Heat transfer coefficient particle-bulk fluid

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. 

Here jh — ( ioo/Cph( ) (Cp(i/A )fand hioc is the local heat-transfer coefficient G is the superficial mass velocity the subscript f denotes properties evaluated at the film temperature Tt = i Ts + Ty,). Here Ts refers to the surface temperature and Th to the bulk fluid temperature. The quantity l/ is an empirical coefficient that depends on the particle shape, e.g., yp = 1.0 for spheres and yp = 0.91 for cylinders. Values of yp for other shapes are tabulated elsewhere (B2, B3). 

Average transport coefficients for transfer between the bulk-fluid and particle surface can be correlated in terms of dimensionless groups that characterize the flow conditions. It is common practice to correlate experimental data in terms of y -factors. Usually, the mass transfer coefficient is obtained from the j factor for mass the heat transfer coefficient is obtained from j factor analogy. There have been many experimental studies of mass transfer in fixed-beds and summaries and analyses of the results are available (Whitaker 1972 Dwivedi and Upadhay 1977). For Reynolds numbers greater than 10, the following relationship (Dwivedi and Upadhay 1977) between jo and the Reynolds number represents available data ... 

The magnitude of the resistances to heat and mass transfer through the boundary layer, i.e., the thickness of the boundary layer, depends on the velocity of the fluid relative to the catalyst particle. As this velocity increases, the heat-transfer coefficient between the bulk fluid and the surface of the catalyst particle increases and the mass-transfer coefficient between the bulk fluid and the catalyst surface increases. Therefore, the magnitude of the concentration and temperature differences between the bulk fluid and the particle surface will depend on the relative velocity, as well as on the properties of the fluid. 

Heat Transfer Let q be the heat flux from the bulk fluid to the surface of the catalyst particle (energy/area-time) and let h be the heat-transfer coefficient (energy/area-time-temperature) between the bulk fluid and the external surface. The flux of energy arriving at the external surface of the catalyst particle is given by... 

The pore diffusivity used in this analysis was determined by the Renkin equation4, the axial dispersion coefficient calculated by assuming a constant Peclet number of 0.2, and the mass transfer coefficient from the bulk to the particle surface calculated by the correlation of Wakao and Kaguei. The product of the heat capacity and density of the solid phase was taken to be the same as that used by Raghavan and Ruthven17. The density of the fluid phase was assumed to be that of pure C02 and was calculated from data provided by the Dionix Corporation in their AI-450 SFC software. Constant pressure heat capacities for the mobile phase were also assumed to be that of pure C02 and were taken from Brunner3. 

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