Knudsen layer phenomenon in high-speed rarefied and micro-scale gas flows have been investigated. Effective mean free path model from the literature have been incorporated in the traditional Navier-Stokes (NS) solver, and it is modified with non-linear constitutive relations to account for the effect of Knudsen layer. First order non-equilibrium boundary conditions are also modified to consider local effective mean free path. The extended solver is validated for the benchmark test cases of Kramer's problem and temperature jump problem, where non-linear flow properties due to momentum and thermal Knudsen layer are accurately captured. Validity of the effective mean free path model is tested in the high-speed micro-scale gas flows is this manuscript. Simulations have been carried out for Mach 4.38 flow over a nano-plate and Mach 10 flow over a micro-cylinder, using direct simulation Monte Carlo method, traditional NS solver with slip-jump boundary conditions, and the extended NS solver with Knudsen layer effects. It is found that flow properties in the near wall region are not much affected by Knudsen layer, but surface flow properties such as heat load, slip velocity and temperature jump are accurately captured. The analysis is important from the perspective of design of micro-scale devices and vehicles operating at high altitude conditions. © 2019 Author(s).