Turbulant conduction

Looking at a little slice of the process fluid as our system, we can derive each of the terms of Eq. (2.18). Potential-energy and kinetic-energy terms are assumed negligible, and there is no work term. The simplified forms of the internal ener and enthalpy are assumed. Diffusive flow is assumed negligible compared to bulk flow. We will include the possibility for conduction of heat axially along the reactor due to molecular or turbulent conduction. 

By analogy with macroscopic electrodynamics, we consider the currents in the turbulent fluid as molecular ones, the averaged actual field h we denote by B, and we introduce 77 here curl 77 = 0 in the region where there are only unordered, turbulence-dependent currents. From (13) we obtain B = (r/ )77 = 77/Rem. Thus, macroscopically, the turbulent conducting fluid acts like a diamagnet1 with very small permeability n 1/Rem. 

However, to solve the heat and mass transfer equations an additional modeling problem has to be overcome. While there are sufficient measurements of the turbulent velocity field available to validate the different i>t modeling concepts proposed in the literature, experimental difficulties have prevented the development of any direct modeling concepts for determining the turbulent conductivity at, and the turbulent diffusivity Dt parameters. Nevertheless, alternative semi-empirical modeling approaches emerged based on the hypothesis that it might be possible to calculate the turbulent conductivity and diffusivity coefficients from the turbulent viscosity provided that sufficient parameterizations were derived for Prj and Scj. 

A local turbulent conduction layer thickness on cold plate m, ft... 

The effective conductivity Aeff is the sum of the molecular and the turbulent conductivity ... 

Figure (10) neatly shows up the importance of the solid for providing a direct pathway for radial heat transfer. Radial mixing experiments in beds of uniform spheres would indicate a turbulent conduction limit to e of MO. Yet, measured Peclet numbers are consistently lower than this, and clearly depend upon the thermal conductivity of the packing. However, the effect of pellet conductivity appears to be logarithmic, rather than linear. 

The turbulent conductivity k d is given in terms of the Reynolds, Prandtl and Peclet numbers by... 

Also shown in Fig. (7), for comparison, is the contribution to kf. due to turbulent conduction (k d) apparent that heat... 

G superficial mass flow velocity kg/m hr. zero-th order Bessel function, first kind, first order Bessel function, first kind, turbulent conductivity (based on unit solids area) w/m °C... 

If oil and water are mixed as an emulsion, dehydration becomes much more difficult. Emulsions can form as oil-in-water or water-in-oil if mixed production streams are subjected to severe turbulence, as might occur in front of perforations in the borehole. Emulsions can be encouraged to break (or destabilise) using chemicals, heat or just gentle agitation. Chemical destabilisation is the most common method and laboratory tests would normally be conducted to determine the most suitable combination of chemicals. 

If these assumptions are satisfied then the ideas developed earlier about the mean free path can be used to provide qualitative but useful estimates of the transport properties of a dilute gas. While many varied and complicated processes can take place in fluid systems, such as turbulent flow, pattern fonnation, and so on, the principles on which these flows are analysed are remarkably simple. The description of both simple and complicated flows m fluids is based on five hydrodynamic equations, die Navier-Stokes equations. These equations, in trim, are based upon the mechanical laws of conservation of particles, momentum and energy in a fluid, together with a set of phenomenological equations, such as Fourier s law of themial conduction and Newton s law of fluid friction. When these phenomenological laws are used in combination with the conservation equations, one obtains the Navier-Stokes equations. Our goal here is to derive the phenomenological laws from elementary mean free path considerations, and to obtain estimates of the associated transport coefficients. Flere we will consider themial conduction and viscous flow as examples. 

Convection Heat Transfer. Convective heat transfer occurs when heat is transferred from a soHd surface to a moving fluid owing to the temperature difference between the soHd and fluid. Convective heat transfer depends on several factors, such as temperature difference between soHd and fluid, fluid velocity, fluid thermal conductivity, turbulence level of the moving fluid, surface roughness of the soHd surface, etc. Owing to the complex nature of convective heat transfer, experimental tests are often needed to determine the convective heat-transfer performance of a given system. Such experimental data are often presented in the form of dimensionless correlations. 

Nonintrusive Instrumentation. Essential to quantitatively enlarging fundamental descriptions of flow patterns and flow regimes are localized nonintmsive measurements. Early investigators used time-averaged pressure traverses for holdups, and pilot tubes for velocity measurements. In the 1990s investigators use laser-Doppler and hot film anemometers, conductivity probes, and optical fibers to capture time-averaged turbulent fluctuations (39). 

Early models used a value for that remained constant throughout the day. However, measurements show that the deposition velocity increases during the day as surface heating increases atmospheric turbulence and hence diffusion, and plant stomatal activity increases (50—52). More recent models take this variation of into account. In one approach, the first step is to estimate the upper limit for in terms of the transport processes alone. This value is then modified to account for surface interaction, because the earth s surface is not a perfect sink for all pollutants. This method has led to what is referred to as the resistance model (52,53) that represents as the analogue of an electrical conductance... 

For turbulent flow of a fluid past a solid, it has long been known that, in the immediate neighborhood of the surface, there exists a relatively quiet zone of fluid, commonly called the Him. As one approaches the wall from the body of the flowing fluid, the flow tends to become less turbulent and develops into laminar flow immediately adjacent to the wall. The film consists of that portion of the flow which is essentially in laminar motion (the laminar sublayer) and through which heat is transferred by molecular conduction. The resistance of the laminar layer to heat flow will vaiy according to its thickness and can range from 95 percent of the total resistance for some fluids to about I percent for other fluids (liquid metals). The turbulent core and the buffer layer between the laminar sublayer and turbulent core each offer a resistance to beat transfer which is a function of the turbulence and the thermal properties of the flowing fluid. The relative temperature difference across each of the layers is dependent upon their resistance to heat flow. 

At high velocities where turbulence dominates, the main body of flowing fluid is well mixed in the direction normal to the flow, minor differences in temperature and concentration can be neglected, and the film concept can be applied. This describes the flow as if all gradients for temperature and concentration are in a narrow film along the interface with the solid (Nernst 1904), and inside the film conduction and diffusion are the transfer mechanisms. This film concept greatly simplifies the engineering calculation of heat and mass transfer. 

Vulis, L. A. 1960. Regarding free turbulent jets computation applying the heat conductivity method. In Proceedings of Acad. Set. Kaz. SSR, Ser. Energy, vol. 2, no. 18. 

Figure 10-50C. Tube-side (inside tubes) liquid film heat transfer coefficient for Dowtherm . A fluid inside pipes/tubes, turbulent flow only. Note h= average film coefficient, Btu/hr-ft -°F d = inside tube diameter, in. G = mass velocity, Ib/sec/ft v = fluid velocity, ft/sec k = thermal conductivity, Btu/hr (ft )(°F/ft) n, = viscosity, lb/(hr)(ft) Cp = specific heat, Btu/(lb)(°F). (Used by permission Engineering Manual for Dowtherm Heat Transfer Fluids, 1991. The Dow Chemical Co.)...

Ya.B. ZeFdovich, FizGoreniyaVzryva 7 (4), 463-76 (1971) CA 77, 64194 (1972) The influence of turbulence and nonturbulence is examined relative to a proplnt burning in a gas flow. Equations indicate exptl methods for determining the magnitudes of the thermal conductivity and viscosity under turbulent flow, and permit a study of thermal flow distribution and temps in a gas wherein an exothermic chem reaction occurs. Equations for non turbulent conditions can be used to calculate the distance from the surface of the proplnt to the zone of intense chem reaction and establish the relation of bulk burning rate to the vol reaction rate. 

Essentially, except for once-through boilers, steam generation primarily involves two-phase nucleate boiling and convective boiling mechanisms (see Section 1.1). Any deposition at the heat transfer surfaces may disturb the thermal gradient resulting from the initial conduction of heat from the metal surface to the adjacent layer of slower and more laminar flow, inner-wall water and on to the higher velocity and more turbulent flow bulk water. 

In most cases where convective heat transfer is taking place from a surface to a fluid, the circulating currents die out in the immediate vicinity of the surface and a film of fluid, free of turbulence, covers the surface. In this film, heat transfer is by thermal conduction and, as the thermal conductivity of most fluids is low, the main resistance to transfer lies there, Thus an increase in the velocity of the fluid over the surface gives rise to improved heat transfer mainly because the thickness of the film is reduced. As a guide, the film coefficient increases as (fluid velocity)", where 0.6 < n < 0.8, depending upon the geometry. 

Although heat transfer to a fluid in streamline flow takes place solely by conduction, it is convenient to consider it here so that the results may be compared with those for turbulent flow. 

If two vessels each containing completely mixed gas, one at temperature T, and the other at a temperature T2, are connected by a lagged non-conducting pipe in which there are no turbulent eddies (such as a capillary tube), then under steady state conditions, the rate of transfer of A by thermal diffusion and molecular diffusion must be equal and opposite, or. 

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