Wall heat transfer coefficients

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. 

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. 

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

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)... 

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... 

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. 

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... 

When we want to look at the connection between the flow behavior and the amount of heat that is transferred into the fixed bed, the 3D temperature field is not the ideal tool. We can look at a contour map of the heat flux through the wall of the reactor tube. Fig. 19 actually displays a contour map of the global wall heat transfer coefficient, h0, which is defined by qw — h0(Tw-T0) where T0 is a global reference temperature. So, for constant wall temperature, qw and h0 are proportional, and their contour maps are similar. The map in Fig. 19 shows the local heat transfer coefficient at the tube wall and displays a level of detail that would be hard to obtain from experiment. The features found in the map are the result of the flow features in the bed and the packing structure of the particles. 

Temperature inside the furnace at the wall Air temperature outside wall Heat transfer coefficients Outside air film (h)... 

De Wasch and Froment (1971) discuss the calculation of the wall heat transfer coefficients for the fluid and gas phases based on a lumped wall heat transfer coefficient. Furthermore, radial heat conduction in the thermal well is neglected since it should be of minor importance for a thin solid well. 

Modeling of the packed bed catalytic reactor under adiabatic operation simply involves a slight modification of the boundary conditions for the catalyst and gas energy balances. A zero flux condition is needed at the outer reactor wall and can be obtained by setting the outer wall heat transfer coefficients /iws and /iwg (or corresponding Biot numbers) equal to zero. Simulations under adiabatic operation do not significantly alter any of the conclusions presented throughout this work and are often used for verification... 

De Wasch and Froment (1971) and Hoiberg et. al. (1971) published the first two-dimensional packed bed reactor models that distinguished between conditions in the fluid and on the solid. The basic emphasis of the work by De Wasch and Froment (1971) was the comparison of simple homogeneous and heterogeneous models and the relationships between lumped heat transfer parameters (wall heat transfer coefficient and thermal conductivity) and the effective parameters in the gas and solid phases. Hoiberg et al. (1971)... 

Develop an analysis to determine the nondimensional wall heat transfer coefficient (i.e., a Nusselt number). Define the heat-transfer coefficient in the ordinary way as... 

Figure 1736. Effective thermal conductivity and wall heat transfer coefficient of packed beds. Re = dpG/fi, dp = 6Vp/Ap, s -porosity, (a) Effective thermal conductivity in terms of particle Reynolds number. Most of the investigations were with air of approx. kf = 0.026, so that in general k elk f = 38.5k [Froment, Adv. Chem. Ser. 109, (1970)]. (b) Heat transfer coefficient at the wall. Recommendations for L/dp above 50 by Doraiswamy and Sharma are line H for cylinders, line J for spheres, (c) Correlation of Gnielinski (cited by Schlilnder, 1978) of coefficient of heat transfer between particle and fluid. The wall coefficient may be taken as hw = 0.8hp.

For many years I have carried around with me two sheets of notepaper that contain heat-exchange coefficient equations. These equations calculate the inside and outside tube wall heat-transfer coefficients for... 

The static contribution l. , incorporates heat transfer by conduction and radiation in the fluid present in the pores, conduction through particles, at the particle contact points and through stagnant fluid zones in the particles, and radiation from particle to particle. Figure 19-20 compares various literature correlations for the effective thermal conductivity and wall heat-transfer coefficient in fixed beds [Yagi and Kunii, AlC hE J. 3 373(1957)]. 

The wall heat transfer coefficients were evaluated from a relation by Hennecke and Schlunder [20]. In our particular case we obtained a value of a = 62 Wm-2K-1 for the reactor in Figure 10 and a s 42 Wm-2 K 1 for the one in Figure 11. ... 

---