Polygonal ducts

A quadrilateral duct is shown schematically in Fig. 5.53. Nakamura et al. [278] analyzed fully developed laminar flow and heat transfer in arbitrary polygonal ducts. Their results are presented in Table 5.55. 

Fully developed flow and heat transfer in a regular polygonal duct with n equal sides, each subtending an angle of 360°/n at the duct center, have been reviewed by Shah and London [1]. The /Re and Nu are given in Table 5.56. 

TABLE 5.56 Fully Developed Laminar Flow Characteristics of Regular Polygonal Ducts [1]... 

For practical calculations, Schenkel [279] proposed the following formula to compute the /Re in regular polygonal ducts ... 

Regular Polygonal Ducts With Centered Circular Cores... 

The product of fully developed friction factor and Reynolds number in laminar flow / Re obtained by Ratkowsky and Epstein [296] for polygonal ducts with centered circular cores (see the inset in Fig. 5.65) are shown in Fig. 5.65. The fully developed NuHi obtained by Cheng and Jamil [297] are given in Fig. 5.66. It can be observed that as -> >, the value of/Re approaches 6.222 for a = 1 (annular duct) /Re approaches 16 for a =0 (circular duct). 

FIGURE 5.65 Fully developed friction factors for regular polygonal ducts with centered circular cores and circular ducts with centered rectangular polygonal cores [2]. 

K. C. Cheng, Laminar Forced Convection in Regular Polygonal Ducts with Uniform Peripheral Heat Flux, /. Heat Transfer, (91) 156-157,1969. 

N. Nakamura, S. Hiraoka, and I. Yamada, Flow and Heat Transfer of Laminar Forced Convection in Arbitrary Polygonal Ducts, Heat Transfer-Jpn. Res., (2/4) 56-63,1974. 

D. A. Ratkowsky, and N. Epstein, Laminar Flow in Regular Polygonal Ducts with Circular Centered Cores, Can. J. Chem. Eng., (46) 22-26,1968. 

Assumptions of the Convective Diffusion Model in Regular Polygon Ducts... 

FULLY DEVELOPED FLUID VELOCITY PROFILES IN REGULAR POLYGON DUCTS... 

Unlike porous pellets, it is mathematically feasible to account for chemical reaction on the well-defined catalytic surfaces that bound the flow regime in regular polygon duct reactors. A qualitative description of the boundary conditions is based on a steady-state mass balance over a differential surface element. Since convective transport vanishes on the stationary catalytic surface, the following contributions from diffusion and chemical reaction are equated, with units of moI/(areatime) ... 

Asako, Y., H. Nakamura and M. Fagri. Developing laminar flow and heat transfer in the entrance region of regular polygonal ducts. International Journal of Heat and Mass Transfer 31 2590-2593,1988. 

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