This invention relates to a process for cooling or liquefying a fluid product (e.g., natural gas) in a heat exchanger, the process comprising: flowing a fluid refrigerant through a set of refrigerant microchannels in the heat exchanger; and flowing the product through a set of product microchannels in the heat exchanger, the product flowing through the product microchannels exchanging heat with the refrigerant flowing through the refrigerant microchannels, the product exiting the set of product microchannels being cooler than the product entering the set of product microchannels. The process has a wide range of applications, including liquefying natural gas.