In the first part of the thesis, an accurate numerical model based on the slip-flow theory is developed to simulate time accurate momentum and heat transport phenomena in complex micro-geometries,encountered in typical components of micro-devices such as micro-capillaries, micro-valves, micro-rotors, and micro-bearings. The present model is based on the spectral element technique which has been used in simulations of incompressible continuum flows. A high-order slip boundary condition is developed to represent the coupling of momentum and heat transfer through thermal creep and viscous heating effects. Analytical solutions for pressure-driven and shear-driven channel flows are employed to validate the numerical model. Numerical results for prototype internal and external flows are also presented. In the second part of the thesis a new spectral element algorithm for viscous compressible flows is developed. This algorithm is still in development stage, and will be used to investigate the compressibility effects in slip-flows in future studies. A preliminary analysis to investigate compressibility effects in micro-channels is performed using the Fanno flow theory and relevant experimental data reported in the literature.