Determination of the interfacial heat transfer coefficient between forced air and sand at Reynold's numbers relevant to smouldering combustion

Heat transfer between flowing air and a fixed sand bed at low Reynold's number (i.e., Re < 30) is central to numerous natural and applied processes, including smouldering combustion. The most widely used correlation for the heat transfer coefficient (hsg) predicts Nusselt numbers so high, it effectively presumes local thermal equilibrium for these systems; an assumption that has never been tested. In this work, twelve column experiments combined with numerical modelling quantify hsg across a range of relevant sand grain sizes (0.125 < dp < 2.000 mm) and air flow rates (0.5 < Re < 31). All of the sand properties were determined independently, with only hsg determined via inverse modelling. A new empirical correlation for hsg is obtained, Nu = 0.001 (Re1.97Pr1/3), which is then validated against two additional experiments. A newly developed criterion for assuming local thermal equilibrium is shown to be violated in all of these convection-dominated experiments and the extent of non-equilibrium between sand and air is quantified. The centerline temperatures are demonstrated to be sensitive not only to hsg but also to a global heat loss coefficient quantified from the experiments in a novel manner. Overall, the new hsg correlation is demonstrated to be reliable for predicting the interphase heat transfer in these systems and its application is expected to be valuable for a wide range of processes including smouldering.