Triangular Ducts

The critical Reynolds number for transition from laminar to turbulent flow in noncirciilar channels varies with channel shape. In rectangular ducts, 1,900 < Re < 2,800 (Hanks and Ruo, Ind. Eng. Chem. Fundam., 5, 558-561 [1966]). In triangular ducts, 1,600 < Re < 1,800 (Cope and Hanks, Ind. Eng. Chem. Fundam., II, 106-117 [1972] Bandopadhayay and Hinwood, j. Fluid Mech., 59, 775-783 [1973]). 

Chapter 4 is devoted to single-phase heat transfer. Data on heat transfer in circular micro-tubes and in rectangular, trapezoidal and triangular ducts are presented. Attention is drawn to the effect of energy dissipation, axial conduction and wall roughness on the thermal characteristics of flow. Specific problems connected with electro-osmotic heat transfer in micro-channels, three-dimensional heat transfer in micro-channel heat sinks and optimization of micro-heat exchangers are also discussed. 

Heat Transfer in Rectangular, Trapezoidal and Triangular Ducts... 

The laminar flowmeter and its matrix element with miniature triangular duct passage having under 0.1 mm effective diameters. (Courtesy of Meriam Instrument Div. of Scott Fetzer Co.)... 

SOLUTION The view factors associated vvith an infinitely long triangular duct are to be determined. 

A furnace is shaped like a long equilateral triangular duct, as shown in Fig. 13-28. The width of each side is 1 m. The base surface has an emissivity of 0.7 and is maintained at a uniform temperature of 600 K. The heated left-side surface closely approximates a blackbody at 1000 K. The right-side surface is well insulated. Determine the rate at which heat must be supplied to the heated side externally per unit length of the duct in order to maintain these operating conditions. 

A furnace is shaped like a long equilateral-triangular duct where the width of each side is 2 m. Heat is supplied from the base surface, whose emissivity is C = 0.8, at a rale of 800 W/m while the side surfaces, whose emissivities ate 0.5, are maintained at 500 K. Neglecting the end effects, determine Ihe temperature of the base surface. Can you treat this geometry as a two-surface enclosure ... 

Lopez de Bertodano M (1992) Turbulent Bubbly Two-Phase Flow in a Triangular Duct. PhD Thesis, Rensselaer Polytechnic Institute, Troy, NY... 

The solution for an equilateral triangular duct is given as (Spurk, 1997) ... 

The flow and heat transfer characteristics of triangular ducts, as shown in Fig. 5.27, are explained in this section. The coordinates shown in Fig. 5.27 are used in the presentation of the results. 

In this section, the laminar flow and heat transfer characteristics are explained for different triangular ducts. 

FIGURE 5.27 Triangular ducts (a) equilateral (b) equilateral with rounded corners (c) isosceles (d) and (e) right and (/) arbitrary. 

Equilateral Triangular Ducts. For equilateral triangle ducts as shown in Fig. 5.27a, the fully developed laminar flow velocity profile and friction factor have been obtained by Marco and Han [155] ... 

Since sharp triangular ducts are rarely seen in practical use, triangular ducts with rounded corners, such as that presented in Fig. 5.275, have been investigated by Shah [172]. His results are presented in Table 5.38, in which the y and ymaj refer to the distances measured from the duct base to the centroid and to the point of maximum fluid velocity, respectively. 

TABLE 5.38 Fully Developed Laminar Flow and Heat Transfer Characteristics of Equilateral Triangular Ducts With Rounded Corners [172]... 

Isosceles Triangular Ducts. For isosceles triangular ducts like those shown in Fig. 5.27c, the velocity distribution and friction factors for fully developed laminar flow are expressed by the following set of equations suggested by Migay [173] ... 

The fully developed Nusselt numbers NuT and Nuhi for laminar flow in isosceles triangular ducts with one wall or more heated are given in Table 5.40. 

Right Triangular Ducts. For right triangular ducts, shown in Fig. 5.21d and e, the fully laminar developed flow and heat transfer characteristics/Re, (°°), Nuhi, and Nuh2 are given in Fig. 5.28 [2]. The data for this figure were taken from Haji-Sheikh et al. [170], Sparrow and Haji-Sheikh [174], and Iqbal et al. [175]. 

Arbitrary Triangular Ducts. For triangular ducts with arbitrary angles such as that shown in Fig. 5.27/ the fully developed friction factors and Nusselt numbers are presented for fully developed laminar flow in Figs. 5.29 and 5.30 [2]. 

Thermally and Simultaneously Developing Flows. Hydrodynamically developing laminar flow in triangular ducts has been solved by different investigators as is reviewed by Shah and London [1]. Wibulswas [160] obtained a numerical solution for the problem of simultaneously... 

TABLE 5.39 Flow and Heat Transfer Characteristics for Fully Developed Laminar Flow in Isosceles Triangular Ducts [1]... 

TABLE 5.40 Fully Developed Nur and Nu//i for Heat Transfer in Isosceles Triangular Ducts With One Wall or More Walls Heated [1]... 

FIGURE 5.28 Fully developed / Re and Nu for right triangular ducts [2]. 

The lower limit of Recrit is considered to be approximately 2000 in triangular ducts [45]. No reliable results for the friction factor and Nusselt number are available for transition flow in triangular ducts. In this section, the turbulent flow and heat transfer characteristics for equilateral, isosceles, and right triangular ducts are presented. 

TABLE 5.41 Local and Mean Nusselt Numbers for Thermally and Simultaneously Developing Laminar Flows and Equilateral Triangular Ducts [160]... 

Equilateral Triangular Ducts. The friction factor for an equilateral triangular duct has been measured by Altemani and Sparrow [176]. Their data are fitted by the following equation in the region of 4000 < Re < 8 x 104 ... 

These researchers have also obtained the fully developed Nusselt numbers for air (Pr = 0.7) in the range of 4000 < Re < 8 x 104 in an equilateral triangular duct with the boundary condition on two walls and the third wall insulated as follows ... 

Isosceles Triangular Ducts. Bhatti and Shah [45] recommended that the friction factor for fully developed turbulent flow in isosceles triangular ducts can be determined using different correlations. For 0 < 2< ) < 60°, the circular duct correlations in Table 5.8 can be used with Dh replaced by Dgt as defined by Bandopadhayay and Ambrose [177] ... 

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