Gradient Boundary Conditions Research Articles

On the applicability of the Taylor—Aris axial diffusion model to tubular reactor calculations

The relationship between the one dimensional Taylor—Aris model and the more detailed diffusion model for the steady state behavior of a tubular reactor is studied for the case of laminar flow and a first order reaction. It is shown that: (1) the Taylor—Aris model is valid provided that ka 2/3·8 2 D < 1; (2) the mean concentration computed using the Taylor—Aris model should be identified as the mean in the plane, C m , and the net flux across any plane perpendicular to the axis of the reactor is C m −[( a 2 U 2/48 D) + D] (∂ C m /∂ z); for large N pe the inlet condition. C m (0) = 1−( ka 2/ D)(1/48+1/ N 2 Pe ), seems to yield better results than the Wehner—Wilhelm boundary condition; and the zero gradient boundary condition is not the proper one to use at the outlet end of the reactor. It seems to be more appropriate to simply truncate a semi-infinite solution.

Isoviscous Lubrication of Rigid Cylinders: A Modification to Classical Theory

Measurements of oil film thickness between lightly loaded lubricated discs show that the original theory of Martin over-estimates the film thickness by between 100 and 800 per cent, depending on the ratio of the difference of the surface velocities and their sum. Theoretical results indicate that the upstream boundary condition could account for the discrepancy between the experimental results and the Martin theory. A procedure for the calculation of load-carrying capacity of lightly loaded cylinders based upon new upstream velocity and velocity gradient boundary conditions suggested by Lauder is presented.

Paper 14: Hydrodynamic Lubrication of Lightly Loaded Finite Cylinders

Theoretical results of the load-carrying capacity of lightly loaded finite cylinders indicate that the effect of side leakage can be secondary to upstream boundary condition considerations. Neglecting side leakage the calculations are extended to cover the experimental results of Crook into the régime where the fluid properties are pressure dependent. The results support the adoption of the new velocity and velocity gradient boundary conditions suggested by Lauder.