Abstract
The incompressible smoothed particle hydrodynamics (ISPH) method is improved by the Taylor expansion to manage the unsteady conformable fractal systems of natural convection within a porous annulus amongst the circular cylinders. The annulus is suspended by a nano-encapsulated phase change material (NEPCM). The inner circular cylinders are fixed at a cool temperature. The ISPH numerical investigations are performed for variable values of the conformable fractal parameter alpha (0.93 - 1), adiabatic length LAdiab(0.5 - 2), Darcy parameter Da (10-2 - 10- 5), thermalradiation parameter Rd (0 - 5), Rayleigh number Ra (103 - 106), the radius of an inner cylinder RCylind(0.15 - 0.4), and the fusion temperature theta f (0.05 - 0.75). The outcome results indicated the novel significance of the conformable fractal parameter in speeding the transition process to a stable condition. The changes in the thermal boundary conditions of the outer walls by altering the adiabatic length affect the temperature distributions, phase change zone, and nanofluid velocity. Increasing thermal radiation improves the isotherms and shrinks a phase change zone. The fusion temperature has a good role in adjusting the situation and power of a phase change zone within a cavity. Contributions of Rayleigh number are less in enhancing convection and phase change zone due to a small area of an annulus. Rayleigh number strengthens the nanofluid velocity in an annulus.