Transfer wall heat

Zenz and Othmer (see Introduction General References ) give an excellent summary of fluidized bed-to-wall heat-transfer investigations. 

As can be seen in the table above, the upper two results for heat transfer coefficients hp between particle and gas are about 10% apart. The lower three results for wall heat transfer coefficients, h in packed beds have a somewhat wider range among themselves. The two groups are not very different if errors internal to the groups are considered. Since the heat transfer area of the particles is many times larger than that at the wall, the critical temperature difference will be at the wall. The significance of this will be shown later in the discussion of thermal sensitivity and stability. 

The temperature is approximately 20°F below the 265°F temperature limit. The sections differ by less than 1 F. This is probably just luck because that good a balance is not really necessary. Also, it should be noted that to maintain simplicity the additional factors were ignored, such as the 10°F temperature pickup in the return stream due to internal wall heat transfer. Also, nozzle pressure drops for the exit and return were not used. Balance piston leakage was not used as it was in Example 5-3. When all the factors are used, the pressures for each section would undoubtedly need additional adjustment as would the efficiency. However, for the actual compression process, the values are quite realistic, and for doing an estimate, this simpler approach may be quite adequate,... 

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... 

Obtain by dimensional analysis a functional relationship for the wall heat transfer coefficient for a fluid flowing through a straight pipe of circular cross-section. Assume that the effects of natural convection can be neglected in comparison with those of forced convection. 

Heat transfer problems become more severe as reaction rates are increased and water-to-monomer ratios are reduced. In addition, as reactor sizes are increased for improved process economics, the amount of wall heat transfer surface area per unit volume will drop and result in a lower reactor space-time yield. 

Heat transfer to wall. Heat transfer to wall. 

Once Xy is known, the wall heat transfer coefficient can... 

Mogeson, P., 1983. Fluid to duct wall heat transfer in duct heat storages, Proceedings of the International Conference on Subsurface Heat Storage in Theory and Parctice, Swedish Council for Building Research. 

No and Kazimi (1982) derived the wall heat transfer coefficient for the forced-convective two-phase flow of sodium by using the momentum-heat transfer analogy and a logarithmic velocity distribution in the liquid film. The final form of their correlation is expressed in terms of the Nusselt number based on the bulk liquid temperature, Nuft ... 

No, H. C., and M. S. Kazimi, 1982, Wall Heat Transfer Coefficients for Condensation Boiling in Forced Convection of Sodium, Nuclear Sci. Eng. 57 319-324. (4)... 

Equations (8) are based on the assumption of plug flow in each phase but one may take account of any axial mixing in each liquid phase by replacing the molecular thermal conductivities fc, and ku with the effective thermal conductivities /c, eff and kn eff in the definition of the Peclet numbers. The evaluation of these conductivity terms is discussed in Section II,B,1. The wall heat-transfer terms may be defined as... 

For gas-liquid flows in Regime I, the Lockhart and Martinelli analysis described in Section I,B can be used to calculate the pressure drop, phase holdups, hydraulic diameters, and phase Reynolds numbers. Once these quantities are known, the liquid phase may be treated as a single-phase fluid flowing in an open channel, and the liquid-phase wall heat-transfer coefficient and Peclet number may be calculated in the same manner as in Section lI,B,l,a. The gas-phase Reynolds number is always larger than the liquid-phase Reynolds number, and it is probable that the gas phase is well mixed at any axial position therefore, Pei is assumed to be infinite. The dimensionless group M is easily evaluated from the operating conditions and physical properties. 

The gas-phase wall heat-transfer coefficient can be evaluated by using the gas-phase Reynolds number and Prandtl number in Eq. (33). The thermal conductivities of liquids are usually two orders of magnitude larger than the thermal conductivities of gases therefore, the liquid-phase wall heat-transfer coefficient should be much larger than the gas-phase wall heat-transfer coefficient, and Eq. (34) simplifies to... 

The wall heat flux qmi cannot be evaluated as in Section II,B. Numerous experimental studies on heat transfer in this two-phase forced-convection region have been carried out, and the results of these investigations are usually presented in the form of a correlation for the wall heat-transfer coefficient hmi, which is defined as in Eq. (32b). Most of these correlations fit one of two generalized forms. The first is... 

A, Cross-sectional area of the ft , Wall heat transfer coefficient... 

Wall heat-transfer term for coefficient between droplets... 

The interfacial heat transfer coefficient can be evaluated by using the correlations described by Sideman (S5), and then the dimensionless parameter Ni can be calculated. If the Peclet numbers are assumed to be infinite, Eqs. (30) can be applied to the design of adiabatic cocurrent systems. For nonadiabatic systems, the wall heat flux must also be evaluated. The wall heat flux is described by Eqs. (32) and the wall heat-transfer coefficient can be estimated by Eq. (33) with... 

From this discussion of parameter evaluation, it can be seen that more research must be done on the prediction of the flow patterns in liquid-liquid systems and on the development of methods for calculating the resulting holdups, pressure drop, interfacial area, and drop size. Future heat-transfer studies must be based on an understanding of the fluid mechanics so that more accurate correlations can be formulated for evaluating the interfacial and wall heat-transfer coefficients and the Peclet numbers. Equations (30) should provide a basis for analyzing the heat-transfer processes in Regime IV. 

In many design problems, the determination of a wall heat-transfer coefficient or the heat flux between the tube wall and the fluid mixture is only part of the required information. The pressure drop within the system, the rate of phase change at the gas-liquid interface, the point at which the tube walls become dry, and the holdup of the fluids at each point in the pipe must all be determined. 

Heat Transfer to the Containing Wall. Heat transfer between the container wall and the reactor contents enters into the design analysis as a boundary condition on the differential or difference equation describing energy conservation. If the heat flux through the reactor wall is designated as qw, the heat transfer coefficient at the wall is defined as... 

However, the energy balance equation appropriate for use in this illustration differs from that employed in the previous case because thermal losses through the reactor walls must be accounted for. It will be of the same general form as equation 12.7.48, but with the wall heat transfer coefficient replaced by an overall heat... 

Lints, M., Particle to Wall Heat Transfer in Circulating Fluidized Beds, Ph.D. Dissertation, MIT (1992)... 

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