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Regression analysis of magnetized fluid flow in a discretely heated square enclosure in the partially filled with porous medium using RSM-CCD

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Abstract

This computational study looks at the dynamics of free convection in a differentially heated square chamber occupied by ionized propane and saturated permeable partition. The modified Navier–Stokes equations and temperature equations are used to describe fluid and porous domain flow and heat transport phenomena. To solve these equations, the Galerkin finite element technique is used. Parametric adjustments are made for various heat source and sink lengths, Rayleigh number, Hartman number, and Darcy number. The results are quantitatively described in terms of the mean Nusselt number along the heated wall as the Rayleigh number increases (104 ≤ Ra ≤ 106). Streamlines and isotherms are used to visualize qualitative insights on these parametric changes. A comparative study is also performed without the porous media. Conclusive data demonstrate that using a permeable partition over a solid partition improves the mean Nusselt value by 26.28% at Ra = 104 and to a highest value of 56.5% at Ra = 106. Notably, this work presents a sensitivity analysis based on response surface methodology, demonstrating subtle connections between magnetohydrodynamics, Rayleigh number, and porous material effects. These findings provide important perspectives for improving thermal control and energy efficiency in advanced magnetohydrodynamic systems.

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Abbreviations

\(g \to\) :

Gravitational force (m s−2)

\(k \to\) :

Thermal conductivity (W K−1 m−1)

\(B_{0} \to\) :

Magnetic field (T)

\(H \to\) :

Heat function

\({\text{Ha}} \to\) :

Hartman number

\({\text{Ra}} \to\) :

Rayleigh number

\(\mu \to\) :

Viscosity (kg m−1 s−1)

\(\Pr \to\) :

Prandtl number

\(P \to\) :

Pressure (N m−2)

\({\text{Nu}}_{{{\text{avg}}}} \to\) :

Average Nusselt number

\(\sigma \to\) :

Electrical conductivity (S m−1)

\(u,v \to\) :

Velocity components (m s−1)

\(\xi \to\) :

Magnetic field angle

\(\alpha \to\) :

Thermal diffusivity (m2s−1)

\(Cp \to\) :

Specific heat (J K−1 kg−1)

\(L_{{\text{r}}} \to\) :

Length of enclosure (m)

\(\varepsilon \to\) :

Porosity

\(\beta \to\) :

Thermal expansion coefficient (K−1)

\(\rho \to\) :

Density (kg m−3)

\(T \to\) :

Temperature (K)

\({\text{Da}} \to\) :

Darcy number

\(\alpha \to\) :

Thermal diffusivity (m2 s−1)

\(\theta \to\) :

Temperature (K−1)

\(h \to\) :

Hot

\(c \to\) :

Cold

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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 Groups Project under grant number  RGP-2-155-1444.

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Authors and Affiliations

  1. School of Applied Sciences, REVA University, Bengaluru, Karnataka, India

    P. V. Ananth Subray, B. N. Hanumagowda & S. V. K. Varma

  2. Department of Mathematics, College of Sciences, King Khalid University, 61413, Abha, Saudi Arabia

    A. S. Alqahtani & M. Y. Malik

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Contributions

PVAS, BNH, and SVKV developed the theoretical formalism and writing–original draft preparation. ASA and MYM performed the numerical simulations. ASA, PVAS, and YMM performed validation, formal analysis and investigation. All authors discussed the results and contributed to the final manuscript. PVAS and BNH supervised the findings of this work.

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Ananth Subray, P.V., Hanumagowda, B.N., Varma, S.V.K. et al. Regression analysis of magnetized fluid flow in a discretely heated square enclosure in the partially filled with porous medium using RSM-CCD. J Therm Anal Calorim (2024). https://doi.org/10.1007/s10973-024-13058-y

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