Convection overall coefficient

Figure 5-24B. Forced convection past heat transfer surfaces improves the overall coefficient of heat transfer. By permission, Weber, A. R, Chem. Engr., Oct. 1953, p. 183 [23].

Now that the overall coefficient U has been broken down into its component parts, each of the individual coefficients /q, hi, and hi must be evaluated. This can be done from a knowledge of the nature of the heat transfer process in each of the media. A study will therefore be made of how these individual coefficients can be calculated for conduction, convection, and radiation. 

U = overall coefficient of heat transfer, gas convection to refractory wall to ambient air. 

T = absolute temperature. Subscript 1 (or G), radiating surface (or gas) temperature subscript E, exit-gas subscript o, base temperatme subscript F, pseudoadiabatic flame temperature based on C averaged from to Te-V = overall coefficient of heat transfer, gas convection to refractory wall to ambient air. 

The hg involves convection and gas radiation to or from a surface, and it is like two resistances in parallel, thus hg = he + hr. Similar to Ohm s Law, (/ = E/Rt), heat flux, q = Q/A = ATfR, or g — UAAT, which is the basic equation of heat transfer. Example 5.1 illustrates the method for calculating U, the overall coefficient of heat transfer. 

Increasing temperature has two effects (1) by decreasing gas density, the gas convective component of heat transfer is decreased slightly, and (2) by increasing the thermal conductivity of the gas, the effectivness of packets of emulsion phase in contact with the transfer surface is increased. The overall effect for Group A and B powders is to increase the convective transfer coefficient as was shown by Botterill and Teoman (1980). In the case of Group D powders where the gas convective... 

The heat-transfer coefficient of most interest is that between the bed and a wall or tube. This heat-transfer coefficient, is made up of three components. To obtain the overall dense bed-to-boiling water heat-transfer coefficient, the additional resistances of the tube wall and inside-tube-waH-to-boiling-water must be added. Generally, the conductive heat transfer from particles to the surface, the convective heat transfer... 

The overall heat transfer coefficient, U, is a measure of the conductivity of all the materials between the hot and cold streams. For steady state heat transfer through the convective film on the outside of the exchanger pipe, across the pipe wall and through the convective film on the inside of the convective pipe, the overall heat transfer coefficient may be stated as ... 

A fire tube contains a flame burning inside a piece of pipe which is in turn surrounded by the process fluid. In this situation, there is radiant and convective heat transfer from the flame to the inside surface of the fire tube, conductive heat transfer through the wall thickness of the tube, and convective heat transfer from the outside surface of that tube to the oil being treated. It would be difficult in such a simation to solve for the heat transfer in terms of an overall heat transfer coefficient. Rather, what is most often done is to size the fire tube by using a heat flux rate. The heat flux rate represents the amount of heat that can be transferred from the fire tube to the process per unit area of outside surface of the fire tube. Common heat flux rates are given in Table 2-11. 

Overall, the RDE provides an efficient and reproducible mass transport and hence the analytical measurement can be made with high sensitivity and precision. Such well-defined behavior greatly simplifies the interpretation of the measurement. The convective nature of the electrode results also in very short response tunes. The detection limits can be lowered via periodic changes in the rotation speed and isolation of small mass transport-dependent currents from simultaneously flowing surface-controlled background currents. Sinusoidal or square-wave modulations of the rotation speed are particularly attractive for this task. The rotation-speed dependence of the limiting current (equation 4-5) can also be used for calculating the diffusion coefficient or the surface area. Further details on the RDE can be found in Adam s book (17). 

The heat transfer term envisions convection to an external surface, and U is an overall heat transfer coefficient. The heat transfer area could be the reactor jacket, coils inside the reactor, cooled baffles, or an external heat exchanger. Other forms of heat transfer or heat generation can be added to this term e.g, mechanical power input from an agitator or radiative heat transfer. The reactor is adiabatic when 7 = 0. 

In preliminary design, the heat duty and furnace efficiency are the prime considerations. However, if the tube area needs to be specified, a preliminary estimate can be obtained from an assumed flux. In the radiant section, this usually lies in the range of 45,000 W m-2 to 65,000 W m 2 of tube surface, with a value of around 55,000 W m 2 most often used. The heat flux is particularly important if a reaction is being carried out in the furnace tubes. Overall heat transfer coefficients in the convection section are in the range 20 to 50 W m-2 K-1. 

The heat transfer from tubes in the freeboard was also measured for the 20 MW model. Figure 45 shows a comparison of the measured overall heat transfer coefficient in the 20 MW pilot plant versus that predicted from the scale model test. When the bed height is lowered, uncovering some tubes, the heat transfer is reduced because there are fewer particles contacting the tube surface. Although the scale model did not include proper scaling for convective heat transfer, the rate of change of the overall heat transfer should be a function of the hydrodynamics. 

In general, gas-to-particle or particle-to-gas heat transfer is not limiting in fluidized beds (Botterill, 1986). Therefore, bed-to-surface heat transfer coefficients are generally limiting, and are of most interest. The overall heat transfer coefficient (h) can be viewed as the sum of the particle convective heat transfer coefficient (h ), the gas convective heat transfer coefficient (h ), and the radiant heat transfer coefficient (hr). 

Overall bed-to-surface heat transfer coefficient = Gas convective heat transfer coefficient = Particle convective heat transfer coefficient = Radiant heat transfer coefficient = Jet penetration length = Width of cyclone inlet = Number of spirals in cyclone = Elasticity modulus for a fluidized bed = Elasticity modulus at minimum bubbling = Richardson-Zaki exponent... 

With the above functions and empirical correlations, it becomes possible to calculate the overall convective heat transfer coefficient hc by Eqs. (16, 4, and 22-24). Figure 26 shows a plot presented by Lints and Glicksman which compares predictions by this method with experimental data from several different sources. Reasonably good agreement is obtained over a range of bed densities corresponding to approximately 0.5 to 3% volumetric solid concentration. 

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