## 1 Introduction  
Molecular dynamics (MD) simulations are widely used in various scientific and engineering fields due to their ability to provide insights into the behavior and interactions of molecules and materials at the atomic and molecular levels. Recently, there have been notable advancements in micro- and nanoelectromechanical systems (MEMS, NEMS), resulting in the creation of diverse applications [1]. Therefore, the examination of gas flows in micro- and nanochannels has become crucial for the development and functioning of microdevices like microvalves, micropumps, and microturbines. This research study emphasizes the significance of examining gas flows in these microchannels and their impact on industrial applications. This study investigates Couette and Poiseuille flows combined using a hard-sphere MD simulation approach. The results show that temperature and velocity slips depend on wall speeds, pressure gradients, and wall temperatures, causing nonlinearities. Since many numerical methods fail to adequately represent nanochannel flows and experimental studies are also very difficult, MD simulations have become very important. When it comes to the theoretical foundation for comprehending the actions of gases on a molecular scale, the kinetic theory of gases is a fundamental principle in physics. This theory considers gases to be ensembles of particles [2; 3]. This technique is considered the fundamental principle of the kinetic theory, which forms the mathematical framework for describing the behavior of gases, called the Maxwell-Boltzmann equation [4; 5]. The approach proposed by [PERSON] (1916) and [PERSON] (1917) provides a more comprehensive solution for transport phenomena [6; 7]. There are two major molecular simulation methods that are based on the kinetic theory of gases, namely, MD Simulation [8] and Direct Simulation Monte Carlo (DSMC) [9]. While DSMC is a probabilistic technique based on molecular collisions, MD provides results that are more realistic and accurate [10; 11]. However, since all collisions are processed in the MD method, higher computational resources are required [12]. In many frequently used analytical and numerical solutions to flow problems, equations are simplified with some assumptions. Among these assumptions, a continuum medium, slip/no-slip boundary conditions, constant fluid properties, simplified diffusion mechanisms, empirical viscosity models, 2-D approaches, steadiness, Newtonian or inviscid fluid models, and an isothermal medium can be counted [13; 14]. In MD, these macro-scale assumptions are unnecessary and, in some cases, even impossible [15]. As computational power increases, MD simulations of gas flow problems interest more scientists [16; 17]. Nevertheless, the difficulty of increasing the number of molecules, thus decreasing the Knudsen number (\(Kn\)), is still the main obstacle. Therefore, in order to overcome these computational limitations, simulations based on the hard-sphere model are preferred [18; 19]. The hard-sphere model is frequently employed in MD simulations for rarefied gas flows because it effectively represents the fundamental features of gas molecules and their interactions in low-density environments [20]. The hard-sphere model describes gas molecules as solid spheres, enabling the computational simulation of molecular movement and collisions efficiently. The Knudsen number is a critical parameter in MD simulations for describing gas movements. MD simulations provide reliable solutions for both low Knudsen numbers (\(Kn<0.01\), for the continuum approach) and high Knudsen numbers (for nanochannels and rarefied gas). For low Knudsen numbers, gas behavior becomes like continuum flow, where the mean free path of gas molecules is significantly shorter than the actual size of the flow area. Under these conditions, the movement of gas can be well characterized using continuum-based models, such as the Navier-Stokes equations.