Critical Reynolds numbers forced convection

The data presented in the previous chapters, as well as the data from investigations of single-phase forced convection heat transfer in micro-channels (e.g., Bailey et al. 1995 Guo and Li 2002, 2003 Celata et al. 2004) show that there exist a number of principal problems related to micro-channel flows. Among them there are (1) the dependence of pressure drop on Reynolds number, (2) value of the Poiseuille number and its consistency with prediction of conventional theory, and (3) the value of the critical Reynolds number and its dependence on roughness, fluid properties, etc. 

The rotation rate should ensure forced convection on the one hand, but laminar flow on the other, so that it remains well below the conditions of the critical Reynolds number, above which turbulent flow sets in ... 

Experimental data associated with gases, water, and viscous oils may be correlated with Eq. (5.150) as shown in Fig 5.22(a), where Rec denotes the critical Reynolds number at which the laminar flow is unstable. Beyond Rec the forced convection eventually becomes turbulent. Equation (5.150) does not correlate the liquid metal data. For liquid metals, viscous forces are small, the momentum equation degenerates to a limit of uniform velocity, and the importance of the Reynolds number diminishes. Consequently, as shown in Fig. 522(b),... 

The Grashof number may be interpreted physically as a dimensionless group representing the ratio of the buoyancy forces to the viscous forces in the free-convection flow system. It has a role similar to that played by the Reynolds number in forced-convection systems and is the primary variable used as a criterion for transition from laminar to turbulent boundary-layer flow. For air in free convection on a vertical flat plate, the critical Grashof number has been observed by Eckert and Soehngen [1] to be approximately 4 x 10". Values ranging between 10" and 109 may be observed for different fluids and environment turbulence levels. ... 

Ihe role played by the Reynolds number in forced convection is played by the Grashof number in natural convection. As such, the Grashof number provides the main criterion in determining whether the fluid flow is laminar or turbulent in natural convection. For vertical plates, for e.Kample, the critical... 

Several factors can affect this enhanced mass transfer. First, as Debenedetti and Reid ( pointed out, the very low kinematic viscosities in conjunction with very high buoyant forces serve to enhance natural convection at the same Reynolds number. This is accentuated by large density differences that can occur as naphthalene dissolves in the C02 It is possible to have very large, negative partial molar volumes (i.e., -2000 cc/mole) for a solute at conditions near the critical point (Eckert et al., (23)) which causes the fluid density to depend strongly on composition. At 35 0 and 100 atm, naphthalene s partial molar volume at infinite dilution is approximately -300 cc/mol. This can cause a significantly higher fluid... 

---