So which ever solid or liquid is having higher value of k, heat transfer will be greater for the one having higher k .Most of the solids have higher thermal conductivity than liquids, so solids have higher heat transfer rate than that of liquid in most of the case. read more
However, if liquids are motion they transfer heat at a faster rate. By using some sort of force to move the liquid, the atoms can move the heat at a faster rate. Think of a heat exchanger; they pass a fluid (a liquid or gas) through the interior of the system to transfer the heat faster. read more
Heat transfer happens everytime there is a temperature difference between two points in some environment. This transfer is a heat energy passing as a consequence of the temperature difference. Conduction is a direct transfer of energy from particle of a matter (solid or liquid) from an elevated energy level, to particles at a lower energetic level, as a consequence of the interaction between the particles. read more