A flow reactor has a module (12) that comprises at least first (20), second (30), and third (40) parallel plates stacked temporarily or permanently together and defining a first thermal fluid layer (25) between the first (20) and second plates (30) and a process fluid layer (35) between the second (30) and third plates (40), the process fluid layer (35) comprising a process fluid passage (32) having two or more U-bends and three or more successive process fluid passage segments joined by respective U-bends, the first thermal fluid layer (25) comprising at least two open thermal fluid channels (26) in the second plate (30), the at least two open channels (26) positioned, when viewed in a plan view of the module (12), between respective adjacent process fluid passage segments.