Convective processes

In this section the correlations used to determine the heat and mass transfer rates are presented. The convection process may be either free or forced convection. In free convection fluid motion is created by buoyancy forces within the fluid. In most industrial processes, forced convection is necessary in order to achieve the most economic heat exchange. The heat transfer correlations for forced convection in external and internal flows are given in Tables 4.8 and 4.9, respectively, for different conditions and geometries. 

Similar convection processes occur in liquids, though at a slower rate according to the viscosity of the liquid. However, it cannot be assumed that convection in a liquid results in the colder component sinking and the warmer one rising. It depends on the liquid and the temperatures concerned. Water achieves its greatest density at approximately 4°C. Hence in a column of water, initially at 4°C, any part to which heat is applied will rise to the top. Alternatively, if any part is cooled below 4°C it, too, will rise to the top and the relatively warmer water will sink to the bottom. The top of a pond or water in a storage vessel always freezes first. 

Nutrient Losses Associated With Biomass Burning. Nutrient losses associated with slash fires occur through volatilization and convective losses of ash. Elements with low temperatures of volatilization (e.g. N, K, S, and some organic forms of P) will be lost in the highest quantities (Table III) (57). Conversely, Ca and Mg have volatilization temperatures higher than that recorded during most vegetation fires. Almost all fire-induced losses of these elements are due to particulate transfer by convective processes. 

The gas-phase mass flux of species k at the surface is a combination of diffusive and convective processes. 

Figure 5.4-42. Breakage of blobs by an inertial-convective process.

The characteristic time constant for mesomixing by the inertial-convective process (Corrsin, 1964) is given by... 

The mechanisms described above tell us how heat travels in systems, but we are also interested in its rate of transfer. The most common way to describe the heat transfer rate is through the use of thermal conductivity coefficients, which define how quickly heat will travel per unit length (or area for convection processes). Every material has a characteristic thermal conductivity coefficient. Metals have high thermal conductivities, while polymers generally exhibit low thermal conductivities. One interesting application of thermal conductivity is the utilization of calcium carbonate in blown film processing. Calcium carbonate is added to a polyethylene resin to increase the heat transfer rate from the melt to the air surrounding the bubble. Without the calcium carbonate, the resin cools much more slowly and production rates are decreased. 

The theory on the level of the electrode and on the electrochemical cell is sufficiently advanced [4-7]. In this connection, it is necessary to mention the works of J.Newman and R.White s group [8-12], In the majority of publications, the macroscopical approach is used. The authors take into account the transport process and material balance within the system in a proper way. The analysis of the flows in the porous matrix or in the cell takes generally into consideration the diffusion, migration and convection processes. While computing transport processes in the concentrated electrolytes the Stefan-Maxwell equations are used. To calculate electron transfer in a solid phase the Ohm s law in its differential form is used. The electrochemical transformations within the electrodes are described by the Batler-Volmer equation. The internal surface of the electrode, where electrochemical process runs, is frequently presented as a certain function of the porosity or as a certain state of the reagents transformation. To describe this function, various modeling or empirical equations are offered, and they... 

If, as is normal, the solution is not stirred, then the conditions of laminar (uniform) diffusion characterising the above description will hold only for a short time. For longer periods, thermal and concentration gradients induce random convection processes and the resultant currents show sizeable fluctuations. 

Numerical simulations of the thermal performance of the module were performed using finite element analysis. In the present model, the fluid path is represented by a series of interconnected nodes. Convection processes are modeled as transfer processes between these nodes (or volumes) and surfaces of the geometrical mesh. In this case, a series of analyses based on knowledge of the fluid properties, flow rates, and the relative sizes of the fluid passages and solid phase interconnections led to the value of 3.88 W/cm -K for the effective heat-transfer coefficient. Convective heat transfer using this coefficient was used on all of the internal free surfaces of the module. 

Transport of gas to the surface. Assuming mixing occurs by molecular diffusion rather than by mechanical or convective processes, the characteristic times for gas-phase diffusion to the surface are in the range 10 l(l-10-4 s for droplets with radii from 10 5 to 10 2 cm, respectively. 

Chemical vapor infiltration (CVl) is similar to CVD in that gaseous reactants are used to form solid products on a substrate, but it is more specialized in that the substrate is generally porous, instead of a more uniform, nominally flat surface, as in CVD. The porous substrate introduces an additional complexity with regard to transport of the reactants to the surface, which can play an important role in the reaction as illustrated earlier with CVD reactions. The reactants can be introduced into the porous substrate by either a diffusive or convective process prior to the deposition step. As infiltration proceeds, the deposit (matrix) becomes thicker, eventually (in the ideal situation) filling the pores and producing a dense composite. 

To develop the governing equations for thermochemical modeling, consider the material volume element in Figure 8.5. Performing an energy balance over this volume while neglecting convective processes yields... 

The surface distribution for mean annual h results from two properties of atmospheric flow conservation of h following the large-scale flow and the maintenance of the vertical profile of h by convective processes. These features of the climate system allow one to quantify the expected errors for assuming that mean annual h is invariant with longitude and altitude for the present-day distribution. Forest et al. (1999) examined the distribution and calculated the expected error from assuming zonal invariance to be 4.5 kJ/kg for the mean annual climate. This error translates to an altitude error of 460 m and is compared with an equivalent error of 540 m from the mean annual temperature approach. Moreover, the uncertainty of the terrestrial lapse rate, y(, increases the expected error in elevation as elevations increase, particularly when small lapse rates are assumed. 

The following processes can be described as selective therapeutic plasmapheresis. In a first step, blood is withdrawn from the patient and separated by crossflow filtration in a hollow-fiber membrane cartridge water and some plasma solutes are transferred through a semipermeable membrane under a convection process. The transmembrane pressure applied from blood to filtrate compartment ensures flow and mass transfers. Then, the filtrate perfuses the adsorption columns where toxins are retained and is finally mixed with blood cells and other plasma components before returning to the patient (Figure 18.11). 

Usually the separation is effective in proportion to E because E represents either the amount of contaminant removed if the rejected solute is undesirable or the amount of product concentrated if the solute is desirable. However, the degree to which the concentration at the interface c0 can be increased to this end is limited because high values augment leakage, resistance to flow, and the risk of precipitation. Consequently, to increase E, efforts are generally made to increase effective diffusivity Dr, which is best done through stirring or convective processes. Thus these processes become important considerations to effective operation. 

Atmospheric precipitation. Atmospheric precipitation over the Black Sea is mostly related to the cyclonic activity. The convective process plays a noticeable role only it near-shore band and on the coasts. An additional influence is provided by the topography of the coastal zone. Throughout the year, the precipitation amount grows from the northwest (380-420 mm/ year) to the southeast, where the Caucasian ridges approach the coastline and are oriented across the principal moisture-bearing airflows (up to 1500-2500 mm/year) (Fig. 8). The greatest number of days with precipita-... 

Ozsoy E, Top Z, White G, Murray JW (1991) Double diffusive intrusions, mixing and deep sea convection processes in the Black Sea. In Izdar E, Murray JW (eds) The Black Sea oceanography. NATO/ASI series. Kluwer Academic, Dordrecht, p 17... 

An electric-resistance analogy can also be drawn for the convection process by rewriting the equation as... 

The discussion and analyses of Chap. 5 have shown how forced-convection heat transfer may be calculated for several cases of practical interest the problems considered, however, were those which could be solved in an analytical fashion. In this way, the principles of the convection process and their relation to fluid dynamics were demonstrated, with primary emphasis being devoted to a clear understanding of physical mechanism. Regrettably, it is not always possible to obtain analytical solutions to convection problems, and the individual is forced to resort to experimental methods to obtain design information, as well as to secure the more elusive data which increase the physical understanding of the heat-transfer processes. 

Our preceding discussions of convection heat transfer have considered homogeneous single-phase systems. Of equal importance are the convection processes associated with a change of phase of a fluid. The two most important examples are condensation and boiling phenomena, although heat transfer with solid-gas changes has become important because of a number of applications. 

Mass transfer can result from several different phenomena. There is a mass transfer associated with convection in that mass is transported from one place to another in the flow system. This type of mass transfer occurs on a macroscopic level and is usually treated in the subject of fluid mechanics. When a mixture of gases or liquids is contained such that there exists a concentration gradient of one or more of the constituents across the system, there will be a mass transfer on a microscopic level as the result of diffusion from regions of high concentration to regions of low concentration. In this chapter we are primarily concerned with some of the simple relations which may be used to calculate mass diffusion and their relation to heat transfer. Nevertheless, one must remember that the general subject of mass transfer encompasses both mass diffusion on a molecular scale and the bulk mass transport, which may result from a convection process. 

Conduction is treated from both the analytical and the numerical viewpoint, so that the reader is afforded the insight which is gained from analytical solutions as well as the important tools of numerical analysis which must often be used in practice. A similar procedure is followed in the presentation of convection heat transfer. An integral analysis of both free- and forced-convection boundary layers is used to present a physical picture of the convection process. From this physical description inferences may be drawn which naturally lead to the presentation of empirical and practical relations for calculating convection heat-transfer coefficients. Because it provides an easier instruction vehicle than other methods, the radiation-network method is used extensively in the introduction of analysis of radiation systems, while a more generalized formulation is given later. 

TDU third dredge-up in an AGB star, a powerful convective process that enriches the outer layers of the star with nucleosynthesis products. 

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