The present study is directed at flow and heat transfer of $CO_2$ and oil mixtures in a circular tube. PAG and POE oils are considered in this study. Flow characteristics of $CO_2$ and oil mixtures have been investigated by flow visualization. Pressure drop has been measured in the range of operating mass flow rate from 0.1 to 0.4 kg/min in a circular tube. Heat transfer characteristics of $CO_2$/oil mixtures have been investigated using a counterflow heat exchanger. In case of pure liquid $CO_2$ as well as $CO_2$ and POE mixtures, flow are seen to be uniform so that $CO_2$ and POE oil are still miscible even at flowing state. However, it is found that $CO_2$ and PAG are not miscible. Pressure drop of $CO_2$/PAG mixtures are much higher than that of $CO_2$/POE mixtures as well as pure $CO_2$ at a fixed mass flow rate. As the concentration of POE oil is increased from 0 to 5 wt%, pressure drop is increased. However, heat transfer rate and heat transfer coefficient of $CO_2$/POE mixtures are much higher than that of $CO_2$/PAG mixtures. The f-factor correlation and Nusselt number correlation for $CO_2$/POE oil mixtures are suggested in this paper.