Gas convection

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. 

J. Fainberg, H.-J. Leister, G. Mueller. Numerical simulation of the LEC-growth of GaAs crystals with account of high-pressure gas convection. J Cryst Growth 750 517, 1997. 

Ackeskog et al. (1993) made the first heat transfer measurements in a scale model of a pressurized bubbling bed combustor. These results shed light on the influence of particle size, density and pressure levels on the fundamental mechanism of heat transfer, e.g., the increased importance of the gas convective component with increased pressure. 

In general, gas-to-particle or particle-to-gas heat transfer is not limiting in fluidized beds (Botterill, 1986). Therefore, bed-to-surface heat transfer coefficients are generally limiting, and are of most interest. The overall heat transfer coefficient (h) can be viewed as the sum of the particle convective heat transfer coefficient (h ), the gas convective heat transfer coefficient (h ), and the radiant heat transfer coefficient (hr). 

Overall bed-to-surface heat transfer coefficient = Gas convective heat transfer coefficient = Particle convective heat transfer coefficient = Radiant heat transfer coefficient = Jet penetration length = Width of cyclone inlet = Number of spirals in cyclone = Elasticity modulus for a fluidized bed = Elasticity modulus at minimum bubbling = Richardson-Zaki exponent... 

The absolute magnitude of the heat transfer coefficient is several folds greater than single-phase gas convection at the same superficial velocity. 

Ebert, T., Glicksman, L., and Lints, M., Determination of Particle and Gas Convective Heat Transfer Components in Circulating Fluidized Bed, Chem. Eng. Sci., 48 2179-2188 (1993)... 

Molems, O., and Schweinzer, J., Prediction of Gas Convective Part of the Heat Transfer to Fluidized Beds, pp. 685-693, Fluidization IV, Eng. Foundation, New York, USA (1989)... 

Synthesis of nano-structured alloys by the inert gas evaporation technique A precursor material, either a single metal or a compound, is evaporated at low temperature, producing atom clusters through homogeneous condensation via collisions with gas atoms in the proximity of a cold collection surface. To avoid cluster coalescence, the clusters are removed from the deposition region by natural gas convection or forced gas flow. A similar technique is sputtering (ejection of atoms or clusters by an accelerated focused beam of an inert gas, see 6.9.3). 

Accurate modeling of the temperature distribution in a PEFC requires accurate information in four areas heat source, thermal properties of various components, thermal boundary conditions, and experimental temperature-distribution data for model validation. The primary mechanism of heat removal from the catalyst layers is through lateral heat conduction along the in-plane direction to the current collecting land (like a heat sink). Heat removed by gas convection inside the gas channel accounts for less than 5% under typical PEFC operating conditions. 

The next development was the use of internal cooling by intermittent water circulation during the regeneration period. The heat was removed by radiation and flue gas convection from the walls of perforated pipes to water-cooled tubular coils installed inside these pipes. Thus, direct contact with the catalyst was avoided, which precluded cooling parts of the catalyst to temperatures at which combustion would stop. Most of the heat of combustion was recovered as steam. This was the basis of the design of the first commercial unit installed and operated in 1936. 

The governing heat transfer modes in gas-solid flow systems include gas-particle heat transfer, particle-particle heat transfer, and suspension-surface heat transfer by conduction, convection, and/or radiation. The basic heat and mass transfer modes of a single particle in a gas medium are introduced in Chapter 4. This chapter deals with the modeling approaches in describing the heat and mass transfer processes in gas-solid flows. In multiparticle systems, as in the fluidization systems with spherical or nearly spherical particles, the conductive heat transfer due to particle collisions is usually negligible. Hence, this chapter is mainly concerned with the heat and mass transfer from suspension to the wall, from suspension to an immersed surface, and from gas to solids for multiparticle systems. The heat and mass transfer mechanisms due to particle convection and gas convection are illustrated. In addition, heat transfer due to radiation is discussed. 

Heat transfer between a fluidized bed and an immersed surface can occur by three modes, namely, particle convection, gas convection, and radiation. 

It is seen that particle convection is important for almost all the conditions, except at low bed temperatures in a bed of large particles, where the gas convection becomes important. 

Development of a mechanistic model is essential to quantification of the heat transfer phenomena in a fluidized system. Most models that are originally developed for dense-phase fluidized systems are also applicable to other fluidization systems. Figure 12.2 provides basic heat transfer characteristics in dense-phase fluidization systems that must be taken into account by a mechanistic model. The figure shows the variation of heat transfer coefficient with the gas velocity. It is seen that at a low gas velocity where the bed is in a fixed bed state, the heat transfer coefficient is low with increasing gas velocity, it increases sharply to a maximum value and then decreases. This increasing and decreasing behavior is a result of interplay between the particle convective and gas convective heat transfer which can be explained by mechanistic models given in 12.2.2, 12.2.3, and 12.2.4. 

The heat transfer rate for the gas convective component can be regarded as comparable to that at incipient fluidizing conditions. Thus, assuming hgc = hmf, Xavier and Davidson (1985) simulated the system by considering a pseudofluid with the apparent thermal conductivity Kd of the gas-solid medium flowing at the same superficial velocity and the same inlet and outlet temperatures as the gas. Therefore, the heat conduction of the fluid flowing... 

For a given system, hmm varies mainly with particle and gas properties. For coarse particle fluidization at U > Umf, the heat transfer is dominated by gas convection. Thus, /tmax can be evaluated from Eq. (12.50). On the other hand, hmax in a fine particle bed can be reasonably evaluated from the equations for hpc. In general, hmM is a complicated function... 

At high temperatures, the decreased gas density can decrease the gas convective component /tgc. On the other hand, the increased gas conductivity at high temperature can increase /tgc, Ke, and hpc- For a bed with small particles, the latter is dominant. Thus, a net increase in hc with increasing temperature can be observed before radiation becomes significant. For Group D particles, hc decreases with increasing temperature [Knowlton, 1992]. The effects of temperature and pressure on hpc, /igc, and Amax are illustrated by Fig. 12.13. 

In circulating fluidized beds, the clusters move randomly. Some clusters are swept from the surface, while others stay on the surface. Thus, the heat transfer between the surface and clusters occurs via unsteady heat conduction with a variable contact time. This part of heat transfer due to cluster movement represents the main part of particle convective heat transfer. Heat transfer is also due to gas flow which covers the surface (or a part of surface). This part of heat transfer corresponds to the gas convective component. 

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