“…Pressure and temperature history throughout the part was calculated from the constitutive equations of mass, momentum and energy, with specific assumptions and boundary conditions for each particular stage. For example, the governing equations for the filling stage are written as35–37 where $ \dot {\varepsilon }_{ij} = {1\over 2}(u_{i,j}+u_{j,i}) $ ; the symbol ‘,’ denotes derivatives, i = 1,2,3 and j = 1,2,3 are the coordinate components; u , P and T are velocity, pressure, and temperature with η, ρ, C p and K being dynamic viscosity, density, specific heat, and the thermal conductivity, respectively.…”