Abstract
In this work, the simulations of fractional-time derivative systems of natural convection in a porous annulus suspended by NEPCM under the magnetic field and thermal radiation influences are conducted by the ISPH method. The annulus is constructed amongst the exterior horizontal wavy cavity and interior horizontal wavy blockage. Here, the novelty is appearing in simulating the powers of a magnetic field on natural convection in a novel shape of an annulus between two horizontal wavy shapes. The outer vertical sides are kept at Th and the flat sides are adiabatic. The inner wavy blockage is kept at Tc with zero velocities. The fractional time-derivative, nanoparticle parameter, dimensionless time parameter, Darcy parameter, Hartmann number, thermal radiation parameter, Rayleigh number effects on the heat transfer within an annulus are examined. The outcomes revealed that the contributions of the time-fractional derivative are appearing well at the initial time step. Increasing nanoparticle concentration to 5% shrinks the nanofluid flow. The heat capacity is affected by the differences in the thermal radiation parameter. The thermal radiation parameter is enhancing the mean Nusselt number and diminishes the nanofluid flow in an annulus. The extra Rayleigh number boosts the temperature strength and nanofluid velocity within an annulus.