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Laser surface melting allows selective and rapid melting and solidification which leads to various improved properties. In this letter heat transfer during pulsed laser melting is critically analyzed for aluminum and iron using a numerical model. Using a pulse of few milliseconds and 0.5 mm spot radius, we show that there is a critical range of peak powers for which complete solidification occurs even before the end of the pulse. This is due to the rate of heat diffusion through the substrate being higher than the decaying laser heat flux. In this range, a directional growth of the solidification front can be expected.