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Thermal study of Darcy–Forchheimer hybrid nanofluid flow inside a permeable channel by VIM: features of heating source and magnetic field

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Abstract

The nanofluids extensively contribute to cope the new heat transport challenges facing by the engineering systems and industries including paint, ceramics, chemical, aerodynamics, electronics, and medical sciences, etc. Thus, the innovations in new nanoliquid models can be disregarded in light of broad applications spectrum. Therefore, the current work concerns with the thermal process of hybrid nanoliquid by adding the important physical phenomenon. The flow of bionanofluid is taken inside a uniform expanding/contracting channel. To increase the model novelty, the significant influence of Lorentz forces, porous media, and heating source is added in the problem formulation. The resultant bionanofluid model is then analyzed via VIM (variational iteration method) and provided a deep discussion. It is inspected that unvarying expansion/contraction in the range of \(\alpha = \, {1.0,2.0,3.0,4.0}\) and \(\alpha =-1.0,-2.0,-3.0,-4.0\), the bionanofluid attained maximum velocity about the central portion and in rest of the part it declines. However, due to increased viscosity of hybrid nanofluid, it reduced rapidly than conventional nanofluid. By increasing the permeability from 0.1 to 0.4, a rapid decrease in the fluid movement is observed. Further, the heat transmission progress reduced against the porous medium and Lorentz forces. The heat generation effects boosted the heating performance of the hybrid nanofluid. Moreover, the skin friction and heat transport rate are also discussed.

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Data availability

The data that support the findings of this study are available within the article.

Abbreviations

\(\widetilde{u}, \widetilde{v}\) :

Velocity components

\(\widetilde{P}\) :

Pressure

\({\rho }_\text{b}\) :

Fluid density

\({\rho }_\text{hbnf}\) :

Density of hybrid nanofluid

\({k}_\text{b}\) :

Thermal conductivity of the basic fluid

\({k}_\text{hbnf}\) :

Thermal conductivity of hybrid nanofluid

\({\mu }_\text{b}\) :

Dynamic of basic fluid

\({\mu }_\text{hbnf}\) :

Dynamic viscosity of hybrid nanofluid

\(\widetilde{T}\) :

Fluid temperature

\({\sigma }_\text{b}\) :

Electrical conductivity of basic fluid

\({\sigma }_\text{hbnf}\) :

Electrical conductivity of hybrid nanofluid

\({\phi }_{1}, {\phi }_{2}\) :

Nanoparticles mass concentration

\(M\) :

Hartmann number

\({D}_\text{a}\) :

Darcy number

\({F}_\text{r}\) :

Forchheimer number

\({R}_\text{e1}\) :

Reynolds number

\({P}_\text{r}\) :

Prandtl number

\(Q\) :

Heat generation number

\({C}_\text{Fl}\) :

Skin friction at the lower plate

\({C}_\text{Fu}\) :

Skin friction at the upper plate

\({N}_\text{ul}\) :

Nusselt number at the lower plate

\({N}_\text{up}\) :

Nusselt number at the upper plate

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Acknowledgements

The authors extend their appreciation to the Deanship of Scientific Research at King Khalid University for funding this work through large group Research Project under grant number RGP2/16/44.

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Authors and Affiliations

  1. Department of Mathematics, Mohi-ud-Din Islamic University, Nerian Sharif, 12080, AJ&K, Pakistan

    Khaleeq ur Rahman &  Adnan

  2. Basic Science Department, College of Science and Theoretical Studies, Saudi Electronic University, 11673, Riyadh, Saudi Arabia

    Nidhish Kumar Mishra

  3. Department of Chemistry, College of Science, King Khalid University, P. O. Box 9004, 61413, Abha, Saudi Arabia

    Mutasem Z. Bani-Fwaz

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  1. Khaleeq ur Rahman
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Rahman, K.u., Adnan, Mishra, N.K. et al. Thermal study of Darcy–Forchheimer hybrid nanofluid flow inside a permeable channel by VIM: features of heating source and magnetic field. J Therm Anal Calorim 148, 14385–14403 (2023). https://doi.org/10.1007/s10973-023-12611-5

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