Equivalent diameter, heat

Maxwell s law 594 Equivalent diameter, heat exchanger 528 Erosion 194... 

Laminar Flow Normally, laminar flow occurs in closed ducts when Nrc < 2100 (based on equivalent diameter = 4 X free area -i-perimeter). Laminar-flow heat transfer has been subjected to extensive theoretical study. The energy equation has been solved for a variety of boundaiy conditions and geometrical configurations. However, true laminar-flow heat transfer veiy rarely occurs. Natural-convecdion effects are almost always present, so that the assumption that molecular conduction alone occurs is not vahd. Therefore, empirically derived equations are most rehable. 

Limiting Nusselt numbers for laminar flow in annuli have been calculated by Dwyer [Nucl. Set. Eng., 17, 336 (1963)]. In addition, theoretical analyses of laminar-flow heat transfer in concentric and eccentric annuh have been published by Reynolds, Lundberg, and McCuen [Jnt. J. Heat Ma.s.s Tran.sfer, 6, 483, 495 (1963)]. Lee fnt. J. Heat Ma.s.s Tran.sfer, 11,509 (1968)] presented an analysis of turbulent heat transfer in entrance regions of concentric annuh. Fully developed local Nusselt numbers were generally attained within a region of 30 equivalent diameters for 0.1 < Np < 30, lO < < 2 X 10, 1.01 <... 

For rectangular ducts Kays and Clark (Stanford Univ, Dept. Mech. Eng. Tech. Rep. 14, Aug. 6, 1953) published relationships for headng and cooling of air in rectangular ducts of various aspect rados. For most noncircular ducts Eqs. (5-39) and (5-40) may be used if the equivalent diameter (= 4 X free area/wetted perimeter) is used as the characteristic length. See also Kays and London, Compact Heat Exchangers, 3d ed., McGraw-Hill, New York, 1984. 

Noncircular Ducts Equations (5-50 ) and (5-50/ ) may be employed for noncircular ducts by using the equivalent diameter D = 4 X free area per wetted perimeter. Kays and London (Compact Heat Exchangers, 3rd ed., McGraw-HiU, New York, 1984) give charts for various noncircular duels encountered in compact heat exchangers. 

Most efficient performance is obtained with plates having open areas equal to 2 to 3 percent of the total heat-transfer area. The plate should be located at a distance equal to four to six hole (or equivalent) diameters from the heat-transfer surface. 

Figure 10-56. Equivalent diameter for tubes on shell side of exchanger taken along the tube axis, (a) Square pitch, (b) triangular pitch on 60° equilateral angles. (Used by permission Kern, D. Q. Process Heat Transfer, V Ed., 1959. McGraw-Hill, Inc. All rights reserved.)...

This unit consists of two pipes or tubes, the smaller centered inside the larger as shown in Figure 10-92. One fluid flows in the annulus between the tubes the other flows inside the smaller tube. The heat transfer surface is considered as the outside surface of the inner pipe. The fluid film coefficient for the fluid inside the inner tube is determined the same as for any straight tube using Figures 10-46-10-52 or by the applicable relations correcting to the O.D. of the inner tube. For the fluid in the annulus, the same relations apply (Equation 10-47), except that the diameter, D, must be the equivalent diameter, D,.. The value of h obtained is applicable directly to the point desired — that is, the outer surface of the inner tube. ... 

The outer and inner tubes extend from separate stationary tube sheets. The process fluid is heated or cooled by heat transfer to/from the outer tube s outside surface. The overall heat transfer coefficient for the O.D. of the inner tube is found in the same manner as for the double-pipe exchanger. The equivalent diameter of the annulus uses the perimeter of the O.D. of the inner tube and the I.D. of the inner tube. Kem presents calculation details. 

Having obtained an accurate correlation for the annulus data at 1000 psia, Barnett applied it, for the same pressure, to the rod-bundle data, and Figs. 36 and 37 are two very convincing demonstrations of the connection that clearly exists between an annulus and a rod bundle. The method used in applying the annulus correlation was to assume a dt value equal to the diameter of the rods in the bundle considered, and a d0 value such that both annulus and bundle had the same heated equivalent diameter dh. All the normal rod-bundle data with vertical upflow were found to be well represented by the annulus correlation, but the nonnormal data showed the same disparity that was found in the rod-bundle analysis. Thus, we have a further indication that the non-normal rod bundles are showing markedly different burn-out behavior. 

The connection that has been shown in Section VIII to exist between burn-out in a rod bundle and in an annulus leads to the question of whether or not a link may also exist between, for example, a round tube and an annulus. Now, a round tube has its cross section defined uniquely by one dimension—its diameter therefore if a link exists between a round tube and an annulus section, it must be by way of some suitably defined equivalent diameter. Two possibilities that immediately appear are the hydraulic diameter, dw = d0 — dt, and the heated equivalent diameter, dh = (da2 — rf,2)/ however, there are other possible definitions. To resolve the issue, Barnett (B4) devised a simple test, which is illustrated by Figs. 38 and 39. These show a plot of reliable burn-out data for annulus test sections using water at 1000 psia. Superimposed are the corresponding burn-out lines for round tubes of different diameters based on the correlation given in Section VIII. It is clearly evident that the hydraulic and the heated equivalent diameters are unsuitable, as the discrepancies are far larger than can be explained by any inaccuracies in the data or in the correlation used. 

For the heat transfer for fluids flowing in non-circular ducts, such as rectangular ventilating ducts, the equations developed for turbulent flow inside a circular pipe may be used if an equivalent diameter, such as the hydraulic mean diameter de discussed previously, is used in place of d. 

The correlation for forced convective heat transfer in conduits (equation 12.10) can be used to predict the heat transfer coefficient in the annulus, using the appropriate equivalent diameter ... 

The heat transfer coefficient to the vessel wall can be estimated using the correlations for forced convection in conduits, such as equation 12.11. The fluid velocity and the path length can be calculated from the geometry of the jacket arrangement. The hydraulic mean diameter (equivalent diameter, de) of the channel or half-pipe should be used as the characteristic dimension in the Reynolds and Nusselt numbers see Section 12.8.1. 

Steady two-phase flow. In rod (or tube) bundles, such as one usually encounters in reactor cores or heat exchangers, the pressure drop calculations use the correlations for flow in tubes by applying the equivalent diameter concept. Thus, in a square-pitched four-rod cell (Fig. 3.51), the equivalent diameter is given by... 

It should also be noted that in single-phase flow heat transfer, the effect of channel size is expressed by equivalent diameter. This concept, however, should be... 

For the forced convective region, only limited data are available on the effects of the different variables involved, since the existence of this region has only been recognized recently. As previously mentioned, the velocity required for the suppression of nucleate boiling increases with pressure further, an increase in pressure reduced the specific volume of the vapour and hence the linear velocity of the two phase mixture at a given quality will be reduced. Thus higher velocities and steam qualities would be required for the forced convective region to be entered at the same heat flux. The effect of diameter is, as far as can be seen from the work of previous experiments and from these experiments, that to be expected with convective heat transfer, namely, that the coefficient is proportional to the diameter or the equivalent diameter to the power —02. 

Calculate the equivalent diameter of the annular space of a double tube-type heat exchanger. The outside diameter of the inner tube d is 4.0 cm and the inside diameter of the outer tube is 6.0 cm. 

In the case where the fluid flow is parallel to the tubes, as in a shell-and-tube heat exchanger without transverse baffles, the equivalent diameter d of the shell side space is calculated as mentioned above, and h at the outside surface of tubes can be estimated by Equation 5.8a with the use of d. ... 

In the case that the cross section of the channel is not circular, the equivalent diameter d defined by Equations 5.10 and 5.11 should be used in place of d- As with heat transfer, taking the wetted perimeter for mass transfer rather than the total wetted perimeter provides a larger value of the equivalent diameter and hence a lower value of the mass transfer coefficient. The equivalent diameter of the channel between two parallel plates or membranes is twice the distance between the plates or membranes, as noted in relation to Equation 5.11. 

The shell-side heat-transfer coefficient in the Kern method is calculated using Equation 10.2. An equivalent diameter is calculated which is representative of the shell-side fluid passage geometry. Equation 10.2 therefore becomes ... 

The equivalent diameter of the annular jacket geometry is the jacket clearance. If the wall thickness is 0.003 m and the thermal conductivity of the metal is 45 J s 1 K-1 m-2, the overall heat transfer coefficient for the circulating water system is U = 700 J s 1 K 1 m-2. 

The heat transfer coefficient h was calculated according to Hand-ley and Heggs (24) with the Reynolds number based upon an equivalent diameter, namely that of a sphere with the same volume as the actual particle. The overall heat transfer coefficient U was calculated from the heat transfer parameters of the two dimensional pseudohomogeneous model (since the interfacial At was found to be negligible), to allow for a consistent comparison with two dimensional predictions and to try to predict as closely as possible radially averaged temperatures in the bed (25). Therefore ... 

The alloy is failed during some cycles of hydrogen sorption - desorption and turns into powder with particles 3-4 microns. The specific surface of such powder can be estimated with assumption of their spherical shape a (1.5-2.0 microns) with equivalent diameter of a particle ded=4s/[ 0(l- )]=1.3-1.6 microns. These values can be used in calculations of gas dynamics of hydrogen flow and heat exchange in a layer. 

When dealing with noncircular ducts it is common to assume that the equations for the heat transfer rate for a circular pipe can be applied to the noncircular duct provided that the correct equivalent diameter is used for the noncircular duct. Now for a circular pipe ... 

The situation is often encountered in which a fluid flows through a conduit having a noncircular cross section, such as an annulus. The heat-transfer coefficients for turbulent flow can be determined by using the same equations that apply to pipes and tubes if the pipe diameter D appearing in these equations is replaced by an equivalent diameter De. Best results are obtained if... 

The difference between the hydraulic radii for heat transfer and for fluid flow should be noted. In the preceding example, the correct equivalent diameter for evaluating friction due to the fluid flow in the annulus would be four times the cross-sectional flow area divided by the wetted perimeter, or 4 x(ttD /4-ttD /4)/(ttD2 + ttD = D2 - D,. 

Dc = clearance between tubes to give smallest free area across shell axis, ft De = equivalent diameter = 4 x hydraulic radius, ft E = power loss per unit of outside-tube heat-transfer area, ft lbf/(hXft2) subscript i designates inside tubes, and subscript o designates outside tubes... 

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