The Analytical Scheme on the Inertial Drag for Buoyancy-driven Nanofluid Flow Under Convective Thermal Surface with the Soret Effect

P.K. Pattnaik1
, Subhajit Panda2, 3
, S.R. Mishra4, *
, Krushna K.P.N. Nayak4
1 Department of Mathematics, Odisha University of Technology and Research, Bhubaneswar, Odisha 751029, India
2 Department of Mathematics, Gandhi Institute for Technology, Bhubaneswar, Odisha, 752054, India
3 Department of Mathematics, National Institute of Technology Mizoram, Aizawl, 796012, India
4 Department of Mathematics, ITER, Siksha ‘O’ Anusandhan Deemed to be University, Bhubaneswar, Odisha 751030, India

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© 2023 Pattnaik et al.

open-access license: This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 International Public License (CC-BY 4.0), a copy of which is available at: This license permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

* Address correspondence to this author at the Department of Mathematics, ITER, Siksha ‘O’ Anusandhan Deemed to be University, Bhubaneswar, Odisha 751030, India; E-mail:



The two-dimensional mixed convection of nanofluid over a vertical expanding surface is analysed in the current discussion. The expanding surface is embedded in a permeable medium.


In advance, Darcy Forchheimer inertial drag is considered along with the influence of Brownian and thermophoresis, which enriches the study. The novelty of the study is due to the mass concentration along with the role of volume concentration in the flow phenomena. The proposed model is designed in association with a characterizing parameter, which is attained by the use of appropriate similarity conversion. Further, the system of first-order differential equations is resolved by employing a shooting-based numerical method, in particular, the Runge-Kutta fourth-order technique.


The simulated results for the said parameters and their behaviour are deployed through graphs and in tabular form.


The physical description of each parameter is deliberated briefly. Finally, the important outcomes of the proposed study reported a remarkable hike in the temperature profile that is observed for the enhanced thermophoresis and Brownian motion. Further, the shear rate also increases for the enhanced mixed convection parameter.

Keywords: Nanofluid, Mixed convection, Darcy-Forchheimer, Thermal radiation, Volume concentration, Mass concentration.