Disclosed is a reactor for reacting fluids such as fluids in continuous flow, the reactor including a multicellular extruded body having cells extending in parallel in a direction from a first end of the body to a second end, the body having a first plurality of cells open at both ends of the body and a second plurality of said cells closed at one or both ends of the body, the second plurality being contiguous cells and cooperating to define at least in part a fluidic passage extending at least partly through the body. The fluidic passage desirably has a serpentine path back and forth along cells of the second plurality of cells, and the passage connects laterally from cell to cell, within cells of the second plurality, at or near the ends of the body.