MHD double diffusion of a nanofluid within a porous annulus using a time fractional derivative of the ISPH method

Using an inner complex blockage within a square cavity is spreading massively for the cooling process. This study adopts the time-fractional derivative of the incompressible smoothed particle hydrodynamics (ISPH) method for studying the magnetic field, diffusion-thermo, and thermo-diffusion impacts on the double diffusion of a nanofluid in a porous annulus between a square cavity and an astroid shape. The alterations of the pertinent parameters, fractional derivative order α between 0.9 and 1, dimensionless time parameter τ between 0 and 0.6, the radius of an astroid Ra between 0.1 and 0.45, solid volume fraction ϕ between 0 and 0.06, Hartman parameter Ha between 0 and 100, Darcy parameter Da between 10−2 and 10−5, and Soret number Sr between 0.1 and 2 supplemented by Dufour number Du between 0.6 and 0.03 on the velocity field, temperature, concentration, and mean of Nusselt and Sherwood numbers are discussed. The main findings of the ISPH numerical simulations showed that a decrease in a fractional derivative order α delivers the sooner steady-state of the double diffusion which suppresses the performed calculations. The velocity field’s maximum powers by 19.23% as Ra increases from 0.1 to 0.45 and it decreases by 16.67%, 28.89%, and 97.99% as ϕ powers from 0 to 0.06, Ha powers from 0 to 100, and Da decreases from 10−2 to 10−5, respectively. The outlines of Nu¯ and Sh¯ are increasing as Ra and ϕ are increased. A growth in Sr supplemented by a reduction in Du is diminishing the distributed concentration and nanofluid velocity within an annulus.