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This paper investigates singularly perturbed parabolic partial differential equations with delay in space, and the right end plane is an integral boundary condition on a rectangular domain. A small parameter is multiplied in the higher order derivative, which gives boundary layers, and due to the delay term, one more layer occurs on the rectangle domain. A numerical method comprising the standard finite difference scheme on a rectangular piecewise uniform mesh (Shishkin mesh) of $N_{r} \times N_{t}$ N r × N t elements condensing in the boundary layers is suggested, and it is proved to be parameter-uniform. Also, the order of convergence is proved to be almost two in space variable and almost one in time variable. Numerical examples are proposed to validate the theory.

Two experimental slurry bubble column facilities comprising of 10.8 and 30.5 ern diameter columns and appropriate for conducting hydrodynamic and heat transfer studies arc described. The average and local gas holdup data are reported for the air-water system as a function of air velocity. The holdups for th" three phases are also reported for the air-water-glass beads system over a range of air velocity values.. The air holdup data are compared with the predictions of some of the commonly used correlations. The heat transfer coefficient for a 19 mm diameter cylindrical probe and the two-and three-phase dispersions are measured as a function of air velocity. Most of these hydrodynamic and heat transfer data correspond to the churn turbulent regime and the values obtained on the two columns differ appreciably from each other under similar operating conditions. This fact indicates that the scaleup of slurry bubble columns could be quite difficult on the basis of data obtained on the bench and pilot-plant scale units. The continuing data from these facilities on different systems will shed more light in the future on this important aspect which is crucial to the commercialization of indirect coal liquefaction technology.

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