An analytical solution for conduction-dominated unidirectional solidification of binary mixtures

In this paper, a fully analytical solution technique is established for the solution of unidirectional, conduction-dominated, alloy solidification problems. By devising appropriate averaging techniques for temperature and phase-fraction gradients, governing equations inside the mushy region are made inherently homogeneous. The above formulation enables one to obtain complete analytical solutions for solid, liquid and mushy regions, without resorting to any numerical iterative procedure. Due considerations are given to account for variable properties and different microscopic models of alloy solidification (namely, equilibrium and non-equilibrium models) in the two-phase domain. The results are tested for the problem of solidification of a NH₄Cl–H₂O solution, and compared with those from existing analytical models as well as with the corresponding results from a fully numerical simulation. The effects of different microscopic models on solidification behaviour are illustrated, and transients in temperature and heat flux distribution are also analysed. A good agreement between the present solutions and results from computational simulation is observed.