TRANSVERSE LAMINAR-FLOW OF NON-NEWTONIAN FLUIDS OVER A BANK OF LONG CYLINDERS

The creeping transverse flow of incompressible Carreau model fluids pa st an array of infinitely long cylinders has been analysed theoretical ly. The hydrodynamic interactions between cylinders have been simulate d using a simple cylinder-in-cylinder free surface cell model. In this formalism, the overall mean porosity characterises an array of cylind ers without any assumption regarding the actual geometrical arrangemen t of the individual cylinders. The resulting non-linear field equation s have been solved approximately by employing the well known velocity and stress variational principles. The resulting upper and lower bound s are non-coincident and diverge increasingly with the rising extent o f non-Newtonian behaviour of the liquid medium. However, the mean valu e of the drag coefficient deviates from the individual bounds by no mo re than 22% and therefore, the use of the arithmetic mean of the upper and lower bounds is suggested. The theoretical predictions reported h erein encompass wide ranges of physical and kinematic conditions as fo llows: 1 greater than or equal to n greater than or equal to 0.2; 0.9 greater than or equal to epsilon greater than or equal to 0.3 and Lamb da less than or equal to 500. The paper is concluded by presenting com parisons between the present predictions and the scant experimental re sults for two limiting cases, namely, for the flow of Newtonian fluids (n = 1) through assemblages of solid rods and random fibrous beds, an d for the dow of power law liquids (i.e., for large values of Lambda) through banks of rods. The correspondence is found to be satisfactory.