Expedition of solidification with dispersing nanoparticles utilizing numerical method

To show the efficacy of size of nanoparticles, numerical modeling for current article has been developed based on homogeneous approximation for nanomaterial. Energy equation with considering one term denoting the phase change process should be solved for illustration of discharging process. The properties of material should be changed according to formulation of homogeneous mixture. The efficacy of size has been added in formula of conductivity factor. Galerkin method for such unsteady process has been applied with incorporating implicit approach. With utilizing adaptive mesh the accuracy of method increases and good agreement has been reported according to validation test. With dispersing nanoparticles, the speed of process increases and changing the size of powder can affect the behavior of system. As diameter of nanoparticles changes about 10 nm from 30 nm, the required time reduces about 19.21%. Required time augments by 18.64% with changing the size of particles from 30 nm to 50 nm. Augmenting the nanoparticles fraction can improves the freezing rate by 66.88%.