Heat transfer coefficient axial distribution

Radial and Axial Distributions of Heat Transfer Coefficient... 

As opposed to the relatively uniform bed structure in dense-phase fluidization, the radial and axial distributions of voidage, particle velocity, and gas velocity in the circulating fluidized bed are very nonuniform (see Chapter 10) as a result the profile for the heat transfer coefficient in the circulating fluidized bed is nonuniform. 

Heat transfer studies on fixed beds have almost invariably been made on tubes of large diameter by measuring radial temperature profiles (1). The correlations so obtained involve large extrapolations of tube diameter and are of questionable validity in the design of many industrial reactors, involving the use of narrow tubes. In such beds it is only possible to measure an axial temperature profile, usually that along the central axis (2), from which an overall heat transfer coefficient (U) can be determined. The overall heat transfer coefficient (U) can be then used in one--dimensional reactor models to obtain a preliminary impression of longitudinal product and temperature distributions. 

The characteristic axial and radial distributions of heat transfer coefficients computed from the preceding formula are shown in Fig. 12. In the calculation, the sectional average voidage e can be established from any of the known... 

Inasmuch as heat transfer depends on the hydrodynamic features of fast fluidization, if the fast fluidized bed is equipped with an abrupt exit, the axial distribution of solids concentration will have a C-shaped curve (Jin et al., 1988 Bai et al., 1992 Glicksman et al., 1991. See Chapter 3, Section III.F.l). The heat transfer coefficient will consequently increase in the region near the exit, as reported by Wu et al. (1987). 

Figure 20 indicates that the ratio of hjh, between probes B and A, is in the range of 1.1 to 1.8 and keeps almost constant along the axial direction of the probe. The ratio of hjhx is large at low gas velocities, and when the probes are located at the center of the bed (see Fig. 20). This implies that the distribution of heat transfer coefficients, even with rings, along the radial direction of the bed becomes flatter at a higher bed level where solids concentration is low. Stated alternatively, with increasing gas velocity the influence of the rings on heat transfer coefficient diminishes.

In Chapter 5, Z. Yu and Y. Jin of THU describe experimental studies of heat transfer between particle suspensions and immersed surfaces, enumerating the effects of variables and of the radial and axial distribution of the heat transfer coefficient. They then present an analysis of the mechanism of heat transfer, particularly in terms of particle convection. 

The solution of Eqs. (S) to (8) or (9) presents the temperature distribution in the channel, from which, as a function of the axial distance, either the wall temperature or the heat flux through the wall may be calculated, depending on whether Eq. (8) or (9) was applied. The results allow calculation of a local heat transfer coefficient, a, or local Nusselt number Nu ... 

In discussing the yield from a reactor, the temperature distribution inside the reactor must be investigated. In the dense phase of fluid beds, the heat-transfer coefiicient between the bed and waU has been widely studied (LIO, MI4, M15, M16, T22, V5, W3, W5). Botterill (B12) has reviewed the recent literature studies of heat transfer in the dilute phase are quite limited in number. Shirai (S9, Sll), Furusaki (F15), and Morooka et al. (M50) studied the heat-transfer coefiicient in the dilute phase as well as in the dense phase. They found that the heat-transfer coefficient between the bed and the wall decreases as the bed density decreases, which will cause an axial distribution of temperature in bed. 

In the case of heat transfer analysis, axial temperature distribution, shown in Figure 3 are specified for the surfaces of both He and sulfuric flow cannels, considering heat transfer coefficients. And outer surface of block is modeled as adiabatic condition. Figures 5 and 6 show the temperature and the stress distributions in the block, respectively. The stress shown in Figure 6 is a coupled stress with thermal stress and static stress caused by the operating pressure difference between He and sulfuric acid. Analytical conditions are as follows ... 

The axial temperature rise in the coolant, Eq. (2.183), the radial temperature drop and the axial temperature distribution in the fuel, the gap, the clad, and the coolant, Eq. (2.188), are sketched in Fig. 2.52. Some typical values encountered in practice for the radial temperature drop are ATpuei 1500 °C, AToap 150 — 300 °C, ATaad 50 °C, and ATbooiam 5 °C (for water). Also, some values for the geometry, thermal conductivity and heat transfer coefficient are ... 

An example of the analyses that were performed and used to define the PTS licensing criteria is presented here. This example uses a vessel fabricated from rolled plate connected with axial welds to form two cylindrical shell courses. Circumferential welds connect the two shell courses. The vessel conditions used in this example are specified in Table 12.2. The pressure and temperature time histories at the vessel inner surface for the postulated transient are shown in Figs 12.2 and 12.3, respectively. The heat transfer coefficient used in the analysis was 2825W/mV°C (500 BTU/(hr-ft -°F)). Table 12.3 presents the frequency distribution for the postulated event. This event is representative of an event that is a significant contributor to TWCF. 

In the above equations, Cpr and Cp< denote heat capacities of the fluid and solid phases, pb is the bed density and hp is the heat transfer coefficient between fluid and particles. Transport of heat through the fluid phase in the axial direction and in the radial direction of the bed by conduction are described by the effective thermal conductivities, ka,i and kas, while in the solid phase thermal conduction can be assumed to be isotropic and the effective thermal conductivity ka can be used to express this effect. Q i represents the heat evolution/absorption by adsorption or desorption on the basis of bed volume. This model neglects the temperature distribution in the radial position of each particle, which may seem contradictory to the case of mass transfer, where intraparticle mass transfer plays a significant role in the overall adsorption rate. Usually in the case of adsorption, the time constant of heat transfer in the particle is smaller than the time constant of intraparticle diffusion, and the temperature in the particle may be assumed to be constant. 

In this correlation the effect of channel entrance loss, wdiich is a stabilizing factor for the system, is not included. The amount of the heat transfer at OFI depends on pressure through saturation temperature, Tg t Since pressure drop characteristics are not required, the accuracy of the prediction does not depend on two phase correlations (subcooled void fi action, pressure drop, and heat transfer coefficient). All two phase effects are included in parameter, 4i , and flow instability is intimately related to pressure drop. The pressure drop depends on the local water quality, which follows firom the axial heat distribution. 

Althou correlations of axial and radial dispersion coefficients for gases throu a fixed bed are available (72.) > corresponding dispersion coefficients for solids are difficialt to estimate. The temperature distributions of solids are indeed affected by these dispersion coefficients as well as other factors s ach as heat transfer coefficients. 

The axial distributions of the enthalpy, temperature, density, and velocity of the coolant and the moderator are determined for a given core power, feedwater temperature, feedwater flow rate, and the pressure. The calculation is carried out iteratively until the temperature distributions are convergent to steady-state values. The fuel and cladding temperatures are calculated for each axial mesh with onedimensional radial heat transfer equations using the coolant and moderator temperature distribution. Steady-state temperature distributions are assumed in the fuel pellet, fuel cladding, and the gap. The heat transfer between fuel pellet and the coolant, as well as the heat transfer between the fuel channel and the water rods is considered. The heat transfer coefficients are calculated by the Oka-Koshizuka correlation, which was developed by using the Jones-Launder k-e turbulence model. 

The following, well-acceptable assumptions are applied in the presented models of automobile exhaust gas converters Ideal gas behavior and constant pressure are considered (system open to ambient atmosphere, very low pressure drop). Relatively low concentration of key reactants enables to approximate diffusion processes by the Fick s law and to assume negligible change in the number of moles caused by the reactions. Axial dispersion and heat conduction effects in the flowing gas can be neglected due to short residence times ( 0.1 s). The description of heat and mass transfer between bulk of flowing gas and catalytic washcoat is approximated by distributed transfer coefficients, calculated from suitable correlations (cf. Section III.C). All physical properties of gas (cp, p, p, X, Z>k) and solid phase heat capacity are evaluated in dependence on temperature. Effective heat conductivity, density and heat capacity are used for the entire solid phase, which consists of catalytic washcoat layer and monolith substrate (wall). 

---