Extensions of Merk's method to the calculation of laminar boundary layer heat transfer from a non-isothermal surface

The Merk's method for calculating non-similar boundary layer heat transfer from an isothermal surface is extended to the case with non-isothermal surface and the reliability of the method is checked in detail. It is shown that except for some small ranges of β (pressure gradient parameter) and γ (wall temperature distribution parameter), the present method yields accurate heat transfer results. Examples of application of the present method are given for a flow around a circular cylinder and for that past a flat plate. The calculations are performed in the limits Pr→∞ and Pr→0, and the results are compared with those derived from the exact asymptotic theories for these limits.     

Characterization of the crossover from capillary invasion to viscous fingering to fracturing during drainage in a vertical 2D porous medium

We experimentally studied the displacement of a viscous wetting fluid (water) by an inviscid non-wetting fluid (air) injected at the bottom of a vertical Hele-Shaw cell filled with glass microbeads. In order to cover a wide parameter space, the permeability of the porous medium was varied by using different bead size ranges and diverse air flow rates were generated by means of a syringe pump. A LED light table was used to back illuminate the experimental cell, allowing a high speed camera to capture images of the drainage process at equal time intervals. The invasion occurred in intermittent bursts. Image processing of the bursts and fractal analysis showed successive transitions from capillary invasion to viscous fingering to fracturing during the same experiment, dependent on the medium permeability, the air injection flow rate, and the vertical position in the cell. The interplay between the capillary, viscous and gravity forces determines the nature of the invasion pattern and the transitions, from capillary invasion to viscous fingering with decreasing fluid pressure on one hand and from viscous fingering to fracturing with decreasing effective overburden pressure on the other hand.