in Wiley InterScience (www.interscience.wiley.com).A phenomenological model of the gas bubble hold-up in slurry bubble columns is presented. The slurry moves upward in the core of the column and downward in the annulus, resembling the riser and downer of an air-lift loop reactor, respectively. The model virtually divides the column in a riser and a downer. The cross-sectional areas of the riser and the downer are experimentally found to be approximately equal. A macroscopic momentum balance over the riser and downer gives the liquid circulation velocity. The gas bubble hold-up is modeled for two size classes: small and large. In the homogeneous regime only small gas bubbles are present. Above the regime transition velocity the churn-turbulent regime exists, characterized by the presence of small and large gas bubbles. High speed video imaging shows that the gas flow up to the regime transition velocity generates small gas bubbles and that the gas flow in excess of the regime transition velocity generates large gas bubbles. Small gas bubbles are present in the riser and in the downer and have a constant slip velocity. The Wallis driftflux model describes the small gas bubble hold-up in the riser and in the downer. Large gas bubbles are only present in the riser. The rise velocity of the large gas bubbles is the sum of the liquid velocity and the slip velocity according to the Davies-Taylor equation. The large gas bubble hold-up is obtained from the volume of gas flowing in large gas bubbles and the rise velocity of the large gas bubbles. For a given column diameter, column height, regime transition velocity, and physical properties of a gasliquid system, the model predicts the total gas hold-up, the hold-up of the small and the large gas bubbles, and the average superficial liquid velocity in the riser and in the downer. Two parameters in the model are determined from experiments in a 29-cm ID bubble column: the ratio of the small gas bubble hold-up in the downer to that in the riser, and the energy dissipation at the top and bottom of the column. The model describes the gas hold-up and liquid velocity data from literature with these parameter values within an error of 6%. The model shows that there is no effect of scale on the gas hold-up for columns larger than 15 cm in diameter.

This communication investigates the unsteady two-dimensional oscillatory flow of an incompressible viscous fluid past an infinite vertical, porous flat plate with the effect of magnetic field. It is assume that free stream velocityoscillates in times about a constant mean. Assuming the periodic heat flux at the plate with the effect of viscous dissipation, the set of non-linear coupled differentialequations is solved by regular perturbationtechnique. The approximate solutions are obtained for velocity and temperature field. The effect of various parameters on mean flow velocity, transient velocity, mean skin friction and transient temperature are discussed and shown graphically.