Gas convective 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. 

For example, for equal volumes of gas and liquid ( =0.5), Eq. (266) predicts that the Stokes velocity (which is already very small for relatively fine dispersions) should be reduced further by a factor of 38 due to hindering effects of its neighbor bubbles in the ensemble. Hence in the domain of high values and relatively fine dispersions, one can assume that the particles are completely entrained by the continuous-phase eddies, resulting in a negligible convective transfer, although this does not preclude the existence of finite relative velocities between the eddies themselves. 

Mixing force mechanical agiiation+ movement of the gas momentum transfer between gas and liquid gravity, convection and concentration gradients... 

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)... 

For the well-mixed continuous-flow liquid phase shown in Fig. 1, the balance equations for oxygen and substrate must account for the supply of each component both by convective flow and by gas-liquid transfer, as well as by the diffusion rate into the biofilm. 

In conduction, heat is conducted by the transfer of energy of motion between adjacent molecules in a liquid, gas, or solid. In a gas, atoms transfer energy to one another through molecular collisions. In metallic solids, the process of energy transfer via free electrons is also important. In convection, heat is transferred by bulk transport and mixing of macroscopic fluid elements. Recall that there can be forced convection, where the fluid is forced to flow via mechanical means, or natural (free) convection, where density differences cause fluid elements to flow. Since convection is found only in fluids, we will deal with it on only a limited basis. Radiation differs from conduction and convection in that no medium is needed for its propagation. As a result, the form of Eq. (4.1) is inappropriate for describing radiative heat transfer. Radiation is... 

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. 

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... 

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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