The annular solidification of an aluminiumsilicon alloy in a graphite mould with a geometry consisting of horizontal concentric cylinders is studied numerically. The analysis incorporates the behavior of nonNewtonian, pseudoplastic (n = 0.2), Newtonian (n = 1), and dilatant (n = 1.5) fluids. The fluid mechanics and heat transfer coupled with a transient model of convection diffusion are solved using the finite volume method and the SIMPLE algorithm. Solidification is described in terms of a liquid fraction of a phase change that varies linearly with temperature. The final results make it possible to infer that the fluid dynamics and heat transfer of solidification in an annular geometry are affected by the non-Newtonian nature of the fluid, speeding up the process when the fluid is pseudoplastic.
List of symbolsCp Specific heat (J/kg K) r o Internal radius of the inner mould r 1 External radius of the inner mould (inner radius of the alloy) r 2Internal radius of the outer mould (outer radius of the alloy) r e External radius of the outer mould R Quotient of the external and internal radii (r 2 /r 1 ) of the alloy f PC Phase change fraction g Gravitational acceleration GrGrashofK) L Enthalpy of solidification (J/kg) n Power index Nu Nusselt number P Pressure (Pa) Lc Characteristic length Pr Prandtl number (Pr = m/a) Ra Rayleigh number (Ra = g Á b Á DT Á Lc 3 /(m Á a)) St Stefan number (St = Cp Á DT/h ls ) t Time (s) T Temperature (°C) u Tangential velocity component (m/s) v Radial velocity component (m/s) h, r Cylindrical coordinatesGreek symbols a Thermal diffusivity (m 2