The main objective of the present thesis is to numerically and analytically investigate the flow and heat transfer phenomena in microscales. Hence, the content of this study is divided into the following two major sections. In the first section, which is related to the numerical study, the lattice Boltzmann method (LBM) is employed to simulate flow and heat transfer processes in microscales. Since common standard LB models are unable to capture the main features of the so-called Knudsen layer, in this study, a correction wall function technique has been employed to enhance the capability of the already mentioned mesoscopic approach in dealing with this kinetic boundary layer. It is shown that such an implementation leads to remarkable improvements in simulating momentum and energy traort phenomena in microscale rarefied gaseous flows, especially in the transition flow regime, without imposing considerable extra computational costs to the solution procedure. In the second section, which is related to the analytical study, an original attempt has been made to present first and second-law analysis of a rarefied gaseous flow confined between two concentrically rotating cylinders throughout the entire slip flow regime. The incompressible Navier-Stokes-Fourier (NSF) equations including viscous dissipation effects in the cylindrical polar coordinate reference frame are analytically solved subject to the so-called slip/jump boundary conditions to obtain the associated velocity and temperature distributions. The solutions are used to carry out a parametric study of rarefaction, dissipation and rotation mode on the corresponding entropy generation characteristics. Imposing two different thermal boundary conditions, namely, UHF and CWT B.Cs, three distinct thermal cases are constructed and then treated separately. The interactive effects of parameters such as the Knudsen number, the Brinkman number, rotation mode and the aspect ratio of the annuli on the velocity and temperature distributions, Nusselt number and heat fluxes at the walls have been studied. Keywords: Microscale flow and heat transfer, Lattice Boltzmann method, Transition flow regime, Analytical solution, First and second laws of thermodynamics, Slip flow regime