Convection, described

A hot-water heating system forces water into pipes, or arrangements of pipes called registers that warm from contact with warm water. Air in the room warms from contact with the pipes. Usually, the pipes are on the floor of a room so that warmer, less dense air around the pipes rises somewhat like a helium-filled balloon rises in air. The warmer air cools as it mixes with cooler air near the ceiling and falls as its density increases. This process is called convection and the moving air is referred to as convection current. The process of convection described here is pipe-to-air and usually does a better job of heating evenly than in an air-to-air convection system—the circulation of air by fans as in a forced-air heating system. 

Convection describes the movement of groups of particles from one place to another within the mixer volume because of the direct action of an impeller or a moving device within the mixer body. As in convection within fluids, this is likely to be a more significant effect than diffusion but diffusional effects will still be present. 

Convection involves the transfer of heat by means of a fluid, including gases and liquids. Typically, convection describes heat transfer from a solid surface to an adjacent fluid, but it can also describe the bulk movement of fluid and the associate transport of heat energy, as in the case of a hot, rising gas. Recall that there are two general types of convection forced convection and natural (free) convection. In the former, fluid is forced past an object by mechanical means, such as a pump or a fan, whereas the latter describes the free motion of fluid elements due primarily to density differences. It is common for both types of convection to occur simultaneously in what is termed mixed convection. In such instance, a modified form of Fourier s Law is applied, called Newton s Law of Cooling, where the thermal conductivity is replaced with what is called the heat transfer coefficient, h ... 

In this chapter we shall consider steady conduction in one-dimensional geometry. Although the main objective is conduction, convection described in terms of an assumed heat transfer coefficient will be included whenever it is pertinent. This may be the case when the heat transfer is desired in terms of ambient temperatures (Section 2.2) or when heat loss normal to the direction of conduction is essential, as in the case of extended surfaces (Section 2.4). Here we continue to employ the five-step formulation but somewhat less explicitly than the way we used it in Chapter 1. Each reader should tailor the degree of elaboration of this formulation to his or her particular needs. 

In this chapter, the circuit models which have been proposed to represent ac polarization impedance are quite simple. They do, however, give a good fit to experimentally determined data. Esthetically, the simple models are appealing and relatively easy to relate to the physical processes of charge migration, diffusion, and convection described in Chapter 3. More sophisticated models could be proposed, but they would not prove any more useful experimentally than the simple circuits. 

The transfer of surface active molecules generates a special interfacial convection described for example by Davies [ 18]. Due to the local convective currents a local increase of surface molecules near the interface produces at some point an increase of surface pressure Att. The monolayer tends to spread further over the surface dragging some adjacent liquid with it. If conditions of viscosity, diffusivity, concentration are fullfilled, according to Sternling and Scriven for example, an eddy of fresh solution would occur to this point amplifying the movement which appears as an "expansion"(figure 3a). Then due to the momentum transfer. 

However, if one is primarily interested on the kinetics of charge transfer it is useful if mass transfer rate can be increased so as to not represent a limiting factor of electrode kinetics (Figure 3). This is possible using methods of forced convection described further on. 

Fig. 18.3-3. Transport across a semipermeable membrane. Here, the solvent flux can be reduced by osmotic pressure and the solute flux can be altered by convection. Describing this transport process requires at least three independent coefficients.

The flow processes are described as Marangoni convections and up to now they were determined by several research centers through numeric simulation works [9]. Due to the... 

The solution flow is nomially maintained under laminar conditions and the velocity profile across the chaimel is therefore parabolic with a maximum velocity occurring at the chaimel centre. Thanks to the well defined hydrodynamic flow regime and to the accurately detemiinable dimensions of the cell, the system lends itself well to theoretical modelling. The convective-diffiision equation for mass transport within the rectangular duct may be described by... 

These should be con describe the same reaction, s but at the limit of fine Physically the interesting f appearance of the pressure p ablej with the consequence describe the system at the at the limit of fine pores, true that the pressure wit ni sense that percentage variat of the pressure variations i permeability, so convective permeability and pressure gr the origin of the two terms... 

The Maxwell class of viscoelastic constitutive equations are described by a simpler form of Equation (1.22) in which A = 0. For example, the upper-convected Maxwell model (UCM) is expressed as... 

The first order derivative in Equation (2.80) corresponds to the convection in a field problem and the examples shown in Figure 2.26 illustraTes the ina bility of the standard Galerkin method to produce meaningful results for convection-dominated equations. As described in the previous section to resolve this difficulty, in the solution of hyperbolic (convection-dominated) equations, upwind-ing or Petrov-Galerkin methods are employed. To demonstrate the application of upwinding we consider the case where only the weight function applied to the first-order derivative in the weak variational statement of the problem, represented by Equation (2.82), is modified. 

The integrals in Equation (3.32) are found using a quadrature over the element domain The viscoelastic constitutive equations used in the described model are hyperbolic equations and to obtain numerically stable solutions the convection terms in Equation (3.32) are weighted using streamline upwinding as (inconsistent upwinding)... 

The most widely used and best known resistance furnaces are iadirect-heat resistance furnaces or electric resistor furnaces. They are categorized by a combination of four factors batch or continuous protective atmosphere or air atmosphere method of heat transfer and operating temperature. The primary method of heat transfer ia an electric furnace is usually a function of the operating temperature range. The three methods of heat transfer are radiation, convection, and conduction. Radiation and convection apply to all of the furnaces described. Conductive heat transfer is limited to special types of furnaces. 

From 760 to 960°C, circulating fans, normally without baffles, are used to improve temperature uniformity and overall heat transfer by adding some convection heat transfer. They create a directional movement of the air or atmosphere but not the positive flow past the heating elements to the work as in a convection furnace. Heating elements ate commonly chrome—nickel alloys in the forms described previously. Sheathed elements are limited to the very low end of the temperature range, whereas at the upper end silicon carbide resistors may be used. In this temperature range the selection of heating element materials, based on the combination of temperature and atmosphere, becomes critical (1). 

The mathematical formulation of forced convection heat transfer from fuel rods is well described in the Hterature. Notable are the Dittus-Boelter correlation (26,31) for pressurized water reactors (PWRs) and gases, and the Jens-Lottes correlation (32) for boiling water reactors (BWRs) in nucleate boiling. 

Analysis of a method of maximizing the usefiilness of smaH pilot units in achieving similitude is described in Reference 67. The pilot unit should be designed to produce fully developed large bubbles or slugs as rapidly as possible above the inlet. UsuaHy, the basic reaction conditions of feed composition, temperature, pressure, and catalyst activity are kept constant. Constant catalyst activity usuaHy requires use of the same particle size distribution and therefore constant minimum fluidization velocity which is usuaHy much less than the superficial gas velocity. Mass transport from the bubble by diffusion may be less than by convective exchange between the bubble and the surrounding emulsion phase. 

Equation 7 shows that as AP — oo, P — 1. The principal advantage of the solution—diffusion (SD) model is that only two parameters are needed to characterize the membrane system. As a result, this model has been widely appHed to both inorganic salt and organic solute systems. However, it has been indicated (26) that the SD model is limited to membranes having low water content. Also, for many RO membranes and solutes, particularly organics, the SD model does not adequately describe water or solute flux (27). Possible causes for these deviations include imperfections in the membrane barrier layer, pore flow (convection effects), and solute—solvent—membrane interactions. 

Convective Heat Transfer Eqnipment nsiug the trne convective mechanism when the heated particles are mixed with (and remain with) the cold particles is nsed so iufreqneutly that performance and sizing eqnatious are not available. Snch a device is the pebble heater as described by Norton (Chem. Metall. E/ig., Jiily 1946). For operation data, see Sec. 9. 

A discussion of retention time in rotary Idlns is given in Brit. Chem. Eng., 27-29 (Januaiy 1966). Rotary-ldln heat control is discussed in detail by Bauer [Chem. Eng., 193-200 (May 1954)] and Zubrzycki [Chem. Can., 33-37 (Februaiy 1957)]. Reduction of iron ore in rotaiy Idlns is described by Stewart [Min. Congr J., 34—38 (December 1958)]. The use of balls to improve solids flow is discussed in [Chem. Eng., 120-222 (March 1956)]. Brisbane examined problems of shell deformation [ Min. Eng., 210-212 (Februaiy 1956)]. Instrumentation is discussed by Dixon [Ind. Eng. Chem. Process Des. Dev., 1436-1441 (July 1954)], and a mathematical simulation of a rotaiy Idln was developed by Sass [Ind. Eng. Chem. Process Des. Dev., 532-535 (October 1967)]. This last paper employed the empirical convection heat-transfer coefficient given previously, and its use is discussed in later correspondence [ibid., 318-319 (April 1968)]. 

Schematic elevation sec tions of a vertical cylindrical, cross-tube convection heater a horizontal-tube cabin heater and a vertical cylindrical, helical-coil heater are shown in Fig. 27-51. The seven basic designs and some variations of them are pictured and described in the reference cited above and by R. K. Johnson Combustion 50(5) 10-16, November 1978).

The convective wave cycle was described in 5.2.4 but its heat transfer properties not quantified. Critoph and Thorpe [22] and Thorpe [23] have measured the convective heat transfer coefficient between flowing gas and the grains within the bed. Preliminary results imply that the pressure drop through the bed can be expressed by a modified Ergun equation ... 

Convection occurs in a moving fluid, generally from the fluid to a solid surface or vice versa. Although heat transfer between single particles is by conduction, it is the energy transfer with the matter that governs the heat transfer. The basic laws of heat and mass transfer have to be considered in order to describe convection mathematically. 

Equations (12.40) to (12.45) describe the velocities u, v, w, the temperature distribution T, the concentration distribution c (mass of gas per unit ma.ss of mixture, particles per volume, droplet number density, etc.) and pressure distribution p. These variables can also be used for the calculation of air volume flow, convective air movement, and contaminant transport. 

The methods of heating TLC/HPTLC plates described above depend on thermal conduction, convection or radiation. Microwave heating involves a special form... 

Determine the tube-side film coefficient for convection or condensation as required, by methods previously described. 

II is via penetration of hot combustion products into the existing pores of the expl. Propagation in Region III is via convective flow between the charge surface and its confinement. This regime is claimed to be affected by confinement expansion (due to pressure), and by fragmentation of the peripheral portions of the expl column. The phenomena in Regions IV and V have already been described in Section VIII under Initiation by Impact Friction... 

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