Wall coefficient

Tube wall coefficient. Heat transfer across the tube wall is described by the Fourier Equation1 ... 

Table 15.4 Tube wall coefficients based on the outer diameter for a variety of metals at 100°C.

Taking the wall coefficient from Table 15.4, the overall heat transfer coefficient can be estimated from ... 

Measurements at the wall of fluidized beds were made by Krishna et al. ( K7,K11), who used an annular cell with varying radial ratios to test the influence of inner tubes on fluidization. Only at low r jr0 values is the inner wall coefficient appreciably higher than the outer wall coefficient (which is itself somewhat lower than in a pipe bed of the same radius). 

Wall coefficients are obtainable from particle-fluid data by a rule of Beek (1962),... 

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.

The two steady-state heat-transfer coefficients, hr and hj, could be further described in terms of the physical properties of the system. The solution-to-wall coefficient for heat transfer, hT in Equation 8.8, is strongly dependent on the physical properties of the reaction mixture (heat capacity, density, viscosity and thermal conductivity) as well as on the fluid dynamics inside the reactor. Similarly, the wall-to-jacket coefficient for heat transfer, hj, depends on the properties and on the fluid dynamics of the chosen cooling liquid. Thus, U generally varies during measurements on a chemical reaction mainly for the following two reasons. 

Definitions Nu = h dp/kf, Pr = Cpfi/k)f, h =, wall coefficient, dp = particle diameter = 6VplAp, kf = fluid molecular conductivity, E = porosity. Re = dpG/fi, G = superficial mass velocity per unit cross section. 

Bed-to-wall coefficients in dilute-phase transport generally can be predicted by an equation of the form of Eq. (5-50). For example,... 

Coefficient of heat transfer of tube wall Coefficient of heat transfer of fouling inside the tube... 

The wall coefficient is usually correlated as a Nusselt number equation, i.e. 

Static contribution to wall coefficient (two-dimensional model) 15-100 W/m K... 

Heat transfer coefficient for a one-dimensional model (ht) Wall coefficient for a two-dimensional model (/ ,) Radial Peclet number for mass dispersion ((Pe)r)... 

Substituting our Moody friction factor into Eq. (13.B.2), we find that n = 7.5. This leads to the flow ratio QbIQf = vb)/ vf) = 1-28. Thus, due to the nonuniform velocity gradient in the inlet ducting, the back cyclones will experience about 30% more vapor flow than the two front cyclones. It is interesting to note that the computed value of the coefficient n, 7.5, is not too different from the Law of the Wall coefficient of 7 often used to describe the velocity profile in fully developed turbulent flow within pipes. 

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