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Numerical study of the thermophoretic velocity of ternary hybrid nanofluid in a microchannel bounded by the two parallel permeable flat plates

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Abstract

In recent times, the field of nanotechnology has been instrumental in driving significant breakthroughs in heat transport. These technological breakthroughs have shown their significance in improving the efficiency of heat exchangers, such as thermal pipes, microfluidic structures, and electronic components that depend on effective heat transfer processes. This study aims to explore innovative methods for enhancing heat transfer effectiveness. The present investigation focuses on the two-dimensional, incompressible, electrically conducting ternary liquid flow between two parallel porous plates in a microchannel. This has been considered with the convective boundary conditions employing the thermophoretic particle deposition phenomena. The numerical results of the mathematical, physical problem entailed a similar solution employed with the RKF-45 method. The stimulus of these process-sensitive non-dimensional parameters has been discussed and presented graphically with validation of the published results. The velocity profiles decline as increment in \(S_{1}\) and \(M_{{\text{F}}}\) whereas the thermal profile lessens with the augmentation in Biot numbers \({\text{Bi}}_{1} \;{\text{and}}\;{\text{Bi}}_{2}\). Moreover, the study emphasizes that the mass and thermal energy distribution rates exhibit a reduction when the solid volume percentage, thermophoretic constraints, and the existence of a porous medium increase. The ramifications of these discoveries are significant in terms of the design and optimization of microfluidic devices and thermal exchangers. The findings are visually shown using illustrations, offering valuable insights into the intricate relationships among the variables under investigation.

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Data availability

Data will be made available on reasonable request.

Abbreviations

\(h\) :

Distance

\(d\) :

Length

\(V\) :

Wall suction/injection velocity

\(u\) :

Axial velocity

\(k_{1}\) :

Permeability of the porous media

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

Specific heat

\(T\) :

Temperature

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

Diffusivity

\(h_{1} ,h_{2}\) :

Convective heat transfer coefficient

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

Thermophoretic velocity

\(\delta\) :

Thermophoretic coefficient

\(T_{r1}\) :

Reference temperature

\(P\) :

Pressure

\(A*\) :

Pressure gradient parameter

\({\text{Re}}\) :

Reynolds number

\(\Pr\) :

Prandtl number

\({\text{Ec}}_{1}\) :

Eckert number

\(S_{1}\) :

Porous media shape factor

\(M_{{\text{F}}}\) :

Magnetic field parameter

\(\tau_{2}\) :

Thermophoretic parameter

\({\text{Sc}}_{1}\) :

Schmidt number

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

Biot number

\(C_{{\text{f}}}\) :

Skin friction coefficient

\({\text{Nu}}\) :

Nusselt number

\({\text{Sh}}\) :

Sherwood number

\(\rho\) :

Density

\(k\) :

Thermal conductivity

\(\theta\) :

Dimensionless temperature

\(\delta\) :

Thermophoretic coefficient

\(\mu\) :

Dynamic viscosity

\(\sigma\) :

Electrical conductivity

\(\chi\) :

Dimensionless concentration

\(\phi\) :

Solid volume fraction

\({\text{thnf}}\) :

Ternary nanofluid

\({\text{nf}}\) :

Nanofluid

\(\left. \begin{gathered} S1 \hfill \\ S2 \hfill \\ S3 \hfill \\ \end{gathered} \right\}\) :

Solid particles

\({\text{hnf}}\) :

Hybrid nanofluid

\(f\) :

Fluid

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Acknowledgements

The author would like to extend his appreciation to the Deanship of Scientific Research at King Khalid University, Saudi Arabia for funding this work through the Research Group Program under grant No. RGP.2/218/44.

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Authors and Affiliations

  1. Department of Mechanical Engineering, National Institute of Technology Arunachal Pradesh, Jote, Papum Pare District, Arunachal Pradesh, 791113, India

    Ram Prakash Sharma

  2. Department of Mathematics, Amrita School of Engineering, Amrita Vishwa Vidyapeetham, Bengaluru, India

    J. K. Madhukesh

  3. Department of Basic & Applied Science, National Institute of Technology Arunachal Pradesh, Jote, Papum Pare District, Arunachal Pradesh, 791113, India

    Sunendra Shukla

  4. Department of Mechanical Engineering, College of Engineering, King Khalid University, 61421, Abha, Saudi Arabia

    Fehmi Gamaoun

  5. Department of Studies in Mathematics, Davangere University, Davangere, Karnataka, 577002, India

    B. C. Prasannakumara

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Contributions

RPS and M developed the theoretical formalism and writing—original draft preparation. The authors SS, FG, P have performed the numerical simulations, validation, formal analysis and investigation. All authors discussed the results and contributed to the final manuscript. RPS and P supervised the findings of this work.

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Correspondence to B. C. Prasannakumara.

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Sharma, R.P., Madhukesh, J.K., Shukla, S. et al. Numerical study of the thermophoretic velocity of ternary hybrid nanofluid in a microchannel bounded by the two parallel permeable flat plates. J Therm Anal Calorim 148, 14069–14080 (2023). https://doi.org/10.1007/s10973-023-12691-3

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