Convective systems

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. 

As with all convective systems, warm air heating installations produce large temperature gradients in the spaces they serve. This results in the inefficient use of heat and high heat losses from roofs and upper wall areas. To improve the energy efficiency of warm air systems, pendant-type punkah fans or similar devices may be installed at roof level in the heated space. During the operational hours of the heating system, these fans work either continuously or under the control of a roof-level thermostat and return the stratified warm air down to occupied levels. 

G3. Grace, T. M., The mechanism of burnout in initially subcooled forced convection systems, TID-19845 (1963). 

One of the simplest models for convective mass transfer is the stirred tank model, also called the continuously stirred tank reactor (CSTR) or the mixing tank. The model is shown schematically in Figure 2. As shown in the figure, a fluid stream enters a filled vessel that is stirred with an impeller, then exits the vessel through an outlet port. The stirred tank represents an idealization of mixing behavior in convective systems, in which incoming fluid streams are instantly and completely mixed with the system contents. To illustrate this, consider the case in which the inlet stream contains a water-miscible blue dye and the tank is initially filled with pure water. At time zero, the inlet valve is opened, allowing the dye to enter the... 

Table 7.1 summarizes the various equations used to describe the convective systems discussed in this present chapter, relating the limiting currents and parameters such as flow rate. 

The principal cause of error in convective systems is non-laminar flow of solution over the face of an electrode. Turbulence and the attendant eddy currents can... 

Convection-based systems fall into two fundamental classes, namely those using a moving electrode in a fixed bulk solution (such as the rotated disc electrode (RDE)) and fixed electrodes with a moving solution (such as flow cells and channel electrodes, and the wall-jet electrode). These convective systems can only be usefully employed if the movement of the analyte solution is reproducible over the face of the electrode. In practice, we define reproducible by ensuring that the flow is laminar. Turbulent flow leads to irreproducible conditions such as the production of eddy currents and vortices and should be avoided whenever possible. 

Provided that the flow is laminar, and the counter electrode is larger than the working electrode, convective systems yield very reproducible currents. The limiting current at a rotated disc electrode (RDE) is directly proportional to the concentration of analyte, according to the Levich equation (equation (7.1)), where the latter also describes the proportionality between the limiting current and the square root of the angular frequency at which the RDE rotates. 

As air is transported rapidly upward, for example in a convective system, cooling occurs (see Chapter 2), leading to the condensation of water as ice crystals. Because of this removal of water as moist tropospheric air rises, air in the stratosphere is very dry, of the order of a few ppm. Some water is also produced directly in the stratosphere from the oxidation of CH4 and H2. The so-called extratropical pump then moves the air poleward and downward at higher latitudes (Path I), warming the air as it descends. 

Direct uses of geothermal heat are very varied. They are largely based on exploitation of low-enthalpy convection systems. Uses include balneotherapy, space heating, and many agricultural and industrial uses. The potential use of geothermal resources is dictated by fluid temperature as described by the Ltndal diagram (Fig. 1). 

The study of rotating disk electrode behavior provides a unique opportunity to develop a model that predicts the effect of diffusion and convection on the current. This is one of the few convective systems that have simple hydrodynamic equations that may be combined with the diffusion model developed herein to produce meaningful results. The effect of diffusion is modeled exactly as it has been done previously. The effect of convection is treated by integrating an approximate velocity equation to determine the extent of convective flow during a given At interval. Matter, then, is simply transferred from volume element to volume element in accord with this result to simulate convection. The whole process repeated results in a steady-state concentration profile and a steady-state representation of the current (the Levich equation). 

The influential parameters in a thermal convection system may be represented by the characteristic length l, velocity U, density p, viscosity fi, specific heat at constant pressure cp, and thermal conductivity K. Thus, we have... 

For a general forced convection system, prove that Nu = /(Re, Pr). 

Note also that, if there are homogeneous chemical reaction terms on the right-hand side of (9.31), they can be accommodated without problems they will lead to some additional terms operated on by What must not be present are convection terms, since these are spatial first derivatives, making the Numerov method, in this form, impossible to use. However, Bieniasz has devised an improved version, called the extended Numerov method [110], which indeed can handle first spatial derivatives and thus convective systems. 

Other convective systems have been used in electroanalytical chemistry. The oldest one is the dropping mercury electrode [74,257]. Convection here arises by virtue of the expansion of the growing mercury drop, and the transport equation is pleasantly simple and unidimensional for the simplified case,... 

Radiation heat-transfer phenomena can be exceedingly complex, and the calculations are seldom as simple as implied by Eq. (1-11). For now, we wish to emphasize the difference in physical mechanism between radiation heat-transfer and conduction-convection systems. In Chap. 8 we examine radiation in detail. 

We shall defer part of our analysis of conduction-convection systems to Chap. 10 on heat exchangers. For the present we wish to examine some simple extended-surface problems. Consider the one-dimensional fin exposed to a surrounding fluid at a temperature T as shown in Fig. 2-9. The temperature of the base of the fin is T0. We approach the problem by making an energy balance on an element of the fin of thickness dx as shown in the figure. Thus... 

Consider the vertical flat plate shown in Fig. 7-1. When the plate is heated, a free-convection boundary layer is formed, as shown. The velocity profile in this boundary layer is quite unlike the velocity profile in a forced-convection boundary layer. At the wall the velocity is zero because of the no-slip condition it increases to some maximum value and then decreases to zero at the edge of the boundary layer since the free-stream conditions are at rest in the free-convection system. The initial boundary-layer development is laminar but at... 

This is the equation of motion for the free-convection boundary layer. Notice that the solution for the velocity profile demands a knowledge of the temperature distribution. The energy equation for the free-convection system is the same as that for a forced-convection system at low velocity ... 

For the free-convection system, the integral momentum equation becomes... 

The integral form of the energy equation for the free-convection system is... 

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