Diameter ratio, heat transfer

Tray options valve usually cheaper than sieve, use for large-diameter columns at moderate to high pressures, moderate turndown ratio. Usually about 120 to 140 values per active m sieve use for large-diameter columns at moderate to high pressures, moderate turndown ratio bubble cap use for columns with small liquid flow rate, high turndown ratio, heat transfer needed internally. 

Determine the surface geometrical properties on each fluid side. This includes the minimum free flow area A , heat transfer surface area A (both primary and secondary), flow lengths L, hydraulic diameter Dh, heat transfer surface area density P, the ratio of minimum free flow area to frontal area o, fin length and fin thickness for fin efficiency determination, and any specialized dimensions used for heat transfer and pressure drop correlations. 

The field of engineering contains many examples of trade-offs. You have seen some of them in previous courses. In distillation there is the classical trade-off between the number of trays (height) and the reflux ratio (energy and diameter). In heat transfer there is the trade-off between heat exchanger size (area) and pressure drop (pump or compressor work) more pressure drop gives higher heat transfer coefficients and smaller areas but increases energy cost. We have mentioned several trade-offs in this book control valve pressure drop versus pump head, robustness versus performance, etc. 

A. Grab, U. Nowak, M. Schreier, R. Adler, Radial heat transfer in fixed-bed packing with small tube/particle diameter ratios. Heat Mass Transfer, 45, 417-425 (2009). 

Previous one-phase continuum models [22], [23], [24,25] and [l6], which are all based on "large diameter tube heat transfer not extrapolate to narrow diameter tubes. These equations systematically underpredict the overall heat transfer coefficient by 40-50, on average. On the other hand, a one-phase model, employing the proper central core apparent solid conductivity [ 3]f and utilising wall heat transfer data measured on beds,of low tube-to-par tide diameter ratio [8], shows a mean error of only 18. ... 

The dimensionless relations are usually indicated in either of two forms, each yielding identical resiilts. The preferred form is that suggested by Colburn ran.s. Am. In.st. Chem. Eng., 29, 174—210 (1933)]. It relates, primarily, three dimensionless groups the Stanton number h/cQ, the Prandtl number c Jk, and the Reynolds number DG/[L. For more accurate correlation of data (at Reynolds number <10,000), two additional dimensionless groups are used ratio of length to diameter L/D and ratio of viscosity at wall (or surface) temperature to viscosity at bulk temperature. Colburn showed that the product of the Stanton number and the two-thirds power of the Prandtl number (and, in addition, power functions of L/D and for Reynolds number <10,000) is approximately equal to half of the Fanning friction fac tor//2. This produc t is called the Colburn j factor. Since the Colburn type of equation relates heat transfer and fluid friction, it has greater utility than other expressions for the heat-transfer coefficient. 

The drag coefficients for disks (flat side perpendicular to the direction of motion) and for cylinders (infinite length with axis perpendicular to the direclion of motion) are given in Fig. 6-57 as a Function of Reynolds number. The effect of length-to-diameter ratio for cylinders in the Newton s law region is reported by Knudsen and Katz Fluid Mechanics and Heat Transfer, McGraw-Hill, New York, 1958). 

A basic stirred tank design is shown in Fig. 23-30. Height to diameter ratio is H/D = 2 to 3. Heat transfer may be provided through a jacket or internal coils. Baffles prevent movement of the mass as a whole. A draft tube enhances vertical circulation. The vapor space is about 20 percent of the total volume. A hollow shaft and impeller increase gas circulation (as in Fig. 23-31). A splasher can be attached to the shaft at the hquid surface to improve entrainment of gas. A variety of impellers is in use. The pitched propeller moves the liquid axially, the flat blade moves it radially, and inclined blades move it both axially and radially. The anchor and some other designs are suited to viscous hquids. 

Wall-to-bed heat-transfer coefficients were also measured by Viswanathan et al. (V6). The bed diameter was 2 in. and the media used were air, water, and quartz particles of 0.649- and 0.928-mm mean diameter. All experiments were carried out with constant bed height, whereas the amount of solid particles as well as the gas and liquid flow rates were varied. The results are presented in that paper as plots of heat-transfer coefficient versus the ratio between mass flow rate of gas and mass flow rate of liquid. The heat-transfer coefficient increased sharply to a maximum value, which was reached for relatively low gas-liquid ratios, and further increase of the ratio led to a reduction of the heat-transfer coefficient. It was also observed that the maximum value of the heat-transfer coefficient depends on the amount of solid particles in the column. Thus, for 0.928-mm particles, the maximum value of the heat-transfer coefficient obtained in experiments with 750-gm solids was approximately 40% higher than those obtained in experiments with 250- and 1250-gm solids. 

The effect of length to diameter ratio (l/d) on the value of the heat transfer coefficient may be seen in Figure 9.24. It is important at low Reynolds numbers but ceases to be significant at a Reynolds number of about 104. 

Figure 9.24. Effect of length diameter ratio on heat transfer coefficient...

Experiments in annular and slug flow were carried out also by Ghajar et al. (2004). The test section was a 25.4 mm stainless steel pipe with a length-to-diameter ratio of 100. The authors showed that heat transfer coefficient increases with increase in liquid superficial velocity not only in annular, but also in slug flow regimes. 

Scale-up is non-geometric with length/diameter ratios varying from 2 1 to 30 1. The non-geometric scale-up helps to increase heat transfer area as reactor volume increases. 

Convective heat transfer to fluid inside circular tubes depends on three dimensionless groups the Reynolds number. Re = pdtu/ii, the Prandtl number, Pr = Cpiilk where k is the thermal conductivity, and the length-to-diameter ratio, L/D. These groups can be combined into the Graetz number, Gz = RePr4/L. The most commonly used correlations for the inside heat transfer coefficient are... 

A critical value of diameter exists when scaling-up a conventional agitated cylindrical reaction vessel, since the ratio of heat transfer area potential heat release is inversely proportional to diameter. 

If high heat-transfer rates are required, small-diameter tubes are used to increase the surface area to volume ratio. Several tubes may be arranged in parallel, connected to a manifold or fitted into a tube sheet in a similar arrangement to a shell and tube heat exchanger. For high-temperature reactions the tubes may be arranged in a furnace. 

If the Nusselt number given by equation 12.13 is less than 3.5, it should be taken as 3.5. In laminar flow the length of the tube can have a marked effect on the heat-transfer rate for length to diameter ratios less than 500. 

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