Heat-transfer coefficients resistance form

Each term in the denominator of Equation 4.11 is the reciprocal of a heat-transfer coefficient, and thus represents a resistance to heat transfer. The first term in the denominator represents the resistance to heat conduction across a scale formed on the inside surface of the tube, where the thickness and the thermal conductivity of the scale is rarely known. The thermal conductivity and the thickness of scale are not reported in the literature, but its reciprocal is designated by Rf i, the resistance to heat transfer caused by the tube-side scale, where... 

Under some surface conditions, the condensate does not form a continuous film. Droplets are formed which grow, coalesce, and then run from the surface. As a fraction of the surface is always directly exposed to the vapor, film resistance is absent, and heat-transfer coefficients, which may be ten times those of film condensation, are obtained. This process is known as dropwise condensation. Although highly desirable, its occurrence, which depends upon the wettability of the surface, is not predictable and cannot be used as a basis for design. 

If scale forms inside and/or outside the tube walls, additional resistance terms (Fig. 4) should be added to Eq. (2). Some typical values of overall heat-transfer coefficients are given in Table 3 for various evaporator designs. 

The overall resistance to the flow of heat from the warm fluid to the cold fluid is a result of three separate resistances operating in series. Two resistances are those offered by the individual fluids, and the third is that of the solid wall. In general, also, as shown in Fig. 11.8, the wall resistance is small in comparison with that of the fluids. The overall coefficient is best studied by analyzing it in terms of the separate resistances and treating each separately. The separate resistances can then be combined to form the overall coefficient. This approach requires the use of individual heat-transfer coefficients for the two fluid streams. 

DROPWISE AND FILM-TYPE CONDENSATION. A vapor may condense on a cold surface in one of two way.s, which are well described by the terms dropwise and film type. In film condensation, which is more common than dropwise condensation, the liquid condensate forms a film, or continuous layer, of liquid that flows over the surface of the tube under the action of gravity. It is the layer of liquid interposed between the vapor and the wall of the tube that provides the resistance to heat flow and therefore fixes the magnitude of the heat-transfer coefficient. 

The net results of this first single-stage evaluation are summarized in Figure 5 in the form of condenser performance vs. reservoir temperature level and reservoir-condenser temperature difference. The curves shown are valid for distillation at atmospheric pressure, a constant disk speed of 60 r.p.m., and an air-vapor gap of 3/s2 inch. Since the test condenser was water-cooled at high flow rates, the over-all heat transfer coefficients shown are considered to be maximum values controlled by the resistance on the diffusion side. 

Low heat transfer coefficient (6.4) is caused by thermal contact resistance at the wall-liquid boundary. Thermal resistance is influenced by surface wetting with coolant, oxide films formed on metal surface, as well as deposits of oxides and other impurities. Thermal contact resistance can hardly be evaluated, only possible upper limit can be specified [6.15, 6.16] ... 

A vessel fitted with a cooling coil and an agitator is shown schematically in Figure 8.23. In this case the thermal resistances to heat transfer arise from the fluid film on the inside of the cooling coil, the wall of the tube (usually negligible), the fluid film on the outside of the coil, and the scale that may form on either siuface. The overall heat transfer coefficient, U, can thus be expressed as ... 

Besides microstructured heat exchanger/reactors constructed in the form of plates as shown in Figure 5.1, shell and tube micro heat exchangers are available. An example is shown in Figure 5.6. The heat transfer within the reactor tubes can be estimated with the asymptotic Nu or with Equation 5.12 for short channels. The outer heat transfer coefficient depends on the flow regime, the arrangement of the tubes, and the presence of baffles [8, 13]. For small-scale systems, capillaries submerged in constant temperature baths are commonly used. In this case, the main heat transfer resistance is mostly located at the outer side of the reactor. 

In actual practice, heat-transfer surfaces do not remain clean. Dirt, soot, scale, and other deposits form on one or both sides of the tubes of an exchanger and on other heat-transfer surfaces. These deposits form additional resistances to the flow of heat and reduce the overall heat-transfer coefficient U. In petroleum processes coke and other substances can deposit. Silting and deposits of mud and other materials can occur. Corrosion products may form on the surfaces which could form a serious resistance to heat transfer. Biological growth such as algae can occur with cooling water and in the biological industries. 

The theory of Jephson (1) assumes a perfect scraping of the barrel surface by the screw flight. In practice a gap exists between the flight and the barrel wall. Therefore a layer of material remains at the wall with a thickness, approximately equal to the flight clearance (8/) that forms an extra thermal resistance to heat transfer. Janeschitz-Kriegl et al. (3) solved this problem by adjusting the boundary conditions for the Jephson model. They assumed a linear variation of temperature over the remaining layer of material from the wall temperature to the bulk temperature and derived for the heat transfer coefficient ... 

In developing the concept of a heat transfer coefficient, we moved away from physics and into the realm of engineering science. Equation (4.15), which is applicable to a clean system, was developed. In it, allowance is made for the thermal resistances within the fluid films and the resistance of the intervening tube wall. However, all industrial systems contain impurities and some will be deposited on the heat transfer surfaces in the form of thin dirt films, which being of low thermal conductivity will generate additional thermal resistances. These films build up with time and the heat exchanger must be sized so that the performance is satisfactory throughout the complete period of operation. 

The overall heat-transfer coefficient includes several resistances in series, but the internal resistance usually controls the heat-transfer rate (hi U). The internal heat-transfer coefficient is a function of several factors such as the impeller type and dimensions, the impeller speed, the reactor diameter, and physical properties of the fluid. Empirical correlations based on dimensionless groups can be used. Equation (65) presents the usual form of these expressions [111], where Nu,Pr and Re are the Nusselt, Prandtl, and Reynolds numbers, (p and (p the viscosity of the reaction medium at the reactor and wall temperatures respectively, and a, f , c, and d are constants. 

In an uninsulated line, cooldown costs are low and a frost due to sublimed water vapor quickly forms on the pipe to provide some insulation. A heat transfer coefficient exists for the boundary layer between the ambient air and the outer piping surface as well as between the inner surface of the tube and the transported cryogen. Consequently, both the frost and the film effects offer resistance to heat influx. 

Thermal. The thermal or hot wire type shown in Fig. 8.20 detects a large difference in heat transfer coefficient between liquid and vapor. Since the heat transfer coefficient is much larger in the liquid than it is in the vapor, one can expect, for a given power input, that the transducer will have a different temperature and hence resistance in the liquid than in the vapor. It is this change in electrical resistance that is actually sensed in a bridge, and hence these devices can be made both simple and fast. Protection in the form of a... 

As indicated in Qhap. 13 all fluids are bounded at the retaining walls by a film of stagnant fluid. Heat must be transferred through these films by conduction. The films are very thin, their thicknesses cannot be easily measured, and hence the thickness L which is involved in the resistance of the film cannot be determined directly. In order to avoid this difficulty, the resistances of fluid films have been correlated by expressing the resistance as 1/h in which h is the film coefficient of heat transfer. From commonly accepted heat-transfer coefficients the apparent film thickness varies from about 0.1 for gases to about 0.0001 in. for condensing steam. If the conduction equation is applied to the transfer of heat from a fluid into a solid partition wall and into another fluid, the conduction equation takes the following form ... 

At the same time, the overall heat transfer coefficient is simpler than the overall mass transfer coefficient developed in Section 8.5. Both coefficients are related to a sum of resistances, but the mass transfer case also involves weighting factors that are often confusing. These factors relate the concentrations on different sides of the interface. In the heat transfer case, the interfacial temperature in, for example, the hot fluid at the wall equals the interfacial temperature of the solid wall in contact with the hot fluid. This equality means no weighting factors and a simpler mathematical form. 

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