The transient freezing of a liquid flowing between two parallel plates is investigated numerically and by visual experiment keeping the wall temperature constant under the freezing point of the fluid. The numerical solution is based on the Lagrangian interpolation equations at the moving boundary. The discrepancy of the numerical calculation from the experiment is of the order of 10 % based on the four-point interpolation method. The wall temperature plays more significant role on fluid solidification than that of inlet fluid temperature and average inlet velocity.