Thermal convection of magnetic fluid in a vertical loop: influence of thermal and magnetic Rayleigh numbers on heat transfer intensity

   Purpose of research. Investigation of the functional relationship between integral heat flux and both thermal and magnetic Rayleigh numbers in combined (gravitational and thermomagnetic) convection of ferrofluid within a closed hydrodynamic loop, with assessment of the thermomagnetic convection mechanisms contribution.

   Methods: Experimental data were obtained from a vertical hydrodynamic loop filled with a magnetite-kerosene-oleic acid ferrofluid, subjected to localized heating and magnetic fields up to 29 kA/m. Four ferrofluid samples with identical particle size distributions but varying magnetic phase concentrations were investigated. The dimensionless integral heat flux, expressed as the Nusselt number (Nu), was determined from steady-state temperature profiles along the circuit. Both gravitational (RaT) and magnetic (Ram) Rayleigh numbers were calculated using the channel diameter and temperature difference across the heated section. The ferrofluid's pyromagnetic coefficient was evaluated via a bidisperse model.

   Results: The experimental results demonstrate that the integral heat flux data, including the zero-field case, follow a universal scaling relation Nu = f(Rae).

   Conclusion: To characterize the experimental results, we employed dimensionless parameters—the Nusselt number (Nu) and the effective Rayleigh number (Rae)—which incorporate the system geometry, the ferrofluid's thermophysical and magnetic properties, and the applied magnetic field conditions. Our analysis demonstrates that a universal scaling relation Nu = f(Rae) can be established by defining the effective Rayleigh number as a linear combination of the thermal (RaT) and magnetic (Ram) Rayleigh numbers: Rae = RaT + ζ⋅Ram. This unified representation successfully describes convective heat transfer across all tested conditions, including ferrofluids of varying concentrations subjected to magnetic fields up to 29 kA/m. The empirical coefficient ζ was determined to be 0.29 in our experimental configuration, though we note this parameter may generally depend on system geometry.

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