| Electromagnetic stirring in castings is one way to refine the cast structure in order to improve the casting's mechanical properties. This study treats an infinitely long circular cylinder which is filled with a liquid metal and which is subjected to a transverse, rotating magnetic field. The role of the pertinent parameters and material properties is studied using Rational Mechanics. Appropriate constitutive relations for the stress and the heat efflux are specified, and the classical result is obtained as a special case. The temperature distribution during solidification is obtained analytically, while the position of the moving solidification front is found numerically. The mechanical problems in the liquid region are solved for the Newtonian fluid model, Einstein's viscosity model, and the Power-law model. The velocity profiles for the first two models and the third model are obtained analytically and numerically respectively. Both the shear rate and the velocity are shown to depend very strongly on the strength of the magnetic induction. Using the Power-law model, the shear stress is shown to reach very high values at the solid-liquid interface. This shear stress breaks the dentrite tips, thus refining the grain size. |
