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The novelty of the present work is studying the influences of thermal radiation and magnetic field on the double diffusion of solid phase in the novel cavity of two linked cylinders suspended by nano-encapsulated phase change materials (NEPCMs) and porous media. The complex cavity contains two circular cylinders connected by an open gate occupied by solid particles. Two different boundary conditions including hot and cold for the solid phase are conducted in this work. The incompressible smoothed particle hydrodynamics (ISPH) method is improved to solve the time-fractional governing equations of the physical problem. The mesh-free nature of the ISPH method helps in treating the different materials of the solid and fluid phases efficiently. The physical parameters are dimensionless time parameter , Hartmann number Ha, thermal radiation parameter Rd, fractional time-derivative , Darcy parameter Da, Rayleigh number Ra, and fusion temperature f. The main findings of the numerical simulations indicated that the fractional time-derivative parameter changes the transmission of heat-mass and nanofluid developments during the initial time steps. The Rayleigh number works well in improving the interactions between the solid and fluid phases due to the high buoyancy forces. Increasing the Rayleigh number improves the intensity of the temperature, concentration, and nanofluid speed in a cavity at Case 1 (C1) and Case 2 (C2). The phase change zone is changing according to the alterations of boundary conditions, Rayleigh number, and fusion temperature. Increasing thermal radiation parameter shrinks the nanofluid movements and mean Nusselt number Nu.
Aly et al. (Thu,) studied this question.