Convection Reynolds number

The convection term in the equation of motion is kept for completeness of the derivations. In the majority of low Reynolds number polymer flow models this term can be neglected. 

As the Reynolds number rises above about 40, the wake begins to display periodic instabiUties, and the standing eddies themselves begin to oscillate laterally and to shed some rotating fluid every half cycle. These still laminar vortices are convected downstream as a vortex street. The frequency at which they are shed is normally expressed as a dimensionless Strouhal number which, for Reynolds numbers in excess of 300, is roughly constant ... 

Eurther research on convective transport under low Reynolds number, quasicontinuum conditions is needed before the optimal design of such a micro heat exchanger is possible. The cooling heat exchanger is usually thermally linked to a relatively massive substrate. The effects of this linkage need to be explored and accurate methods of predicting the heat-transfer and pressure-drop performance need to be developed. 

Characterization and influence of electrohydro dynamic secondary flows on convective flows of polar gases is lacking for most simple as well as complex flow geometries. Such investigations should lead to an understanding of flow control, manipulation of separating, and accurate computation of local heat-transfer coefficients in confined, complex geometries. The typical Reynolds number of the bulk flow does not exceed 5000. 

To the extent that radiation contributes to droplet heatup, equation 28 gives a conservative estimate of the time requirements. The parameter ( ) reflects the dependence of the convective heat-transfer coefficient on the Reynolds number ... 

Pressure drop due to hydrostatic head can be calculated from hquid holdup B.]. For nonfoaming dilute aqueous solutions, R] can be estimated from f i = 1/[1 + 2.5(V/E)(pi/pJ ]. Liquid holdup, which represents the ratio of liqmd-only velocity to actual hquid velocity, also appears to be the principal determinant of the convective coefficient in the boiling zone (Dengler, Sc.D. thesis, MIT, 1952). In other words, the convective coefficient is that calciilated from Eq. (5-50) by using the liquid-only velocity divided by in the Reynolds number. Nucleate boiling augments conveclive heat transfer, primarily when AT s are high and the convective coefficient is low [Chen, Ind Eng. Chem. Process Des. Dev., 5, 322 (1966)]. 

Correlations for forced convection over tubes in crossflow are complicated by the effect of the tube bank arrangement. For the range of Reynolds numbers likely to be encountered in industrial boilers the following equations may be used ... 

F3. Firstenberg, H., Goldmann, K., Lo Bianco, L., Preiser, S., and Rabinowitz, G., Compilation of experimental forced convection quality burnout data with calculated Reynolds numbers, NDA-2131-16 (1960). 

An attempt has been made by Johnson and co-workers to relate such theoretical results with experimental data for the absorption of a single carbon dioxide bubble into aqueous solutions of monoethanolamine, determined under forced convection conditions over a Reynolds number range from 30 to 220. The numerical results were found to be much higher than the measured values for noncirculating bubbles. The numerical solutions indicate that the mass-transfer rate should be independent of Peclet number, whereas the experimentally measured rates increase gradually with increasing Peclet number. The discrepancy is attributed to the experimental technique, where-... 

Equation 9.215 is valid for Reynolds Numbers in excess of 10,000. Where the Reynolds Number is less than 2000, the flow will be laminar and, provided natural convection effects... 

Garner and Keey(52 53) dissolved pelleted spheres of organic acids in water in a low-speed water tunnel at particle Reynolds numbers between 2.3 and 255 and compared their results with other data available at Reynolds numbers up to 900. Natural convection was found to exert some influence at Reynolds numbers up to 750. At Reynolds numbers greater than 250, the results are correlated by equation 10.230 ... 

A study of forced convection characteristics in rectangular channels with hydraulic diameter of 133-367 pm was performed by Peng and Peterson (1996). In their experiments the liquid velocity varied from 0.2 to 12m/s and the Reynolds number was in the range 50, 000. The main results of this study (and subsequent works, e.g., Peng and Wang 1998) may be summarized as follows (1) friction factors for laminar and turbulent flows are inversely proportional to Re and Re ", respectively (2) the Poiseuille number is not constant, i.e., for laminar flow it depends on Re as PoRe ° (3) the transition from laminar to turbulent flow occurs at Re about 300-700. These results do not agree with those reported by other investigators and are probably incorrect. 

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. 

Convective heat transfer to fluid inside circular tubes depends on three dimensionless groups the Reynolds number. Re = pdtu/ii, the Prandtl number, Pr = Cpiilk where k is the thermal conductivity, and the length-to-diameter ratio, L/D. These groups can be combined into the Graetz number, Gz = RePr4/L. The most commonly used correlations for the inside heat transfer coefficient are... 

The secondary flows from natural convection can become larger than the primary flow, so it seems likely that the secondary flows might become turbulent or nonsteady. Shown in Tables 1 and 2 are the dimensionless groups at the inlet and outlet, based on cup-average quantities, as well as the Reynolds numbers for the primary and secondary flows (Reynolds numbers defined in terms of the respective total mass flowrate, the viscosity and the ratio of tube perimeter to tube area). 

Fluid flow and reaction engineering problems represent a rich spectrum of examples of multiple and disparate scales. In chemical kinetics such problems involve high values of Thiele modulus (diffusion-reaction problems), Damkohler and Peclet numbers (diffusion-convection-reaction problems). For fluid flow problems a large value of the Mach number, which represents the ratio of flow velocity to the speed of sound, indicates the possibility of shock waves a large value of the Reynolds number causes boundary layers to be formed near solid walls and a large value of the Prandtl number gives rise to thermal boundary layers. Evidently, the inherently disparate scales for fluid flow, heat transfer and chemical reaction are responsible for the presence of thin regions or "fronts in the solution. 

John C. Berg, Andreas Acrivos, and Michel Boudart, Evaporation Convection H. M. Tsuchiya, A. G, Fredrickson, and R. Aiis, Dynamics of Microbial Cell Populations Samuel Sideman, Direct Contact Heat Transfer between Immiscible Liquids Howard Brenner, Hydrodynamic Resistance of Particles at Small Reynolds Numbers... 

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 ... 

The Peclet number Pe = v /Dc, where Dc is the diffusion coefficient of a solute particle in the fluid, measures the ratio of convective transport to diffusive transport. The diffusion time Tp = 2/D< is the time it takes a particle with characteristic length to diffuse a distance comparable to its size. We may then write the Peclet number as Pe = xD/xs, where xv is again the Stokes time. For Pe > 1 the particle will move convectively over distances greater than its size. The Peclet number can also be written Pe = Re(v/Dc), so in MPC simulations the extent to which this number can be tuned depends on the Reynolds number and the ratio of the kinematic viscosity and the particle diffusion coefficient. 

Below a Reynolds number of about 2000 the flow in pipes will be laminar. Providing the natural convection effects are small, which will normally be so in forced convection, the following equation can be used to estimate the film heat-transfer coefficient ... 

The suppression factor fs is obtained from Figure 12.57. It is a function of the liquid Reynolds number ReL and the forced-convection correction factor fc. 

In convective diffusion to a rotating disk, the characteristic velocity V0 is given by the product of the disk radius r, as a characteristic dimension of the system, and the radial velocity co, so that the Reynolds number is given by the equation... 

---