Performance Improvement of Solar Thermal Systems using Magnetic Nanofluids” funded by the Department of Science and Technology (DST), Govt. of India under India-South Africa Joint Science and Technology Research Collaboration vide Sanction no.: DST/INT/South Africa/P-08/2021 dtd. 16 Sept. 2021.

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Authors and Affiliations

  1. Department of Studies and Research in Mathematics, Tumkur University, Tumakuru, Karnataka, India

    Mallikarjun B. Patil & K. C. Shobha

  2. Department of Mechanical Engineering, Birla Institute of Technology and Science Pilani, Pilani Campus, Vidhya Vihar, Pilani, Rajasthan, 333031, India

    Suvanjan Bhattacharyya

  3. Department of Sustainable and Renewable Energy Engineering, University of Sharjah, 27272, Sharjah, United Arab Emirates

    Zafar Said

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Patil, M.B., Shobha, K.C., Bhattacharyya, S. et al. Soret and Dufour effects in the flow of Casson nanofluid in a vertical channel with thermal radiation: entropy analysis. J Therm Anal Calorim 148, 2857–2867 (2023). https://doi.org/10.1007/s10973-023-11962-3

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