Transient magneto-buoyant convection of a magnetizable nanofluid inside a circle sensible storage subjected to double time-dependent thermal sources

Thermal and flow behaviors of sensible heat energy storage unit subjected to uniform and nonuniform magnetic field effects and to double time dependent heat sources were numerically investigated. The sensible heat energy storage unit is occupied with the nanofluid consisting in Cu nanoparticles dispersed into water and subjected to two variable magnetic sources. The dimensionless governing equations are established and solved via finite element numerical approach. An excellent consistency with published data has been observed during validation of the results. The influence of a certain range of key nondimensional parameters on the transient problem including the frequency of sinusoidal time-dependent temperature imposed from heat sources (λ = 0.1–50), temperature-dependent amplitude of sinusoidal fluctuations (Λ = 0–1), the magnetic number (Mn = 0–5000) and Hartmann number (Ha = 0–50) for two separate Rayleigh number (Ra = 10⁴ and 10⁶) was considered. According to the findings, temperature-varying boundaries affect convective flow, heat exchange, thermal stratification, and total heat content. The oscillations amplitudes for the average time-dependent Nusselt number grow as Ra, Λ and λ increase and Ha decreases. Total heat content in the storage unit is found to have higher mean values at steady development for higher Ra values when Ha = 0. Mn values slightly enhance the mean values of heat content.