Frost formation is a renowned phenomenon in HVAC, aeronautical and refrigeration industries. In this paper, numerical modeling and parametric study of the frost formation in the interrupted Micro Channels Heat sinks (MCHS) is investigated considering microfluidic effects in slip flow regime. For numerical modeling, basic equations of humid air and frost including continuum, momentum, energy and phase change mechanism are numerically solved and results are compared with reported data. Knudsen number (Kn) is changed so that slip flow regime requirement is accomplished. This requirement is also considered for setting boundary conditions. The effect of different parameters like cold surface temperature, time and Kn are studied on the frost formation and details of the flow field. Results revealed that with an increase in time and a decrease in Kn and cold surface temperature, weight and thickness of the frost increase. Moreover, with thicker frost maximum flow velocity rises in the microchannel. The details of frost formation and flow field, revealed by the numerical results can remarkably assist designing interrupted microchannel.