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Revolutionizing heat transfer: exploring ternary hybrid nanofluid slip flow on an inclined rotating disk with thermal radiation and viscous dissipation effects

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Abstract

The primary aim of this study is to investigate the influence of a time-varying magnetic field on the unsteady slip flow of a ternary hybrid nanofluid over an inclined rotating disk, and to analyze the associated heat transfer mechanism. The hybrid nanofluid is composed of copper, titanium, and aluminium oxide suspended in water, serving as the base fluid. The heat transfer mechanism considered in this study comprises Joule heating and viscous dissipation. Results demonstrate that the inclusion of thermal radiation significantly enhances the heat transfer system and renders it more realistic under the effects of convection. The mathematical problem is defined by a set of non-linear partial differential equations and associated slip boundary conditions. Using a suitable similarity transformation, the proposed mathematical system is transformed into a system of nonlinear ordinary differential equations incorporating slip boundary conditions. Subsequently, the transformed equations are solved using the Homotopy Analysis Method (HAM). Graphs of the accurate results of the dimensionless velocity and temperature for various flow parameters provide a better understanding of the heat transfer characteristics of this system. It is observed that the influence of the magnetic reduces the heat transfer rate for stable non-zero slip. These findings have important implications for the design and optimization of heat transfer systems in engineering applications.

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Abbreviations

\(B_{0}\) :

Magnetic field \(\left( {{\text{NA}}^{ - 1} {\text{m}}^{ - 1} } \right)\)

\(F_{0}\) :

Non-uniform inertia coefficient

\(T_{\infty }\) :

Ambient temperature \(\left( {\text{K}} \right)\)

\(r,z\;\&\; \varphi\) :

Coordinates \(\left( {\text{m}} \right)\)

\(u,v\;\&\; w\) :

Velocity Components \(\left( {{\text{ms}}^{ - 1} } \right)\)

\(F^{\prime}\left( \eta \right)\;\&\; G\left( \eta \right)\) :

Radial and azimuthal velocities

\(\Theta \left( \eta \right)\) :

Dimensionless temperature

\(T\) :

Fluid temperature \(\left( {\text{K}} \right)\)

\(T_{{\text{w}}}\) :

Surface temperature

\(q_{{\text{r}}}\) :

Radiation heat flux \(\left( {{\text{kgs}}^{ - 3} } \right)\)

\(k\) :

Thermal conductivity \(\left( {{\text{wm}}^{ - 1} {\text{K}}^{ - 1} } \right)\)

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

Thermal expansion coefficient

\(k_{0}\) :

Darcy coefficient

\(S\) :

Unsteady parameter

\(M\) :

Magnetic parameter

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

Reynold number

\(\Pr\) :

Prandtl number

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

Eckert number

\(C_{{\text{F}}} \;\&\; C_{{\text{G}}}\) :

Skin friction

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

Nusselt number

\(\mu\) :

Dynamic viscosity \(\left( {{\text{kgm}}^{ - 1} {\text{s}}^{ - 1} } \right)\)

\(\upsilon\) :

Kinematic viscosity \(\left( {{\text{m}}^{2} {\text{s}}^{ - 1} } \right)\)

\(\rho\) :

Density \(\left( {{\text{kgm}}^{ - 3} } \right)\)

\(\sigma\) :

Electrical conductivity \(\left( {{\text{sm}}^{ - 1} } \right)\)

\(\phi\) :

Volume fraction nanoparticles

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

Specific heat capacity \(\left( {{\text{jkg}}^{ - 1} {\text{K}}^{ - 1} } \right)\)

\(\theta\) :

Angle

\(\varepsilon\) :

Velocity slip parameter

\(\gamma\) :

Thermal slip parameter

\(\tau\) :

Combine Grashof and Reynold number

\(f\) :

Base Fluid

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

Nanofluid

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

Ternary hybrid nanofluid

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

Hybrid nanofluid

\(\infty\) :

Ambient condition

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Acknowledgements

This work is partially funded by the Future university in egypt engineering research project 2023.

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Authors and Affiliations

  1. Department of Mathematics, City University of Science and Information Technology, Peshawar, 25000, Pakistan

    Muhammad Usman

  2. Department of Mathematics, Faculty of Science, University of Tabuk, Tabuk, 71491, Saudi Arabia

    Mounirah Areshi

  3. Department of Mathematics, Islamia College Peshawar, Peshawar, 25000, Pakistan

    Naseem Khan

  4. Center of Research, Faculty of Engineering, Future University in Egypt, New Cairo, 11835, Egypt

    Mohamed Sayed Eldin

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  1. Muhammad Usman
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Usman, M., Areshi, M., Khan, N. et al. Revolutionizing heat transfer: exploring ternary hybrid nanofluid slip flow on an inclined rotating disk with thermal radiation and viscous dissipation effects. J Therm Anal Calorim 148, 9131–9144 (2023). https://doi.org/10.1007/s10973-023-12299-7

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