Nowdays computer simulations along with the experimental works have contributions to understand the physical phenomena's. Due to the existing experimental limitations in micro and nano-scales, computational tools assist researchers in understanding the micro and Nano phenomena. Molecular dynamics is one of the most accurate tools to simulate the micro and nano scale problems and its use is ever growing. Traort properties and heat transfer coefficients of materials in micro and nano scales are demanded in everyday use of these materials. With the advancement of nanotechnology, the use of nano devices increases daily and Heat transfer plays a significant role in the design and fabrication of nano devises. In this study, first the thermal conductivity of a static liquid argon is calculated using both Green-Kubo and non equilibrium molecular dynamic methods and results are compared with the existing experimental data. Then the thermal conductivity coefficient of a Ar-Cu nano- fluid at four different compositions is calculated for two different potentials. In the first case for interaction between copper particles the EAM potential, and in the second LJ potential is used. Then the heat transfers in Poiseuille and Couette flow are being investigated. To make sure that the heat transfer calculations is correct we first solved the problem under a temperature gradient and compared the results with the existing data where a good agreement was found. Then the heat transfer for an ordinary fluid and a nano-fluid in a Poiseuille flow is investigated. In both cases it was found that by increasing the driving force the heat transfer will increase. It was also observed that by increasing the composition of the copper in a nano-fluid the heat transfer will increase too. The heat transfer for an ordinary fluid and a nano-fluid in a Couette flow at different upper wall velocities is also investigated. Heat transfer was calculated for different velocities of upper wall. In this case it was found that by increasing the upper wall velocity the heat transfer will increase in general. However, this increase is more pronounced for an ordinary fluid than a nano-fluid. This effect is due to the fact that the velocity gradients near the wall for a nano-fluid are less than an ordinary fluid. At the end, the heat transfer for an unstable state in a Poiseuille flow is calculated. To ensure the accuracy of the calculation the specific heat capacity of argon is calculated and compared to the experimental results. Then the specific heat capacity of Ar-Cu nano-fluid is calculated. All simulations were performed using the LAM software. However, to calculate the temperature distribution, the velocity, location and mass of the particles are taken from the LAM output and by using C++ programming code, the calculation is done. Keywords : Molecular dynamics simulation, nano-channel, nano-fluid, heat transfer, thermal conductivity coefficient