A numerical simulation of flame propagation in a micro combustor was carried out. Combustor has a sub -millimeter depth cylindrical internal volume and axisymmetric one-dimensional was used to simplify the geometry. Semi-empirical heat transfer model was used to account for the heat loss to the walls during the flame propagation. A detailed chemical kinetics model of $H_2/Air$ with 10 species and 16 reaction steps was used to calculate the combustion. An operator-splitting PISO scheme that is non-iterative, time-dependent, and implicit was used to solve the system of transport equations. The computation was validated for adiabatic flame propagation and showed good agreement with existing results of adiabatic flame propagation. A full simulation including the heat loss model was carried out and results were compared with measurements made at corresponding test conditions. The heat loss that adds its significance at smaller value of combust or height obviously affected the flame propagation speed as final temperature of the burnt gas inside the combustor. Also, the distribution of gas properties such as temperature and species concentration showed wide variation inside the combustor, which affected the evaluation of total work available of the gases.