Heat transfer coefficients at the wall

Derive an expression relating the pressure drop for the turbulent flow of a fluid in a pipe to the heat transfer coefficient at the walls on the basis of the simple Reynolds analogy. Indicate the assumptions which are made and the conditions under which you would expect it to apply closely. Air at 320 K and atmospheric pressure is flowing through a smooth pipe of 50 mm internal diameter, and the pressure drop over a 4 m length is found to be 150 mm water gauge. By how much would you expect the air temperature to fall over the first metre if the. wall temperature there is 290 K ... 

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... 

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 heat transfer for a fluid flowing through a circular pipe, the dimensional analysis is detailed in Section 9.4.2 and, for forced convection, the heat transfer coefficient at the wall is given by equations 9.64 and 9.58 which may be written as ... 

Derive an expression relating the pressure drop for the turbulent flow of a fluid in a pipe to the heat transfer coefficient at the walls on the basis of the simple Reynolds analogy. Indicate the assumptions which are made and the conditions under which it would be expected to apply closely. 

A more notable correlation for the heat-transfer coefficient at the wall of mechanically agitated contactors is given by Perry and Chilton (1973) as... 

Mahalingam, M and Ajit, Kumar Kolar. "Experimental Correlation for Average Heat Transfer Coefficient at the Wall of a Circulating Fluidized Bed, in Circulating Fluidized Bed Technology IV (Amos A. Avidan, ed.), pp. 390-395. Somerset, Pennsylvania (1993). 

There is even more uncertainty in estimating the heat-transfer coefficient at the wall of the tube than in estimating the effective thermal conductivity in the bed of catalyst. The measurement is essentially a difficult one, depending either on an extrapolation of a temperature profile to the wall or on determining the resistance at the wall as the difference between a measured over-all resistance and a calculated resistance within the packed bed. The proper exponent to use on the flow rate to get the variation of the coefficient has been reported as 0.33 (C4), 0.47 (C2), 0.5 and 0.77 (HI), 0.75 (A2), and 1.00 (Ql). 

Operating conditions The reactor is 10 cm ID, input of ethylbenzene is 0.069 kg mol/h, input of steam is 0.69 kgmol/h, total of 2,500 kg/h. Pressure is 1.2 bar, inlet temperature is 600°C. Heat is supplied at some constant temperature in a jacket. Performance is to be found with several values of heat transfer coefficient at the wall, including the adiabatic case. 

For non-adiabatic reactors, along with radial dispersion, heat transfer coefficient at the wall between the reaction mixture and the cooling medium needs to be specified. Correlations for these are available (cf. % 10) however, it is possible to modify the effective radial thermal conductivity (k ), by making it a function of radial position, so that heat transfer at the wall is accounted for by a smaller k value near the tube-wall than at the tube center (11). 

TABLE 17.18. Formulas for the Heat Transfer Coefficient at the Walls of Packed Vessels ... 

Liquid holdup is defined as the volume of liquid contained in the bed per unit bed volume. It is a function of the physical properties of the fluid phases and the bed characteristics. It is a basic parameter for reactor design, because it is related to other important parameters, namely, pressure gradient, gas-liquid interfacial area, the mean residence time of the liquid phase, catalyst loading per unit volume, axial dispersion coefficient, mass transfer characteristics, and heat transfer coefficient at the wall, etc. The optimal value of liquid holdup is desirable for better performance of TBR as a high value of liquid holdup will increase mass transfer resistance while too low a value of liquid holdup will decrease the proper utilization of the catalyst bed. Sometimes, the term total liquid saturation (j t) is used to describe the amount of liquid in the bed. It is defined as the volume of liquid present in a unit void volume of the reactor. Thus, the liquid holdup and total liquid saturation are related as ... 

Heat Transfer to the Wall A number of investigations of heat-transfer coefficients at the wall in fluidized beds have been reported, and in all cases the values found for h, were considerably larger than those for an empty tube at the same fluid velocity. Presumably this is because the motion of solid particles near the wall tends to prevent the development of a slow-moving layer or film of gas, and the heat-carrying capacity of the particles themselves as they move between the center and the wall of the reactor is significant. 

Heat-transfer coefficient between reactor and surroundings (if there is a flat temperature proflle or if a radial average temperature is used). Heat-transfer coefficient at the wall (if there is a radial temperature gradient). 

Tsotsas E, Schltinder E (1990) Heat transfer in packed beds with fluid flow remarks on the meaning and the calculation of a heat transfer coefficient at the wall. Chem Eng Sci 45 819-837... 

Also, heat transfer in three-phase fixed-bed reactors has been investigated using a two-dimensional homogeneous model with two parameters [94, 96]—the bed radial effective thermal conductivity and the heat transfer coefficient at the wall ... 

Implicit in Equation (8.5) is that the granular material might be treated as a continuum having average or effective thermo-physical properties from which the heat transfer coefficient at the wall might... 

Dou et al. (1993) measured the convective heat transfer coefficient at the wall of the FFB described above. They used a small heat transfer surface of ih = 3.2 cm, located 5.5 m above the air inlet port. These investigators also obtained measurements of the cross-sectional bed density (p ) at this elevation. Their data, for two mass fluxes of particles, are ... 

Convective cooling of an electrical heater and measuring its temperature according to method B avoids some sources of error, like measuring the heated fluid temperature or the unknown amount of heat dissipated into the substrate. For this reason, many sensors are located on a thin membrane or are fabricated on polymers or on other thermal insulations. This minimizes the parasitic heat loss and increases the sensor s accuracy. The convective heat transfer into the fluid 2f is determined by the heat transfer coefficient at the wall and by the temperature difference. 

When the wall temperature is not a constant, but varies with z, a separate heat balance for the cooling medium has to be formulated. Note that 7 in eq. (8.20c) is the temperature in the bed close to the wall. In the boundary conditions (8.20a) and (8.20b) the gas temperatures have to be averaged over the cross section of the reactor. The heat transfer coefficient at the wall is dependent on the gas flow rate, the particle diameter and the physical constants of the gas. The following correlation is recommoided ... 

We can compare this with the rate of radial heat transport in the bed, by dividing the effective conductivity by the radius of the bed, which gives 208 W/m K. Apparently, the heat transfer coefficient at the wall is rate determining. Still, the influence of the limited rate of radial heat transport on the reaction rate can be considerable. 

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