The objective of this paper is to investigate the behavior of two well-known boundary-driven molecular dynamics (MD) approaches, namely, reverse nonequilibrium molecular dynamics (RNEMD) and heat exchange algorithm (HEX), as well as introducing a modified HEX model (MHEX) that is more accurate and computationally efficient to simulate the mass and heat transfer mechanism. For this investigation, the following binary mixtures were considered: one equimolar mixture of argon (Ar) and krypton (Kr), one nonequimolar liquid mixture of hexane (nC_{6}) and decane (nC_{10}), and three nonequimolar mixtures of pentane (nC_{5}) and decane. In estimating the Thermodiffusion factor in these mixtures using the three methods, it was found that consistent with the findings in the literature, RNEMD predictions have the largest error with respect to the experimental data. Whereas, the MHEX method proposed in this work is the most accurate, marginally outperforming the HEX method. Most importantly, the computational efficiency of MHEX method is the highest, about 7% faster than the HEX method. This makes it more suitable for integration with multiscale computational models to simulate thermodiffusion in a large system such as an oil reservoir.