This chapter presents a numerical study using the single-relaxation-time lattice Boltzmann method (SRT-LBM) to investigate natural convection in an air-filled square cavity. The main objective is to analyze the influence of the Knudsen number on the flow behavior by applying velocity slip and temperature jump boundary conditions on the active walls, while also investigating the effect of the heated zone length ( \(h=\) H/2, \(H\) ). A sinusoidal temperature profile is imposed along the left vertical wall, and simulations are carried out at a fixed Rayleigh number (Ra = 104), with the Knudsen number varying from 0 to 0.1. The results show that as Kn increases, the Nusselt number decreases, indicating lower heat transfer due to rarefaction. The sinusoidal heating causes heat to concentrate near the center of the wall, especially when the heated length is reduced to half the wall height \(h=\) H/2, leading to more localized thermal effects and better control of temperature gradients. These findings highlight the importance of considering both heating geometry and rarefaction effects in the design of energy-efficient cooling systems, particularly in microscale applications. The numerical results agree well with existing literature, confirming the reliability of the SRT-LBM approach used in this work.