Convection transitional flow

ESDU 93018 (2001) Forced convection heat transfer in straight tubes. Part 2 laminar and transitional flow. ESDU 98003-98007 (1998) Design and performance evaluation of heat exchangers the effectiveness-NTU method. 

Recirculation of fluid by convection ( multipass flow) is another possible regime (cf. Etheridge etal, 1983). While convection is widely recognized in shallow hydrothermal systems, the conventional wisdom is that permeability is too small in the deep crust to allow the downward penetration of fluid necessary for convection (cf. Walther and Orville, 1982 England and Thompson, 1984 Hanson, 1997 Manning and Ingebritsen, 1999). Nonetheless, study of active mountain belts in New Zealand and Pakistan has shown that shallow fluids can penetrate to at least mid-cmstal levels near the brittle-ductile transition (cf. Koons and Craw, 1991 Templeton etal, 1998 Poage et al, 2000). For example, fluid... 

M. S. Bhatti andR. K. Shah. "Thrbulent and Transition Flow Convective Heat Transfer in Ducts. Tn Handbook of Single-Phase Convective Heat Transfer, ed. S, Kaka9, R. K. Shah, and W. Aung, New York Wiley Interscience, 1987. 

Convective heat transfer analysis for a gaseous flow in microchannels was performed in [24]. A Knudsen range of 0.06-1.1 was considered. In this range, flow is called transition flow. Since the eontinuum assumption is not valid, DSMC technique was applied. Reference [24] considered the uniform heat flux boundary condition for two-dimensional flow, where the channel height varied between 0.03125 and 1 micrometer. It was concluded that the slip flow approximation is valid for Knudsen numbers less than 0.1. The results showed a reduction in Nusselt number with increasing rarefaetion in both slip and transition regimes. 

ESDU 93018 (2001) Forced convection heat transfer in straight tubes. Part 2 laminar and transitional flow. 

The ability to capture the hot spot within the bed by flow reversal rehes on the large difference in the characteristic time for convective mass (flow) and conductive energy transport. Flow switching can be easily accomplished, as this occurs on a time-scale that is much shorter than the characteristic time of transit of a creeping hot spot to traverse the length of the reactor. 

W. W. Humphreys and J. R. Welty, Natural Convection With Mercury in a Uniformly Heated Vertical Channel During Unstable Laminar and Transitional Flow, AIChE Journal (21/2) 268-274, 1975. 

Steam-liquid flow. Two-phase flow maps and heat transfer prediction methods which exist for vaporization in macro-channels and are inapplicable in micro-channels. Due to the predominance of surface tension over the gravity forces, the orientation of micro-channel has a negligible influence on the flow pattern. The models of convection boiling should correlate the frequencies, length and velocities of the bubbles and the coalescence processes, which control the flow pattern transitions, with the heat flux and the mass flux. The vapor bubble size distribution must be taken into account. 

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. 

Hint Use a version of Equation (11.49) but correct for the spherical geometry and replace the convective flux with a diffusive flux. Example 11.14 assumed piston flow when treating the moving-front phenomenon in an ion-exchange column. Expand the solution to include an axial dispersion term. How should breakthrough be defined in this case The transition from Equation (11.50) to Equation (11.51) seems to require the step that dVsIAi =d Vs/Ai] = dzs- This is not correct in general. Is the validity of Equation (11.51) hmited to situations where Ai is actually constant ... 

Diffusion in a convective flow is called convective diffusion. The layer within which diffnsional transport is effective (the diffnsion iayer) does not coincide with the hydrodynamic bonndary layer. It is an important theoretical problem to calcnlate the diffnsion-layer thickness 5. Since the transition from convection to diffnsion is gradnal, the concept of diffusion-layer thickness is somewhat vagne. In practice, this thickness is defined so that Acjl8 = (dCj/ff) Q. This calcniated distance 5 (or the valne of k ) can then be used to And the relation between cnrrent density and concentration difference. 

Some transition times calculated for this type of free convection, following a concentration step in 0.05 M CuS04 solution with excess H2S04, are given in Table IV. It can be seen that the transition times (to a flux 1°() in excess of the steady-state flux) vary appreciably along the plate also in forced convection (which is discussed below) the transition times are generally shorter, except at very low flow rates. 

Table IV includes theoretical transition times (C2, R14, SI7c) in laminar flow between parallel plates, following a concentration step at the wall (Leveque mass transfer). Clearly, in laminar flow (Re 100 or lower), transition times are comparable to those in laminar free convection. Here, however, the dependence on concentration (through the diffusivity) is weak. The dimensionless time variable in unsteady-state mass transfer of the Leveque type is...

Schutz s correlation for free convection at a sphere, Eq. (25) in Table VII, takes pure diffusion into account by means of the constant term Sh = 2. According to his measurements using local spot electrodes, the flow here is not laminar but already in transition to turbulence. 

The interaction of forced and natural convective flow between cathodes and anodes may produce unusual circulation patterns whose description via deterministic flow equations may prove to be rather unwieldy, if possible at all. The Markovian approach would approximate the true flow pattern by subdividing the flow volume into several zones, and characterize flow in terms of transition probabilities from one zone to others. Under steady operating conditions, they are independent of stage n, and the evolution pattern is determined by the initial probability distribution. In a similar fashion, the travel of solid pieces of impurity in the cell can be monitored, provided that the size, shape and density of the solids allow the pieces to be swept freely by electrolyte flow. 

---