Large scale natural convection currents in the tubes of vertical shell-and-tube heat exchangers may occur -mixed with a forced tubeside flow- in energy recovery systems. Severe losses in performance, as observed in an industrial application, may be due to those unwanted recirculation flows. Analytical solutions for temperatures in a heat exchanger with backflow in some of the tubes as well as tracer experiments show that the unwanted recirculation flows may in fact occur in industrial heat exchangers. The case of pure natural convection in a tube bundle has also been studied. Explicit analytical solutions were found for some simple cases. Small scale experiments with two and three tubes, and numerical calculations did confirm the theoretical predictions. From the results obtained, conclusions can be drawn leading to simple recommendations for industrial practice and to a number of open questions for further research.