Convective transfer Coefficient

Sparrow, E. M., and Kalejs, J. P. (1977). Local convective transfer coefficients in a channel downstream of a partially constricted inlet. Int. ]. Heat Mass Transfer 20, 1241-1249. 

Increasing temperature has two effects (1) by decreasing gas density, the gas convective component of heat transfer is decreased slightly, and (2) by increasing the thermal conductivity of the gas, the effectivness of packets of emulsion phase in contact with the transfer surface is increased. The overall effect for Group A and B powders is to increase the convective transfer coefficient as was shown by Botterill and Teoman (1980). In the case of Group D powders where the gas convective... 

Convective mass transfer in the gas channels is defined in terms of constant convective transfer coefficient as defined in Chapter 6. 

The heat-transfer coefficient of most interest is that between the bed and a wall or tube. This heat-transfer coefficient, is made up of three components. To obtain the overall dense bed-to-boiling water heat-transfer coefficient, the additional resistances of the tube wall and inside-tube-waH-to-boiling-water must be added. Generally, the conductive heat transfer from particles to the surface, the convective heat transfer... 

Fundamental models correctly predict that for Group A particles, the conductive heat transfer is much greater than the convective heat transfer. For Group B and D particles, the gas convective heat transfer predominates as the particle surface area decreases. Figure 11 demonstrates how heat transfer varies with pressure and velocity for the different types of particles (23). As superficial velocity increases, there is a sudden jump in the heat-transfer coefficient as gas velocity exceeds and the bed becomes fluidized. 

I ewton s Cooling L w of Heat Convection. The heat-transfer rate per unit area by convection is directly proportional to the temperature difference between the soHd and the fluid which, using a proportionaUty constant called the heat-transfer coefficient, becomes... 

Table 2. Values of the Convective Heat-Transfer Coefficient ...

In the forced convection heat transfer, the heat-transfer coefficient, mainly depends on the fluid velocity because the contribution from natural convection is negligibly small. The dependence of the heat-transfer coefficient, on fluid velocity, which has been observed empirically (1—3), for laminar flow inside tubes, is h for turbulent flow inside tubes, h and for flow outside tubes, h. Flow may be classified as laminar or... 

Correlations for Convective Heat Transfer. In the design or sizing of a heat exchanger, the heat-transfer coefficients on the inner and outer walls of the tube and the friction coefficient in the tube must be calculated. Summaries of the various correlations for convective heat-transfer coefficients for internal and external flows are given in Tables 3 and 4, respectively, in terms of the Nusselt number. In addition, the friction coefficient is given for the deterrnination of the pumping requirement. 

The convective heat-transfer coefficient and friction factor for laminar flow in noncircular ducts can be calculated from empirically or analytically determined Nusselt numbers, as given in Table 5. For turbulent flow, the circular duct data with the use of the hydrauhc diameter, defined in equation 10, may be used. 

Effect of Uncertainties in Thermal Design Parameters. The parameters that are used ia the basic siting calculations of a heat exchanger iaclude heat-transfer coefficients tube dimensions, eg, tube diameter and wall thickness and physical properties, eg, thermal conductivity, density, viscosity, and specific heat. Nominal or mean values of these parameters are used ia the basic siting calculations. In reaUty, there are uncertainties ia these nominal values. For example, heat-transfer correlations from which one computes convective heat-transfer coefficients have data spreads around the mean values. Because heat-transfer tubes caimot be produced ia precise dimensions, tube wall thickness varies over a range of the mean value. In addition, the thermal conductivity of tube wall material cannot be measured exactiy, a dding to the uncertainty ia the design and performance calculations. 

The values of CJs are experimentally determined for all uncertain parameters. The larger the value of O, the larger the data spread, and the greater the level of uncertainty. This effect of data spread must be incorporated into the design of a heat exchanger. For example, consider the convective heat-transfer coefficient, where the probabiUty of the tme value of h falling below the mean value h is of concern. Or consider the effect of tube wall thickness, /, where a value of /greater than the mean value /is of concern. 

Characterization and influence of electrohydro dynamic secondary flows on convective flows of polar gases is lacking for most simple as well as complex flow geometries. Such investigations should lead to an understanding of flow control, manipulation of separating, and accurate computation of local heat-transfer coefficients in confined, complex geometries. The typical Reynolds number of the bulk flow does not exceed 5000. 

The effective thermal conductivity of a Hquid—soHd suspension has been reported to be (46) larger than that of a pure Hquid. The phenomenon was attributed to the microconvection around soHd particles, resulting in an increased convective heat-transfer coefficient. For example, a 30-fold increase in the effective thermal conductivity and a 10-fold increase in the heat-transfer coefficient were predicted for a 30% suspension of 1-mm particles in a 10-mm diameter pipe at an average velocity of 10 m/s (45). 

A manufacturing technology to produce very small encapsulated phase-change materials has been developed (47). These encapsulated phase-change materials were appHed in a convective heat-transfer test section, and a 50—100% higher heat-transfer coefficient was reported. 

To the extent that radiation contributes to droplet heatup, equation 28 gives a conservative estimate of the time requirements. The parameter ( ) reflects the dependence of the convective heat-transfer coefficient on the Reynolds number ... 

Likewise, the microscopic heat-transfer term takes accepted empirical correlations for pure-component pool boiling and adds corrections for mass-transfer and convection effects on the driving forces present in pool boiling. In addition to dependence on the usual physical properties, the extent of superheat, the saturation pressure change related to the superheat, and a suppression factor relating mixture behavior to equivalent pure-component heat-transfer coefficients are correlating functions. 

To model convection drying both the heat transfer to the coated web and the mass transfer (qv) from the coatiag must be considered. The heat-transfer coefficient can be taken as proportional to the 0.78 power of the air velocity or to the 0.39 power of the pressure difference between the air in the plenum and the ambient pressure at the coatiag. The improvement in heat-transfer coefficients in dryers since the 1900s is shown in Figure 20. The mass-transfer coefficient for solvent to the air stream is proportional to the heat-transfer coefficient and is related to it by the Clulton-Colbum analogy... 

Natural convection occurs when a solid surface is in contact with a fluid of different temperature from the surface. Density differences provide the body force required to move the flmd. Theoretical analyses of natural convection require the simultaneous solution of the coupled equations of motion and energy. Details of theoretical studies are available in several general references (Brown and Marco, Introduction to Heat Transfer, 3d ed., McGraw-HiU, New York, 1958 and Jakob, Heat Transfer, Wiley, New York, vol. 1, 1949 vol. 2, 1957) but have generally been applied successfully to the simple case of a vertical plate. Solution of the motion and energy equations gives temperature and velocity fields from which heat-transfer coefficients may be derived. The general type of equation obtained is the so-called Nusselt equation hL I L p gp At cjl... 

Mass-Transfer Coefficient Denoted by /c, K, and so on, the mass-transfer coefficient is the ratio of the flux to a concentration (or composition) difference. These coefficients generally represent rates of transfer that are much greater than those that occur by diffusion alone, as a result of convection or turbulence at the interface where mass transfer occurs. There exist several principles that relate that coefficient to the diffusivity and other fluid properties and to the intensity of motion and geometry. Examples that are outlined later are the film theoiy, the surface renewal theoiy, and the penetration the-oiy, all of which pertain to ideahzed cases. For many situations of practical interest like investigating the flow inside tubes and over flat surfaces as well as measuring external flowthrough banks of tubes, in fixed beds of particles, and the like, correlations have been developed that follow the same forms as the above theories. Examples of these are provided in the subsequent section on mass-transfer coefficient correlations. 

For subcooling, a liquid inventory may be maintained in the bottom end of the shell by means of a weir or a hquid-level-controUer. The subcoohng heat-transfer coefficient is given by the correlations for natural convection on a vertical surface [Eqs. (5-33 ), (5-33Z )], with the pool assumed to be well mixed (isothermal) at the subcooled condensate exit temperature. Pressure drop may be estimated by the shell-side procedure. 

A pseudo-convective heat-transfer operation is one in which the heating gas (generally air) is passed over a bed of solids. Its nse is almost exchisively limited to drying operations (see Sec. 12, tray and shelf dryers). The operation, sometimes termed direct, is more aldu to the coudnctive mechanism. For this operation, Tsao and Wheelock [Chem. Eng., 74(13), 201 (1967)] predict the heat-transfer coefficient when radiative and conductive effects are absent by... 

A discussion of retention time in rotary Idlns is given in Brit. Chem. Eng., 27-29 (Januaiy 1966). Rotary-ldln heat control is discussed in detail by Bauer [Chem. Eng., 193-200 (May 1954)] and Zubrzycki [Chem. Can., 33-37 (Februaiy 1957)]. Reduction of iron ore in rotaiy Idlns is described by Stewart [Min. Congr J., 34—38 (December 1958)]. The use of balls to improve solids flow is discussed in [Chem. Eng., 120-222 (March 1956)]. Brisbane examined problems of shell deformation [ Min. Eng., 210-212 (Februaiy 1956)]. Instrumentation is discussed by Dixon [Ind. Eng. Chem. Process Des. Dev., 1436-1441 (July 1954)], and a mathematical simulation of a rotaiy Idln was developed by Sass [Ind. Eng. Chem. Process Des. Dev., 532-535 (October 1967)]. This last paper employed the empirical convection heat-transfer coefficient given previously, and its use is discussed in later correspondence [ibid., 318-319 (April 1968)]. 

Equations (13-115) to (13-117) contain terms, for rates of heat transfer from the vapor phase to the hquid phase. These rates are estimated from convective and bulk-flow contributions, where the former are based on interfacial area, average-temperature driving forces, and convective heat-transfer coefficients, which are determined from the Chilton-Colburn analogy for the vapor phase and from the penetration theoiy for the liquid phase. 

Experimental gas-solid mass-transfer data have been obtained for naphthalene in CO9 to develop correlations for mass-transfer coefficients [Lim et al., Am. Chem. Soc. Symp. Ser, 406, 379 (1989)]. The data were correlated over a wide range of conditions with the following equation for combined natural and forced convection ... 

There will also be heat loss from tire substrate due to convection cuiTents caused by the teirrperamre differential in the suiTounding gas phase, but this will usually be less than the radiation loss, because of the low value of the heat transfer coefficient, / , of gases. The heat loss by this mechanism, Qc, can be calculated, approximately, by using tire Richardson-Coulson equation... 

Open Tube Sections (Air Cooled) Plain or finned tubes No shell required, only end heaters similar to water units. Condensing, high level heat transfer. Transfer coefficient is low, if natural convection circulation, but is improved with forced air flow across tubes. 0.8-1.8... 

The convective wave cycle was described in 5.2.4 but its heat transfer properties not quantified. Critoph and Thorpe [22] and Thorpe [23] have measured the convective heat transfer coefficient between flowing gas and the grains within the bed. Preliminary results imply that the pressure drop through the bed can be expressed by a modified Ergun equation ... 

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