Rectangular flow channels

For gradual changes in channel cross section and hquid depth, and for slopes less than 10°, the momentum equation for a rectangular channel of width b and liquid depth h may be written as a differential equation in the flow direction x. 

The rectangular channels tested have three characteristic dimensions the flow width (which measures 1 in. for all the data shown in Table III), an equivalent heated width (which measures approximately 0.9 in.), and the internal spacing S between the flat heating surfaces. The heated width and the flow width are not the same, due to the way the channels are constructed,... 

J6. Jiji, L. M Incipient boiling and the bubble boundary layer formation over a heated plate for forced convection flow in a pressurized rectangular channel, Ph.D. Thesis, Univ. of Michigan, Ann Arbor, 1962. 

The perimeter is therefore a minimum when the cross-section for flow is a minimum. For a rectangular channel, of depth D and width B ... 

For a liquid which is flowing with a velocity u in a rectangular channel of width B, the depth of liquid is initially D. As a result of a change in conditions at the downstream end of the channel, the level there suddenly increases to some value D2. A wave therefore Lends to move upstream against the motion of the oncoming fluid. For two sections, 1 and 2, one on each side of the wave at any instant, as shown in Figure 3.22. the rate of accumulation of fluid between the two sections is given by ... 

If a liquid is flowing in a rectangular channel in which a hydraulic jump occurs between sections 1 and 2, as shown in Figure 3.23, then the conditions after the jump can be determined by equating the net force acting on the liquid between the sections to the rate of change of momentum, if the frictional forces at the walls of the channel may be neglected. 

A study of forced convection characteristics in rectangular channels with hydraulic diameter of 133-367 pm was performed by Peng and Peterson (1996). In their experiments the liquid velocity varied from 0.2 to 12m/s and the Reynolds number was in the range 50, 000. The main results of this study (and subsequent works, e.g., Peng and Wang 1998) may be summarized as follows (1) friction factors for laminar and turbulent flows are inversely proportional to Re and Re ", respectively (2) the Poiseuille number is not constant, i.e., for laminar flow it depends on Re as PoRe ° (3) the transition from laminar to turbulent flow occurs at Re about 300-700. These results do not agree with those reported by other investigators and are probably incorrect. 

Warrier et al. (2002) conducted experiments of forced convection in small rectangular channels using FC-84 as the test fluid. The test section consisted of five parallel channels with hydraulic diameter = 0.75 mm and length-to-diameter ratio Lh/r/h = 433.5 (Fig. 4.5d and Table 4.4). The experiments were performed with uniform heat fluxes applied to the top and bottom surfaces. The wall heat flux was calculated using the total surface area of the flow channels. Variation of single-phase Nusselt number with dimensionless axial distance is shown in Fig. 4.6b. The numerical results presented by Kays and Crawford (1993) are also shown in Fig. 4.6b. The measured values agree quite well with the numerical results. 

From the visual studies on the flow patterns for circular, trapezoidal and rectangular channels it may be concluded that as the tube diameter decreases, transitions between flow regimes occur at different combinations of superficial gas and liquid velocities. 

Equation (5.26) was developed using the available air-water two-phase flow data obtained in circular and rectangular channels with d = l—A mm. 

Me et al. (2006) addressed the differences in gas-liquid two-phase flow characteristics that occur in conventional size channels and micro-channels by examining the two-phase flow pattern, interfacial wave, void fraction and friction pressure drop data obtained in circular and rectangular channels with a hydraulic diameter ranging from 50 pm to 6.0 mm. 

The heat transfer coefficient of boiling flow through a horizontal rectangular channel with low aspect ratio (0.02-0.1) was studied by Lee and Lee (2001b). The mass flux in these experiments ranged from 50 to 200 kg/m s, maximum heat flux was 15 kW/m, and the quality ranged from 0.15 to 0.75, which corresponds to annular flow. The experimental data showed that under conditions of the given experiment, forced convection plays a dominant role. 

Shuai J, Kulenovic R, DroU M (2003) Heat transfer and pressure drop for flow boiling of water in narrow vertical rectangular channels. In Proceedings for 1st International Conference on Micro-channels, Rochester, New York, 24-25 April 2003, ICMM 2003-1084 Staniszewski BE (1959) Nucleate boihng bubble growth and departure MIT DSR Project N7-7673, Technical Report N16... 

Tran TN, Wambsganss MW, France DM (1996) Small circular and rectangular channel boiling with two refrigerants. Int J Multiphase Flow 22 485-498 Unal HC (1975) Determination of the initial point of net vapor generation in flow boiling system. Int J Heat Mass Transfer 18 1095-1099... 

Landerman (1994) developed an analytical model for two-phase boiling heat transfer in a high aspect ratio rectangular channel. The flow regimes in the channel were mapped and then the heat transfer and wall temperature were evaluated, using heat transfer coefficients taken from the literature. 

The special flow conditions in circular (capillaries, tubes) or rectangular channels cause very different stresses depending on the position of the particles in the flow cross section. With laminar flow, for example the following applies to velocity gradient (see e.g. [37]) ... 

C = 8 applies to circular cross sections. For rectangular channels with large width-to-height ratios b/D >l, C = 6. Equation (14) is valid for pipe flow for Re = u D/v < 2300, the transition point for rectangular channels is at Re = 1500. 

For laminar flow in channels of rectangular cross-section, the velocity profile can be determined analytically. For this purpose, incompressible flow as described by Fq. (16) is assumed. The flow profile can be expressed in form of a series expansion (see [100] and references therein), which, however, is not always useful for practical applications where often only a fair approximation of the velocity field over the channel cross-section is needed. Purday [101] suggested an approximate solution of the form... 

Fully developed laminar flow in curved rectangular channels, J. Fluids Eng. 3 (1976) 42-48. 

This sheet micro flow reactor (Figure 4.32) was used for investigating spatially two-dimensional effects in reaction media using agar gel induced by electric fields [68]. This device utilizes an adapted Petri dish which comprises a rectangular channel... 

Figure 5.6 Flow pattern map for a gas/liquid flow regime in micro channels. Annular flow wavy annular flow (WA) wavy annular-dry flow (WAD) slug flow bubbly flow annular-dry flow (AD). Transition lines for nitrogen/acetonitrile flows in a triangular channel (224 pm) (solid line). Transition lines for air/water flows in triangular channels (1.097 mm) (dashed lines). Region 2 presents flow conditions in the dual-channel reactor ( ), with the acetonitrile/nitrogen system between the limits of channeling (I) and partially dried walls (III). Flow conditions in rectangular channels for a 32-channel reactor (150 pm) (T) and singlechannel reactor (500 pm) (A) [13].

Figure 3.20 Flow patterns for rectangular channels at two different pressures. (From Hosier, 1968. Copyright 1968 by American Institute of Chemical Engineers, New York. Reprinted with permission.)...

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