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LSM analysis of thermal enhancement in KKL model-based unsteady nanofluid problem using CCM and slanted magnetic field effects

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Abstract

The main emphasis of the current work is to study a proficient nanofluid model. Thermal conductivity of nanofluid is estimated via KKL (Koo–Kleinstreuer–Li) model keeping the nanoparticles influence up to 0.6%. Further, inclined magnetic field, viscous forces and Cattaneo–Christov effects are included in the analysis. The obtained KKL-nanofluid model is studied via LSM over the domain. From the model outcomes, it is examined that dynamic viscosity, density and heat capacity of the functional liquid enhanced from 1.0025 to 1.01516, 1.00706 to 1.04237 and 1.00106 to 1.00638, by taking the Al2O3 amount from 0.15 to 0.6%, respectively. Keeping the inclined Lorentz forces strength from 1.0 to 4.0 leads to drops in the fluid gesture in the lower half of the domain. Implication of magnetic field from various angles (\(\gamma ={35}{^\circ }, {45}{^\circ }, {55}{^\circ }, {65}{^\circ })\) highly resists the movement. Moreover, inclusion of \({\alpha }_{1}=\mathrm{0.1,0.2,0.3,0.4}\), \({\alpha }_{2}=\mathrm{0.2,0.4,0.6,0.8}\), \({E}_{\mathrm{c}1}=\mathrm{0.1,0.2,0.3,0.4}\) and nanoparticles amount \(\phi =\mathrm{0.02,0.04,0.06,0.08}\) positively enhanced the working fluid temperature and the fluid molecules gained much temperature when the plate accelerated outward from the lower once. For the particular setup, the radiative flux and Lorentz forces in the existence of CCM controlled the fluid temperature. Thus, the temperature performance of the fluid diminished when the magnetic field acted through increasing angle.

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Abbreviations

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

Velocity components along the coordinates (m/s)

\({\check{p}}\) :

Pressure (Pa)

\({\check{T}}\) :

Temperature (K)

\({\check{u}}_\text{nf}\) :

Improved dynamic viscosity (kg/m s)

\({\check{u}}_\text{f}\) :

Base liquid dynamic viscosity (kg/m s)

\({\rho }_{\mathrm{nf}}\) :

Improved density of nanoliquid (kg/m3)

\({\rho }_{\mathrm{f}}\) :

Density of base liquid (kg/m3)

\({\check{\sigma}}_\text{nf}\) :

Improved electrical conductivity (S/m)

\({k}_{\mathrm{nf}}\) :

Enhanced thermal conductivity (W/mK)

\({\left({c}_{\mathrm{p}}\right)}_{\mathrm{nf}}\) :

Enhanced heat capacity (J/K)

\(\eta\) :

Similarity variable

\(F\) :

Dimensionless velocity

\(\beta\) :

Dimensionless temperature

\(M\) :

Hartman number

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

Prandtl number

\({E}_{\mathrm{c}1}\) :

Eckert number

\({R}_{\mathrm{d}}\) :

Radiation number

\(\phi\) :

Nanoparticles concentration

\({\alpha }_{1}\) :

Thermal relaxation number

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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 RGP. 2/7/44.

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Authors and Affiliations

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

    Adnan & Aneesa Nadeem

  2. Department of Physics, College of Science, King Khalid University, 61413, Abha, Saudi Arabia

    Nejla Mahjoub Said

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Adnan, Nadeem, A. & Said, N.M. LSM analysis of thermal enhancement in KKL model-based unsteady nanofluid problem using CCM and slanted magnetic field effects. J Therm Anal Calorim 149, 839–851 (2024). https://doi.org/10.1007/s10973-023-12801-1

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