The history of fluid solidification study in stagnation flow is limited to few cases. Among these few studies only some articles have considered the fluid viscosity and yet pressure variations along thickness of viscous layer has not been taken into account and also energy equation has been assumed to be one-dimensional. In this study the solidification of stagnation flows is modeled as an accelerated flat plate moving toward an impinging fluid. The unsteady momentum equations taking into account the pressure variations along viscous layer thickness are reduced to ordinary differential equations by use of proper similarity variables and are solved by using a fourth-order Runge-Kutta integrating method at each prescribed interval of time. In addition, energy equation is solved numerically at any step for known velocity and the problem is presented in a two-dimensional Cartesian coordinate. Comparisons of these solutions are made with existing special ranges of past solutions. The fluid temperature distribution, transient velocity components distribution, and the most important of all the rate of solidification or the solidification front are presented for different values of non-dimensional Prandtl and Stefan numbers. Results show that, increase of Prandtl numbers up to ten times or increase of heat diffusivity ratios up to two times causes a decrease of the ultimate frozen thickness almost by half while Stefan number has no effect on this thickness and its effect is only on freezing time.

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