Convection, thermal

One major goal of this section is to understand what drives flow in thermal convection at steady state it may not be the buoyancy as one may believe. The benefit of buoyancy is that it will (if it is large enough) cause instabilities and these instabilities will cause a horizontal density 

General theory of phase equilibria and Irreversible phenomena 89 

Now let us examine the Bp/Bz) term. In general, for a single-component fluid, p p T, P), and therefore 

The effect of pressure in density variation does not contribute to thermal convection (see Problem 2.17), and therefore we write 

The temperature dependence of the density can be approximated using the Taylor series, 

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Although it is hard to draw a sharp distinction, emulsions and foams are somewhat different from systems normally referred to as colloidal. Thus, whereas ordinary cream is an oil-in-water emulsion, the very fine aqueous suspension of oil droplets that results from the condensation of oily steam is essentially colloidal and is called an oil hydrosol. In this case the oil occupies only a small fraction of the volume of the system, and the particles of oil are small enough that their natural sedimentation rate is so slow that even small thermal convection currents suffice to keep them suspended for a cream, on the other hand, as also is the case for foams, the inner phase constitutes a sizable fraction of the total volume, and the system consists of a network of interfaces that are prevented from collapsing or coalescing by virtue of adsorbed films or electrical repulsions. 

There are three distinct support systems for double seals. They are often referred to as barrier tanks . The term barrier tank was initially applied to the thermal convection tank, although the term today refers to any of the three support systems. Each support system has different attributes. 

Conducts a re-circulated flow by thermal convection. When enough heat is generated inside the mechanical seal, it expands initiating a flow into the tank where it cools and contracts and is brought again into the seal. 

Tests in thermal convection loops with a maximum temperature of 800 C showed that nickel and nickel-rich alloys with chromium and other additions were relatively very susceptible to the mass-transfer type of attack by lead. On the other hand nickel-rich alloys with molybdenum were among the better of the alloys tested (Table 7.35). 

Table 7.36 Results in thermal convection loop tests of material in contact with molten lead...

Loop Tests Loop test installations vary widely in size and complexity, but they may be divided into two major categories (c) thermal-convection loops and (b) forced-convection loops. In both types, the liquid medium flows through a continuous loop or harp mounted vertically, one leg being heated whilst the other is cooled to maintain a constant temperature across the system. In the former type, flow is induced by thermal convection, and the flow rate is dependent on the relative heights of the heated and cooled sections, on the temperature gradient and on the physical properties of the liquid. The principle of the thermal convective loop is illustrated in Fig. 19.26. This method was used by De Van and Sessions to study mass transfer of niobium-based alloys in flowing lithium, and by De Van and Jansen to determine the transport rates of nitrogen and carbon between vanadium alloys and stainless steels in liquid sodium. 

The thermal-convection loops are limited to flow velocities up to about 6 cm s . Where higher velocities are required, the liquid must be pumped, either mechanically or electromagnetically the latter is usually preferred as it avoids the problem of leakage at the pump seal. Basically, these forced-convection systemsconsist of (c) a hot leg, where the liquid metal is... 

The linear instability theory of the behavior of a system near the bifurcation point can be successfully applied to many self-organization problems, such as thermal convection in hydrodynamics4 and crystal growth in solution.5 In these theories, various initial fluctuations play important roles. Occasionally the fluctuations arise from the thermal motion of atoms or molecules. If a system reaches an unstable mode over... 

Axial heat conduction in the polymer is neglected due to its low thermal conductivity and its relatively small magnitude, compared with axial thermal convection. 

Benard convection cells [27, 28] a liquid with an inverse temperature gradient (hot below and cool on top) may exhibit thermal convection. Less dense parts of the liquid well upward whereas denser parts show down-welling. The convection cells may arrange in hexagonal order in which the center of each cell wells downwards and the rim wells upwards. The cells stem from the concerted movement of many molecules and cease when the temperature gradient is below a threshold at which the thermal equilibrium canbe reached solely bythermalconductionandnotconvection. 

Tests at the boiling point should be conducted with minimum possible heat input, ana boiling chips should be used to avoid excessive turbulence and bubble impingement. In tests conducted below the boiling point, thermal convection generally is the only source of liquid velocity. In test solutions of high viscosities, supplemental controlled stirring with a maraetic stirrer is recommended. 

Resolution depends upon differences in mobilities of the species. Background electrolyte of low ionic strength is advantageous, not only to increase electrophoretic (solute) mobilities, but also to achieve low electrical conductivity and thereby to reduce the thermal-convection current for any given field [Finn, in Schoen (ed.), New Chemical Engineering Separation Teehniques, Interscience, New York, 1962]. 

An entirely different type of transport is formed by thermal convection and conduction. Flow induced by thermal convection can be examined by the phaseencoding techniques described above [8, 44, 45] or by time-of-flight methods [28, 45]. The latter provide less quantitative but more illustrative representations of thermal convection rolls. The origin of any heat transport, namely temperature gradients and spatial temperature distributions, can also be mapped with the aid of NMR techniques. Of course, there is no direct encoding method such as those for flow parameters. However, there are a number of other parameters, for example, relaxation times, which strongly depend on the temperature so that these parameters can be calibrated correspondingly. Examples are described in Refs. [8, 46, 47], for instance. 

Figure 2.9.9(a) shows a schematic representation of a thermal convection cell in Rayleigh-Benard configuration [8]. With a downward temperature gradient one expects convection rolls that are more or less distorted by the tortuosity of the fluid filled pore space. In the absence of any flow obstacles one expects symmetrical convection rolls, such as illustrated by the numerical simulation in Figure 2.9.9(b). 

Fig. 2.9.10 Maps of the temperature and of the experimental data. The right-hand column convection flow velocity in a convection cell in refers to numerical simulations and is marked Rayleigh-Benard configuration (compare with with an index 2. The plots in the first row, (al) Figure 2.9.9). The medium consisted of a and (a2), are temperature maps. All other random-site percolation object of porosity maps refer to flow velocities induced by p = 0.7 filled with ethylene glycol (temperature thermal convection velocity components vx maps) or silicon oil (velocity maps). The left- (bl) and (b2) and vy (cl) and (c2), and the hand column marked with an index 1 represents velocity magnitude (dl) and (d2).

Bolton EW, Lasaga AC, Rye DM (1996) A model for the kinetic control of quartz dissolution and precipitation in porous media flow with spatially variable permeability Eormulation and examples of thermal convection. J Geophys Res 101 22,157-22,187 Bolton EW, Lasaga AC, Rye DM (1997) Dissolution and precipitation via forced-flux injection in the porous medium with spatially variable permeability Kinetic control in two dimensions. J Geophys Res 102 12,159-12,172... 

In the conditions described by the curve ( dew point temperature ), dew or clouds are formed, i.e. the water vapor condenses. If the conditions shown in the part above the curve are achieved, the condensed water vapor falls in the form of precipitation. In the conditions below the curve, water vapor enrichment or a cooling-off may occur without causing any formation of dew or precipitation. Since the air temperature is substantially determined by relief and altitude, these factors also have an impact on the maximum possible water vapor content in the air. In principle, precipitation is formed when air masses cool down, the consequences of which can be either dynamic (orographical and frontal induced precipitation) or thermal (convective induced precipitation) (Fig. 2, [6]). 

Other factors do intervene. Significant solar heating of the soil surface, so that the soil becomes warmer than the air, causes vertical thermal convection currents to develop within the boundary layers. This introduces turbulence or instability that acts to move the chemical signature up into the free air. When the molecules are moved into the free flow of the air, the effect is to reduce the concentration by dilution. Conversely, when the soil surface is cooler than the air, thermal convection is inhibited, with the result that the molecules are effectively trapped in the boundary layer. This effect is strengthened by the cooling of the air adjacent to the surface, which increases its viscosity. Higher viscosity lowers the Reynold s number, thus decreasing boundary layer thickness. 

Turbulence also effects plume homogeneity. Turbulence interacts with the plume on different scales. It may be induced by the plume s flowing past a surface, by thermal convection cells, or by cross currents in the water. When the scale is large relative to the diameter of the plume, the effect is somewhat like twisting or rolling a ribbon. When the scale is comparable to the diameter of the plume, it directly affects the cross-sectional homogeneity of the plume. 

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