A fluid media such as oil or water, and a selected effective amount of carbon nanomaterials necessary to enhance the thermal conductivity of the fluid. One of the preferred carbon nanomaterials is a high thermal conductivity graphite, exceeding that of the neat fluid to be dispersed therein in thermal conductivity, and ground, milled, or naturally prepared with mean particle size less than 500 nm, and preferably less than 200 nm, and most preferably less than 100 nm. The graphite is dispersed in the fluid by one or more of various methods, including ultrasonication, milling, and chemical dispersion. Carbon nanotubes with graphitic structure is another preferred source of carbon nanomaterial, although other carbon nanomaterials are acceptable. To confer long term stability, the use of one or more chemical dispersants is preferred. The thermal conductivity enhancement, compared to the fluid without carbon nanomaterial, is proportional to the amount of carbon nanomaterials (carbon nanotubes and/or graphite) added.