Transport, heats

If the flow is incompressible, the resulting equation is analogous to equation (2.18)  

The most common sources and sinks of heat are short-wave radiation (sunshine), long-wave radiation (such as from a radiator), and heat sources and sinks from reactions. There are also boundary sources and sinks, such as evaporation and freezing. Application of equation (4.4) will be demonstrated through the following examples. 

EXAMPLE 4.1 Formation of ice on a lake surface (heat transfer with an abrupt change in boundary temperature) 

There is no flow in the ice, and the lake below the ice is assumed to be calm. The snow has precluded radiation from entering the ice, and mediates the high and low temperatures. In addition, the 5 cm of snow is equivalent to approximately 50 cm of ice, in terms of themal resistance. We will therefore set our depth of ice at 70 cm. Then, the following terms in equation (4.4) may be estimated  

dT/dx = dT/dy = 0, where z is the vertical coordinate. This is because of exposure to similar boundary conditions at the ice surface. 

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To proceed with the topic of this section. Refs. 250 and 251 provide oversights of the application of contemporary surface science and bonding theory to catalytic situations. The development of bimetallic catalysts is discussed in Ref. 252. Finally, Weisz [253] discusses windows on reality the acceptable range of rates for a given type of catalyzed reaction is relatively narrow. The reaction becomes impractical if it is too slow, and if it is too fast, mass and heat transport problems become limiting. 

The thermal conductivity of polymeric fluids is very low and hence the main heat transport mechanism in polymer processing flows is convection (i.e. corresponds to very high Peclet numbers the Peclet number is defined as pcUUk which represents the ratio of convective to conductive energy transport). As emphasized before, numerical simulation of convection-dominated transport phenomena by the standard Galerkin method in a fixed (i.e. Eulerian) framework gives unstable and oscillatory results and cannot be used. 

Derivation of the working equations of upwinded schemes for heat transport in a polymeric flow is similar to the previously described weighted residual Petrov-Galerkm finite element method. In this section a basic outline of this derivation is given using a steady-state heat balance equation as an example. 

Extension of the streamline Petrov -Galerkin method to transient heat transport problems by a space-time least-squares procedure is reported by Nguen and Reynen (1984). The close relationship between SUPG and the least-squares finite element discretizations is discussed in Chapter 4. An analogous transient upwinding scheme, based on the previously described 0 time-stepping technique, can also be developed (Zienkiewicz and Taylor, 1994). 

The productivity of DR processes depeads oa chemical kinetics, as weU as mass and heat transport factors that combine to estabhsh the overall rate and extent of reduction of the charged ore. The rates of the reduction reactions are a function of the temperature and pressure ia the reductioa beds, the porosity and size distribution of the ore, the composition of the reduciag gases, and the effectiveness of gas—sohd contact ia the reductioa beds. The reductioa rate geaerahy iacreases with increasing temperature and pressure up to about 507 kPa (5 atm). 

M. M. El-Wakil, Nuclear Heat Transport, American Nuclear Society, La Grange Park, lU., 1978. 

Above-Ground Retorting. AGR processes can be grouped into DH or IH processes. Numerous design configurations as well as a variety of heat-transport mediums have been used in the indirect heated processes (Table 7). 

PETROSIX. The PETROSIX technology is operated in the IH mode using hot recycle gas as the heat-transport medium. The PETROSIX retort has only one level of heat input, uses countercurrent flows, and uses a circular grate to control the flow of soflds (Eig. 3). The PETROSIX has been operated by Petrobras (Brazil) since the 1950s and is one of the few retorting processes producing shale oil in 1995. 

UNISHALE B. The UNISHALE process, like the Paraho process, uses lump feed and countercurrent flows, and can be operated ia either the DH or IH mode. The UNISHALE B process is an IH process that uses hot recycled gas as the heat-transport medium (Fig. 6). The unique feature of the UNISHALE processes is the rock pump. The soflds move upward through the retort as the vapors are moving downward. The rock pump was used ia the UNISHALE technology at Parachute, Colorado to produce more than 0.64 x 10 m (four million battels) of cmde shale oil. Operations were shut down in 1991. 

Flow Regimes in Multiphase Reactors. Reactant contacting, product separations, rates of mass and heat transport, and ultimately reaction conversion and product yields are strong functions of the gas and Hquid flow patterns within the reactors. The nomenclature of commonly observed flow patterns or flow regimes reflects observed flow characteristics, ie, armular, bubbly, plug, slug, spray, stratified, and wavy. 

Reaction and Transport Interactions. The importance of the various design and operating variables largely depends on relative rates of reaction and transport of reactants to the reaction sites. If transport rates to and from reaction sites are substantially greater than the specific reaction rate at meso-scale reactant concentrations, the overall reaction rate is uncoupled from the transport rates and increasing reactor size has no effect on the apparent reaction rate, the macro-scale reaction rate. When these rates are comparable, they are coupled, that is they affect each other. In these situations, increasing reactor size alters mass- and heat-transport rates and changes the apparent reaction rate. Conversions are underestimated in small reactors and selectivity is affected. Selectivity does not exhibit such consistent impacts and any effects of size on selectivity must be deterrnined experimentally. 

Scale-Up Principles. Key factors affecting scale-up of reactor performance are nature of reaction zones, specific reaction rates, and mass- and heat-transport rates to and from reaction sites. Where considerable uncertainties exist or large quantities of products are needed for market evaluations, intermediate-sized demonstration units between pilot and industrial plants are usehil. Matching overall fluid flow characteristics within the reactor might determine the operative criteria. Ideally, the smaller reactor acts as a volume segment of the larger one. Elow distributions are not markedly influenced by... 

Vacuum Insulation Heat transport across an evacuated space (1.3 X lO"" Pa or lower), is by radiation and by conduction through the residual gas. The heat transfer by radiation generally is predominant and can be approximated by... 

The insertion of low-emissivity floating shields within the evacuated space can effectively reduce the heat transport by radiation. The effect of the shields is to greatly reduce the emissivity factor. For example, for N shields or N + 2) surfaces, an emissivity of the outer and inner surface of and an emissivity of the shields of the emissivity factor reduces to... 

The shock wave is subject to other dissipative effects, however, such as viscosity and heat transport. It is these dissipative mechanisms that are responsible for preventing the shock from becoming a true, infinitesimally thin discontinuity. In reality, the velocity gradient can only increase until... 

A second mechanism of heat transport is illustrated by a pot of water set to boil on a stove - hotter water closest to the flame will rise to mix with cooler water near the top of the pot. Convection involves the bodily movement of the more energetic molecules in a liquid or gas. The third way, that heat energy can be transferred from one body to another, is by radiation this is the way that the sun warms the earth. The radiation flows from the sun to the earth, where some of it is absorbed, heating the surface. 

Automatic trip of heat transport pump on high bearing temperature to prevent bearing damage service water is lost and the operator fails to take corrective action... 

Rapid bolt-up and fill-up provisions for the heat transport system to allow the steam generators to function as a heat sink in the event of problems with the shutdown cooling heat sink when the heat transport system is drained to the header level... 

Heat transport through surface boundary layers... 

Convection is the heat transfer in the fluid from or to a surface (Fig. 11.28) or within the fluid itself. Convective heat transport from a solid is combined with a conductive heat transfer in the solid itself. We distinguish between free and forced convection. If the fluid flow is generated internally by density differences (buoyancy forces), the heat transfer is termed free convection. Typical examples are the cold down-draft along a cold wall or the thermal plume upward along a warm vertical surface. Forced convection takes place when fluid movement is produced by applied pressure differences due to external means such as a pump. A typical example is the flow in a duct or a pipe. 

Overview of combined modeling of heat transport and air movement, AIVC Technical Note TN 40. Coventry Air Infiltration and Ventilation Centre, 1993. 

Uorer V., Weber A. Air, contaminant and heat transport models Integration and application. Energy and Buildings, vol. 30, p. 97—104, 1999. 

M. Yao, D. H. Matthiesen, A. Chait. Numerical simulation of heat transport and fluid flow in directional crystal growth of GaAs. Numer Heat Transf A 30 685, 1996. 

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