Volume 1, Issue 2, International Journal of Thermo-Fluid Systems and Sustainable Energy
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International Journal of Thermo-Fluid Systems and Sustainable Energy, Volume 1, Issue 2, 2025: 64-74

Open Access | Research Article | 25 November 2025
Multiple Slip Mechanism for Converging/Diverging Flow of Second Grade Nanofluids with Thermal Performance
1 Department of Mathematics and Statistics, University of Haripur, Haripur 22620, Pakistan
* Corresponding Author: Hashim, [email protected]
ARK: ark:/57805/ijtsse.2025.412468
Received: 01 September 2025, Accepted: 02 October 2025, Published: 25 November 2025  
Abstract
This study presents a comprehensive numerical investigation of the flow and heat transfer characteristics of a second-grade nanofluid in a converging/diverging channel, incorporating the significant effects of multiple slip mechanisms. The analysis considers velocity, thermal, and solutal slip conditions at the channel walls, providing a more realistic model of nanofluid behavior in micro-environments or with specific surface interactions. The governing equations, derived from the principles of conservation of mass, momentum, and energy, are formulated using a non-Newtonian second-grade fluid model to account for viscoelastic effects, combined with the Buongiorno model to capture the Brownian motion and thermophoresis mechanisms of nanoparticles. The resulting system of highly non-linear, coupled partial differential equations is transformed into a set of ordinary differential equations using a similarity transformation approach. The ensuing boundary value problem is solved computationally using the robust MATLAB bvp4c solver. The results are meticulously analyzed to elucidate the intertwined influence of the second-grade fluid parameter (viscoelasticity), the nanoparticle volume fraction, the slip parameters, and the channel geometry (converging/diverging angle) on the velocity profile, temperature distribution, and thermal performance. Key findings indicate that velocity slip and thermal slip parameters substantially reduce skin friction and enhance the local Nusselt number, respectively, thereby critically optimizing the thermal performance of the system. Furthermore, the converging channel geometry is shown to synergize with the viscoelastic nature of the second-grade fluid to significantly augment heat transfer rates compared to the diverging case.

Graphical Abstract
Multiple Slip Mechanism for Converging/Diverging Flow of Second Grade Nanofluids with Thermal Performance

Keywords
second grade nanofluid
converging/diverging channel
multiple slip
heat transfer enhancement
viscoelastic fluid
numerical solution

Data Availability Statement
Data will be made available on request.

Funding
This work was supported without any funding.

Conflicts of Interest
The authors declare no conflicts of interest.

Ethical Approval and Consent to Participate
Not applicable.

References
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Cite This Article
APA Style
Hashim, & Iftikhar, A. L. (2025). Multiple Slip Mechanism for Converging/Diverging Flow of Second Grade Nanofluids with Thermal Performance. International Journal of Thermo-Fluid Systems and Sustainable Energy, 1(2), 64–74. https://doi.org/10.62762/IJTSSE.2025.412468
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TY  - JOUR
AU  - Hashim
AU  - Iftikhar, Akhunzadi Laiba
PY  - 2025
DA  - 2025/11/25
TI  - Multiple Slip Mechanism for Converging/Diverging Flow of Second Grade Nanofluids with Thermal Performance
JO  - International Journal of Thermo-Fluid Systems and Sustainable Energy
T2  - International Journal of Thermo-Fluid Systems and Sustainable Energy
JF  - International Journal of Thermo-Fluid Systems and Sustainable Energy
VL  - 1
IS  - 2
SP  - 64
EP  - 74
DO  - 10.62762/IJTSSE.2025.412468
UR  - https://www.icck.org/article/abs/IJTSSE.2025.412468
KW  - second grade nanofluid
KW  - converging/diverging channel
KW  - multiple slip
KW  - heat transfer enhancement
KW  - viscoelastic fluid
KW  - numerical solution
AB  - This study presents a comprehensive numerical investigation of the flow and heat transfer characteristics of a second-grade nanofluid in a converging/diverging channel, incorporating the significant effects of multiple slip mechanisms. The analysis considers velocity, thermal, and solutal slip conditions at the channel walls, providing a more realistic model of nanofluid behavior in micro-environments or with specific surface interactions. The governing equations, derived from the principles of conservation of mass, momentum, and energy, are formulated using a non-Newtonian second-grade fluid model to account for viscoelastic effects, combined with the Buongiorno model to capture the Brownian motion and thermophoresis mechanisms of nanoparticles. The resulting system of highly non-linear, coupled partial differential equations is transformed into a set of ordinary differential equations using a similarity transformation approach. The ensuing boundary value problem is solved computationally using the robust MATLAB bvp4c solver. The results are meticulously analyzed to elucidate the intertwined influence of the second-grade fluid parameter (viscoelasticity), the nanoparticle volume fraction, the slip parameters, and the channel geometry (converging/diverging angle) on the velocity profile, temperature distribution, and thermal performance. Key findings indicate that velocity slip and thermal slip parameters substantially reduce skin friction and enhance the local Nusselt number, respectively, thereby critically optimizing the thermal performance of the system. Furthermore, the converging channel geometry is shown to synergize with the viscoelastic nature of the second-grade fluid to significantly augment heat transfer rates compared to the diverging case.
SN  - 3069-1877
PB  - Institute of Central Computation and Knowledge
LA  - English
ER  - 
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@article{Hashim2025Multiple,
  author = {Hashim and Akhunzadi Laiba Iftikhar},
  title = {Multiple Slip Mechanism for Converging/Diverging Flow of Second Grade Nanofluids with Thermal Performance},
  journal = {International Journal of Thermo-Fluid Systems and Sustainable Energy},
  year = {2025},
  volume = {1},
  number = {2},
  pages = {64-74},
  doi = {10.62762/IJTSSE.2025.412468},
  url = {https://www.icck.org/article/abs/IJTSSE.2025.412468},
  abstract = {This study presents a comprehensive numerical investigation of the flow and heat transfer characteristics of a second-grade nanofluid in a converging/diverging channel, incorporating the significant effects of multiple slip mechanisms. The analysis considers velocity, thermal, and solutal slip conditions at the channel walls, providing a more realistic model of nanofluid behavior in micro-environments or with specific surface interactions. The governing equations, derived from the principles of conservation of mass, momentum, and energy, are formulated using a non-Newtonian second-grade fluid model to account for viscoelastic effects, combined with the Buongiorno model to capture the Brownian motion and thermophoresis mechanisms of nanoparticles. The resulting system of highly non-linear, coupled partial differential equations is transformed into a set of ordinary differential equations using a similarity transformation approach. The ensuing boundary value problem is solved computationally using the robust MATLAB bvp4c solver. The results are meticulously analyzed to elucidate the intertwined influence of the second-grade fluid parameter (viscoelasticity), the nanoparticle volume fraction, the slip parameters, and the channel geometry (converging/diverging angle) on the velocity profile, temperature distribution, and thermal performance. Key findings indicate that velocity slip and thermal slip parameters substantially reduce skin friction and enhance the local Nusselt number, respectively, thereby critically optimizing the thermal performance of the system. Furthermore, the converging channel geometry is shown to synergize with the viscoelastic nature of the second-grade fluid to significantly augment heat transfer rates compared to the diverging case.},
  keywords = {second grade nanofluid, converging/diverging channel, multiple slip, heat transfer enhancement, viscoelastic fluid, numerical solution},
  issn = {3069-1877},
  publisher = {Institute of Central Computation and Knowledge}
}

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