Effect of inviscid stagnation flow on the freezing of fluid -- a theoretical analysis (Q1975849)

This paper considers the solidification problem for an inviscid stagnation flow toward a cold substrate. Initially \((t=0)\), the fluid is kept at a uniform temperature higher than the freezing temperature of the fluid. For \(t>0\), the temperature of the substrate is suddenly lowered to \(T_c\) (cold temperature of solid surface), and is maintained constant. As a result, the solidification occurs at the substrate surface, and the solid layer grows with time. In the absence of fluid flow, this problem reduces to well-known Stefan problem with Neumann's solution. Here the author obtains an analytical solutions for the initial stage of freezing and for final equilibrium state. The initial-stage solution is obtained by expanding it in powers of non-dimensional time \((\tau\ll 1)\), while the final equilibrium-state solution is found by using steady-state governing equations. The main physical quantities of interest are the growth rate of solid and the heat transfer rate at the surface of solid and on the liquid side of solid-liquid interface. The author shows that the equilibrium state is dependent on \(\theta_R/K_R\), but independent of the Stefan number Ste and the ratio of thermal diffusivities \(\alpha_R\), where \(\theta_R\) and \(K_R\) are temperature ratio and ratio of thermal conductivities. Some interesting results are presented in three graphs. The paper is well written and gives all details needed for a physical justification of the results.