Heat transfer particle to fluid

Particle-to-fluid heat-transfer coefficients in gas fluidized beds are predicted by the relation (Zenz and Othmer, op. cit.)... 

Following the form suggested by Equation (14.14), heat transfer to the fluid phase can be estimated by the Yoshida et al. (1962) correlations for particle to fluid heat transfer coefficients ... 

Investigator Type of correlation Phases involved Correlation equation Range of applicability Ranz and Marshall [26] Particle-to-fluid heat transfer (single-particle system) Fluid-solid Nu = 2 + 0.6Rep 2 Pr1/3 Re, > 50... 

Wakao N, Kaguei S, Funazkri T. Effect of fluid dispersion coefficients on particle-to-fluid heat transfer coefficients in packed beds. Correlation of nusselt numbers. Chemical Engineering Science 1979 34(3) 325-336. 

Mears [97] found that the reaction rates in fixed-bed catalytic reactors are highly affected by two heat transfer resistances resistance to radial heat transfer and resistance to particle-to-fluid heat transfer. Considerable effort has therefore been directed toward finding the effective radial conductivity and the fluid-to-wall heat transfer coefficient (which represents the radial heat transport) and particle-liquid heat transfer coefficient (which represents particle-to-fluid heat transport). 

Holman IP, Moore W, Wong VM. Particle-to-fluid heat transfer in water-fluidized systems. Ind Eng Chem Fundam 4 21-31, 1965. 

IV. Particle-to-fluid heat transfer in tubular reactors... 

Fig. 7 shows clearly that for Peclet numbers less than 10 to 10, depending on the number of particle layers, the average particle-to-fluid heat transfer is entirely hydraulically controlled, which means that the number of transfer units is independent of the suface area per unit volume. Independent of the fluid flow rate as well as of the thermal properties of the fluid. 

At the present state these correlations together with Eq. 23 for the prediction of the apparent heat conductivity amd Eq. 6, 7 for the particle-to-fluid heat transfer may be recommended for application in tubular reactor design. These correlations give fairly reliable parameters for either homogeneous or heterogeneous one or two dimensional models for the mathematical simulation of packed bed reactors. 

H. Martin 1978, (Low Peclet number particle-to-fluid heat and mass transfer in packed beds), Chem. Eng. Sci. 33, 913-919. 

Lints, M. C., and Glicksman, L. R., Parameters Governing Particle-to-Wall Heat Transfer in a Circulating Fluidized Bed, Circ. Fluid. Bed Tech. IV, 297-304 (19923)... 

There is conflicting evidence regarding the extent to which imposed vibrations increase particle to fluid heat and mass transfer rates (G2), with some authors even claiming that transfer rates are decreased. For sinusoidal velocity variations superimposed on steady relative motion, enhancement of transfer depends on a scale ratio A/d and a velocity ratio Af /Uj (G3). These quantities are rather like the scale and intensity of turbulence (see Chapter 10). For Af /Uj < l/2n, the vibrations do not cause reversal in the relative motion and the enhancement of mass transfer has been correlated (G3) by... 

When strongly exothermic or endothermic reactions occur in the catalyst pellet, the temperature cannot be regarded as uniform throughout the catalyst particle. To describe heat transfer through a catalyst particle it is usually considered to be homogeneous. So, the heat flow is described by the conventional heat conduction equation used for isotropic solids or stagnant fluids. When chemical reactions take place, the energy balance equation is... 

Gravitational settling of particle in fluid Flow of viscoelastic fluid Pressure and momentum in fluid Unsteady state heat transfer/mass transfer Fluid flow with free surface Gravitational settling of particle in fluid Heat transfer by natural convection Heat transfer to fluid in tube Flow of fluid exhibiting yield stress... 

Developed for a single wet particle, taking into account the resistance of the liquid vapors around the particle to the heat transfer by Spalding number, B. Cp denotes the heat capacity of the liquid vapors in the gas phase and Hfg is the latent heat of evaporation for the fluid. 

Nelson, P. A., Galloway, T. R., Particle to fluid heat and mass transfer in dense systems of fine particles. Chemical Engineering Science, 1975, 30(1), 1... 

Hughmark employed this u to derive a correlation for Son and Hanratty (1967) and Hughmark (1971,1974) correlated wall to fluid heat transfer in pipe flow based on the relatively simple and well-established boundary layer theory. In the case of pipe flow, momentum transfer is solely by skin friction because of the geometry involved. Nonetheless, this approach was extended to particle-fluid mass transfer in turbulent flow. The correlation proposed was of the following form ... 

Wakao, N., Particle-to-fluid heat/mass transfer coefficients in packed bed catalytic reactors, in Recent Advances in the Engineering Analysis of Chemically Reacting Systems (Ed. L.K. Doraiswamy), Wiley Eastern, New Delhi, 1984. 

An important mixing operation involves bringing different molecular species together to obtain a chemical reaction. The components may be miscible liquids, immiscible liquids, solid particles and a liquid, a gas and a liquid, a gas and solid particles, or two gases. In some cases, temperature differences exist between an equipment surface and the bulk fluid, or between the suspended particles and the continuous phase fluid. The same mechanisms that enhance mass transfer by reducing the film thickness are used to promote heat transfer by increasing the temperature gradient in the film. These mechanisms are bulk flow, eddy diffusion, and molecular diffusion. The performance of equipment in which heat transfer occurs is expressed in terms of forced convective heat transfer coefficients. 

A certain amount of information on particle-to-liquid and bed-to-wall heat transfer is available for single-phase fluid flow through a packed bed. It is not clear, however, to what extent this information can be applied to... 

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