Region stabilized flow

In the stabilized region of flow, the average fluid velocity V is directed along the tube axis and depends only on the distance Y from the tube wall. The integration of the Reynolds equations (1.1.18) yields the following expression for the shear stress [289, 427] ... 

The experiments show that in the region of stabilized flow, two characteristic subregions can be singled out [56, 398], namely,... 

Let us discuss qualitative specific features of convective heat and mass transfer in a turbulent flow through a circular tube and plane channel in the region of stabilized flow. Experimental evidence indicates that several characteristic regions with different temperature profiles can be distinguished. At moderate Prandtl numbers (0.5 < Pr < 2.0), the structure and sizes of these regions are similar to those of the wall layer and the core of the turbulent stream considered in Section 1.6. 

If the fluid temperature at the entry cross-section is equal to the wall temperature Ts, then, along some initial part of the tube, the fluid is gradually heated by internal friction until a balance is achieved between the heat withdrawal through the walls and the dissipative heat release. In the region where such an equilibrium is established, the fluid temperature does not vary along the channel, that is, the temperature field is stabilized (provided that the velocity profile is also stabilized). In what follows we just study this thermally and hydrodynamically stabilized flow. 

Now let us consider a steady-state hydrodynamically stabilized flow of a non-Newtonian fluid through a plane channel of width 2h. Let us introduce Cartesian coordinates X, with X-axis directed downstream along the lower wall and with coordinate measured inward the channel along the normal to this wall (0 < < 2h). Since the problem is symmetric about the midline = h, it suffices to consider the lower half of the region, 0 < < /i. 

The most useful mathematical formulation of a fluid flow problem is as a boundary value problem. This consists of two main parts a set of differential equations to be satisfied within a region of interest and a set of boundary conditions to be satisfied on the surfaces of that region. Sometimes additional conditions are also of interest, eg, when one is investigating the stability of a flow. 

In the case of laminar flow, the velocity of the gas at the deposition surface (the inner wall of the tube) is zero. The boundary is that region in which the flow velocity changes from zero at the wall to essentially that of the bulk gas away from the wall. This boundary layer starts at the inlet of the tube and increases in thickness until the flow becomes stabilized as shown in Fig. 2.4b. The reactant gases flowing above the boundary layer have to diffuse through this layer to reach the deposition surface as is shown in Fig. 2.3. 

FIGURE 13.7 Performance of a laminar flow, tubular reactor for the bulk polymerization of styrene Tin = 35°C and F = 1 h. (a) Stability regions, (b) Monomer-conversion within the stable region. 

After reduction and surface characterization, the iron sample was moved to the reactor and brought to the reaction conditions (7 atm, 3 1 H2 C0, 540 K). Once the reactor temperature, gas flow and pressure were stabilized ( 10 min.) the catalytic activity and selectivity were monitored by on-line gas chromatography. As previously reported, the iron powder exhibited an induction period in which the catalytic activity increased with time. The catalyst reached steady state activity after approximately 4 hours on line. This induction period is believed to be the result of a competition for surface carbon between bulk carbide formation and hydrocarbon synthesis.(6,9) Steady state synthesis is reached only after the surface region of the catalyst is fully carbided. 

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