Heat transfer problems

That such a process is today commercially important is a measure of the success of chemical engineers in overcoming heat transfer problems involved with masses incapable of being stirred. An idea of the extent of the problem can be gauged from the fact that it takes six hours to cool a sample of polystyrene from 160°C using a cooling medium at 15°c when the heat transfer distance is two inches. 

The problem is different from typical heat transfer problems. The heat balance is not straightforward because the outlet temperatures are unknown. A trial-and-error procedure is therefore required. 

The problems experienced in drying process calculations can be divided into two categories the boundary layer factors outside the material and humidity conditions, and the heat transfer problem inside the material. The latter are more difficult to solve mathematically, due mostly to the moving liquid by capillary flow. Capillary flow tends to balance the moisture differences inside the material during the drying process. The mathematical discussion of capillary flow requires consideration of the linear momentum equation for water and requires knowledge of the water pressure, its dependency on moisture content and temperature, and the flow resistance force between water and the material. Due to the complex nature of this, it is not considered here. 

Clearly, the maximum degree of simplification of the problem is achieved by using the greatest possible number of fundamentals since each yields a simultaneous equation of its own. In certain problems, force may be used as a fundamental in addition to mass, length, and time, provided that at no stage in the problem is force defined in terms of mass and acceleration. In heat transfer problems, temperature is usually an additional fundamental, and heat can also be used as a fundamental provided it is not defined in terms of mass and temperature and provided that the equivalence of mechanical and thermal energy is not utilised. Considerable experience is needed in the proper use of dimensional analysis, and its application in a number of areas of fluid flow and heat transfer is seen in the relevant chapters of this Volume. 

Qu et al. (2000) carried out experiments on heat transfer for water flow at 100 < Re < 1,450 in trapezoidal silicon micro-channels, with the hydraulic diameter ranging from 62.3 to 168.9pm. The dimensions are presented in Table 4.5. A numerical analysis was also carried out by solving a conjugate heat transfer problem involving simultaneous determination of the temperature field in both the solid and fluid regions. It was found that the experimentally determined Nusselt number in micro-channels is lower than that predicted by numerical analysis. A roughness-viscosity model was applied to interpret the experimental results. 

A variety of studies can be found in the literature for the solution of the convection heat transfer problem in micro-channels. Some of the analytical methods are very powerful, computationally very fast, and provide highly accurate results. Usually, their application is shown only for those channels and thermal boundary conditions for which solutions already exist, such as circular tube and parallel plates for constant heat flux or constant temperature thermal boundary conditions. The majority of experimental investigations are carried out under other thermal boundary conditions (e.g., experiments in rectangular and trapezoidal channels were conducted with heating only the bottom and/or the top of the channel). These experiments should be compared to solutions obtained for a given channel geometry at the same thermal boundary conditions. Results obtained in devices that are built up from a number of parallel micro-channels should account for heat flux and temperature distribution not only due to heat conduction in the streamwise direction but also conduction across the experimental set-up, and new computational models should be elaborated to compare the measurements with theory. 

Heat transfer problems become more severe as reaction rates are increased and water-to-monomer ratios are reduced. In addition, as reactor sizes are increased for improved process economics, the amount of wall heat transfer surface area per unit volume will drop and result in a lower reactor space-time yield. 

The heat transfer problem which must be solved in order to calculate the temperature profiles has been posed by Lee and Macosko(lO) as a coupled unsteady state heat conduction problem in the adjoining domains of the reaction mixture and of the nonadiabatic, nonisothermal mold wall. Figure 5 shows the geometry of interest. The following assumptions were made 1) no flow in the reaction mixture (typical molds fill in <2 sec.) ... 

Example 8.12 Use the backward differencing method to solve the heat transfer problem of Example 8.3. Select A-t = 0.25 and A = 0.0625. 

To identify the governing processing and material parameters, a one dimensional case was analyzed. The heat transfer problem renders an exact solution, [10], which can be presented as an infinite series... 

High gas solubility Weak solvation High diffusion rates Ease of control over properties Good mass transfer Readily available Possible heat-transfer problems... 

To show how numerical models work we start with the one-dimensional heat transfer problem. 

Two-phase mass transfer and heat transfer without phase change are analogous, and the results of mass-transfer studies can be used to help clarify the heat-transfer problems. Cichy et al. (C5) have formulated basic design equations for isothermal gas-liquid tubular reactors. The authors arranged the common visually defined flow patterns into five basic flow regimes, each... 

Anionic polymerization of polystyrene takes place very rapidly- much faster than free radical polymerization. When practiced on a large scale, this gives rise to heat transfer problems and limits its commercial practice to special cases, such as block copolymerization by living reactions. We employ anionic polymerization to make tri-block copolymer rubbers such as polystyrene-polybutadiene-polystyrene. This type of synthetic rubber is widely used in the handles of power tools, the soft grips of pens, and the elastic side panels of disposable diapers. 

The focus of the remainder of this chapter is on interstitial flow simulation by finite volume or finite element methods. These allow simulations at higher flow rates through turbulence models, and the inclusion of chemical reactions and heat transfer. In particular, the conjugate heat transfer problem of conduction inside the catalyst particles can be addressed with this method. 

To obtain approximate solutions for convection heating problems, we only need to identify a heat transfer problem that has a given theoretical or empirical correlation for hc. This is usually given in the form of the Nusselt number (Nu),... 

Although HR-600/Thermid-600 provided promising neat resin and composite properties, major processing problems have plagued these as well as other acetylene-terminated oligomers. Resin flow and wetting is inhibited due to the reaction of the terminal ethynyl groups prior to the formation of a complete melt or soft state. This becomes even more severe due to heat transfer problems as... 

Although the stoichiometry for reaction (9.1) suggests that one only needs 1 mol of water per mole of methane, excess steam must be used to favor the chemical equilibrium and reduce the formation of coke. Steam-to-carbon ratios of 2.5-3 are typical for natural gas feed. Carbon and soot formation in the combustion zone is an undesired reaction which leads to coke deposition on downstream tubes, causing equipment damage, pressure losses and heat transfer problems [21]. 

To solve the filling flow and heat transfer problem with this reacting system, we need to specify the x-direction momentum and energy balances. The x-direction momentum equation during filling is... 

To minimize the heat transfer problem occasioned by the high rates of polymerization encountered, the dilatometers were constructed with a surface-to-volume ratio (in the bulb) of approximately 6 to 1. This was achieved by constructing thin, long rectangular paddle-like bulbs, 8.5 cm. long by 2.5 cm. wide by 0.5 cm. thick. This design also assures uniformity of radiation dose rate from front to rear of the sample. 

In this new process the H2S/SO2 reaction is carried out in liquid sulfur at pressures in excess of five atmospheres. Typical Claus catalysts are still employed but temperatures are lower (below the dewpoint of sulfur) and thus the redox reaction occurs in the liquid sulfur phase at the surface of the catalyst. Vapor losses due to sulfur mist entrainment are reduced and interstage condensers in the tradition Claus train are not required thus avoiding wasteful heat transfer problems. The authors claim that overall sulfur recoveries in excess of 99% are possible without the use of tail gas clean up units. 

The success of the ID fluid dynamic model to describe the flow field in the DPF channel (Konstandopoulos and Johnson, 1989 Konstandopoulos et al., 1999, 2003) is an indication for the existence of a (nearly) self-similar flow field. A necessary condition for the application of the ID model for the heat transfer problem as well, is that the wall velocity ww variation must be small along the characteristic channel length required for establishment of a steady heat transfer pattern (i.e. a length of a2ftz/y.lh). In transferring the above to the case of flow and heat transfer in a DPF channel we may formally write the heat balance as... 

Surface condenser problems. These include undersized surface condenser area, water-side fouling, lack of water flow, condensate backup, and excessive cooling-water inlet temperature. To determine whether a poor vacuum in a surface condenser is due to such heat-transfer problems, plot the same point on the chart shown in Fig. 18.4. If this point is on or slightly below the curve, it is poor heat transfer in the surface condenser itself that is hurting the vacuum. 

C12. Colburn, A. P., Proc. General Discussion on Heat Transfer Problems, p. 1. Inst. Mech. Engrs, London, 1951. 

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