Heat transfer between gas and particles

Ga.s-to-Pa.rticle Heat Transfer. Heat transfer between gas and particles is rapid because of the enormous particle surface area available. A Group A particle in a fluidized bed can be considered to have a uniform internal temperature. For Group B particles, particle temperature gradients occur in processes where rapid heat transfer occurs, such as in coal combustion. 

Heat transfer between gas and particle phases tend to be efficient due to the large volumetric concentration of interface surface. Hence this topic is rarely of significant concern and will not be dealt with in this chapter. Most of the chapter concerns heat transfer between the two-phase medium and submerged surfaces. This is the most pertinent engineering problem since heat addition or extraction from the fluidized or conveyed mixture is commonly achieved by use of heat exchangers integral to the vessel wall or submerged in the particle/gas medium. 

This section discusses the behavior of heat transfer between gas and particles, and between the bed and the surface in a spouted bed. 

A review of the heat transfer characteristics of fluidized beds has been given by Yates [143]. It is generally accepted that the heat transfer between gas and particles is very efficient in fluidized beds as a result of the high surface area of the particle phase. The heat transfer fluxes between an immersed surface and the gas-fluidized bed material are more important from a practical design... 

The heat transfer between gas and particles suspended in the fluidized bed is most efficient. The heat of reaction is endothermic, so this requires heat to be provided directly by the gas phase. The heat source can be obtained from the combustion of carbon or a material not converted in a secondary system. The latter is very favorable, but very complex from the point of view of fluid dynamics. 

Gas to particle heat transfer coefficients are t3q>ically small, of the order of 5-20 W m K. However, because of the very large heat transfer surface area provided by a mass of small particles (1 m of 100 pm particles has a surface area of 60 000 m ), the heat transfer between gas and particles is rarely limiting in fluid bed heat transfer. One of the most commonly used correlations for gas-particle heat transfer coefficient is that of Kunii and Levenspiel (1969) ... 

The equations describing the concentration and temperature within the catalyst particles and the reactor are usually non-linear coupled ordinary differential equations and have to be solved numerically. However, it is unusual for experimental data to be of sufficient precision and extent to justify the application of such sophisticated reactor models. Uncertainties in the knowledge of effective thermal conductivities and heat transfer between gas and solid make the calculation of temperature distribution in the catalyst bed susceptible to inaccuracies, particularly in view of the pronounced effect of temperature on reaction rate. A useful approach to the preliminary design of a non-isothermal fixed bed catalytic reactor is to assume that all the resistance to heat transfer is in a thin layer of gas near the tube wall. This is a fair approximation because radial temperature profiles in packed beds are parabolic with most of the resistance to heat transfer near the tube wall. With this assumption, a one-dimensional model, which becomes quite accurate for small diameter tubes, is satisfactory for the preliminary design of reactors. Provided the ratio of the catlayst particle radius to tube length is small, dispersion of mass in the longitudinal direction may also be neglected. Finally, if heat transfer between solid cmd gas phases is accounted for implicitly by the catalyst effectiveness factor, the mass and heat conservation equations for the reactor reduce to [eqn. (62)]... 

Heat and mass transfer between gas and particles are high when comparing with those of other gas-solid reactors and there is a very good quality of contact between reactants of a gas-solid reaction. 

Mass transfer between gas and particles affects gas-solids contact efficiencies in CFB risers. The mass transfer from a single particle to the suspension in CFB risers has been studied based on the sublimation of naphthalene spheres (Haider and Basu, 1988 Li et al., 1998), dehydration of 2-propanol (Masai et al., 1985), adsorption of CCI4, naphthalene, H2S, and NO (Kwauk et al., 1986 van der Ham et al., 1991, 1993 Vollert and Werther, 1994), and heat transfer between a heat pulse and suspension (Dry et al., 1987). For one-dimensional steady-state plug flow of the gas, a mass balance of the adsorbed species in a differential volume element of the reactor (Kwauk et al., 1986 Vollert and Werther, 1994) yields... 

Fluidized beds are widely used to achieve either chemical reactions or physical processing that require interfacial contact between gas and particles. Heat transfer is important in many of these applications, either to obtain energy transfer between the solid and gas phases or to obtain energy transfer between the two-phase mixture and a heating/cooling medium. The latter case is particularly important for fluidized bed reactors which require heat addition or extraction in order to achieve thermal control with heats of reaction. 

Martin, H., Heat Transfer Between Gas Fluidized Beds of Solid Particles and the Surface of Immersed Heat Exchanger Element, Parts I II, Chem. Eng. Process, 18 157-169,199-223 (1984)... 

Note that /ep in Eq. (5.238) is replaced with /Ep for Eq. (5.240), where /Ep is the heat generated by thermal radiation per unit volume and Qap is the heat transferred through the interface between gas and particles. Thus, once the gas velocity field is solved, the particle velocity, particle trajectory, particle concentration, and particle temperature can all be obtained directly by integrating Eqs. (5.235), (5.237), (5.231), and (5.240), respectively. Since the equations for the gas phase are coupled with those for the solid phase, final solutions of the governing equations may have to be obtained through iterations between those for the gas and solid phases. 

The heat and mass transfer coefficients between gas and particle are computed according to Gnielinski [25]. 

Goedicke, F Nicolai, R., Tanner, H., and Reh, L. Particle Induced Heat Transfer Between Walls and Gas-Solid Fluidized Beds, in Circulating Fluidized Bed Technology IV (Amos A. Avidan, ed.), pp. 356-361. Somerset, Pennsylvania (1993). 

Heat-transfer coefficient, W/m -°C or Btu/ft -h-°F between gas and particle hy, between gas and surface of slab... 

The importance of the intraparticle heat transfer resistance is evident for particles with relatively short contact time in the bed or for particles with large Biot numbers. Thus, for a shallow spouted bed, the overall heat transfer rate and thermal efficiency are controlled by the intraparticle temperature gradient. This gradient effect is most likely to be important when particles enter the lowest part of the spout and come in contact with the gas at high temperature, while it is negligible when the particles are slowly flowing through the annulus. Thus, in the annulus, unlike the spout, thermal equilibrium between gas and particles can usually be achieved even in a shallow bed, where the particle contact time is relatively short. 

Sf, = the source/sink terms due to the combustion of volatiles, radiation, and heat transfer between combusting char particles and gas phase. 

Heat transfer in gas-fluidized bed can occur by conduction, convection, and radiation depending on the operating conditions. The contribution of the respective modes of heat transfer to the coefficient of heat transfer depends on particle classification, flow condition, fluidization regimes, type of distributor, operating temperature, and pressure. Heat transfer between a single particle and gas phase can be defined by the conventional equation of heat transfer ... 

Through a stirring effect and the convective mass transfer caused by the rising bubbles in a fluidized bed, intensive particle motion is observed. This is favorable for the mass and heat transfer between the gas and product and for the heat transfer between product and heat exchanger. Due to good solid mixing an almost uniform tempera-... 

Martin H. Heat transfer between gas fluidized beds of solid particles and the surfaces of immersed heat exchanger elements, part I. Chem Eng Processes 18 157-169, 1984a. 

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