Solidification and melting modeling on microfluidics are solved using Lambert W's function and error's functions. Models are formulated using the heat's diffusion equation. The generic posed case is the melting of a slab with time dependent surface temperature, having a micro or nano-fluid liquid phase. At the beginning the solid slab is at melting temperature. A slab's face is put and maintained at temperature greater than the melting limit and varying in time. Lambert W function and error function are applied via Maple to obtain the analytic solution evolution of the front of microfluidic-solid interface, it is analytically computed and slab's corresponding melting time is determined. It is expected to have analytical results to be useful for food engineering, cooking engineering, pharmaceutical engineering, nano-engineering and bio-medical engineering.