Rectangular ducts aspect ratio

Therefore, the unified model employs two empirical parameters a and P) and two known parameters b = -I and cTo- Although this empiricism is not desired, the a value in varies from zero in the slip flow regime to an order-one value of o as oo. Finally, the model is adapted to the finite aspect ratio rectangular ducts using a standard aspect ratio correction given in Eq. (7). 

The volumetric flow rate Q (leakage rate) of a fluid in laminar flow through a high aspect ratio (h/w 1) rectangular duct (i.e., the seal volume) of width, w, height, h, and path length, z, in the flow direction is given by ... 

This section describes a spreadsheet to solve for the two-dimensional velocity profile in a rectangular duct. It also determines the factor /Re, given an aspect ratio. The spreadsheet is laid out to correspond to the mesh shown in Fig. D.5. The spreadsheet itself is shown in Fig. D.6. 

The variation of the mean Nusselt number with aspect ratio as given by this program is shown in Fig. 4.13. This Nusselt number is based on the duct height, W. Now, for a rectangular duct, the hydraulic diameter is given by ... 

Variation of Nusselt number with aspect ratio for a rectangular duct... 

For rectangular ducts Kays and Clark (Stanford Univ., Dept. Mech. Eng. Tech. Rep. 14, Aug. 6, 1953) published relationships for heating and cooling of air in rectangular ducts of various aspect ratios. 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. 

Equation 10.59 was solved by Schechter [49] using a variational principle and by Wheeler and Wissler [50] using a numerical method. Wheeler and Wissler also presented an approximate equation for the square duct geometry. Schechter reported approximate velocity profiles for a power law fluid flowing through rectangular ducts having aspect ratios 0.25, 0.50, 0.75, and 1.0. His results may be expressed as follows ... 

The values of a and b depend on the geometry of the duct. Table 10.7 presents these values for a rectangular channel as a function of the aspect ratio a. It is of interest to note that a and b are 0.25 and 0.75 for the circular duct, and that the generalized Reynolds number Re becomes identical to that proposed by Metzner and Reed [26]. 

A number of analytical results are available for fully developed Nusselt values for the laminar flow of power law fluids in rectangular channels having aspect ratios ranging from 0 (i.e., plane parallel plates) to 1.0 (i.e., a square duct). Newtonian results (n = 1) are available for the T, HI, and H2 boundary conditions for the complete range of aspect ratios. Another limiting case for which many results are available is the slug or plug flow condition, which corresponds to n = 0. At other values of n, results are available for plane parallel plates and for the square duct. 

Although the rectangular channel data are somewhat higher (5 to 10 percent) than the circular tube correlation equations, it appears that the circular tube predictions may be used for engineering estimates of the asymptotic heat transfer for rectangular ducts having an aspect ratio of approximately 0.5 to 1.0. 

The Nu and / factors are also dependent upon the duct cross-sectional shape in laminar flow, and are practically independent of the duct shape in turbulent flow. The influence of variable fluid properties on Nu and / for fully developed laminar flow through rectangular ducts has been investigated by Nakamura et al. [57]. They concluded that the velocity profile is strongly affected by the p /p ratio, and the temperature profile is weakly affected by the p /pm ratio. They found that the influence of the aspect ratio on the correction factor (p ,/pm)m for the friction factor is negligible for p /pm < 10. For the heat transfer problem, the Sieder-Tate correlation (n = -0.14) is valid only in the narrow range of 0.4 < p /pm < 4. 

Effect of Aspect Ratio on Conversion in Rectangular Ducts... 

Higher conversion of reactants is obtained in rectangular ducts when the aspect ratio is larger (see Table 23-6). However, for very small Damkohler numbers (i.e., < 5 X 10 ), reactant conversion is independent of aspect ratio (i.e., 1 < <... 

TABLE 23-6 Effect of Aspect Ratio and Damkohler Number on Reactant Conversion for Viscous Flow in Rectangular Ducts"... 

Smaller aspect ratios exert a stronger influence on reactant conversion when the Damkohler number is larger because the comer regions are critically important in the diffusion-controlled regime, where the rate of reactant consumption is governed by its rate of diffusion toward the active surface (see Table 23-6). When the Damkohler number is 10, viscous flow in tubes and rectangular ducts yields comparable graphs of I Abuik vs. when the aspect ratio is 2.3. However, an... 

ASPECT RATIO - The ratio of the length to the width, of a rectangular air grille or duct. 

It can be noticed how the presence of Joule heating reduces the value of the Nusselt number dramatically, while a decrease in the value of the aspect ratio 5 dampens this effect. The value of the Nusselt number for a perfectly flat velocity profile (slug flow) for a rectangular duct, Nujf, is also plotted in Fig. 5 for the rectangular crosssection considered. It is evident that the values of the Nusselt number approach the corresponding Nusf when kDi increases, so much more so the lower the value of M. ... 

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