Channel rectangular channels

Equation (6.27) was obtained for circular channels. Rectangular channels with four or three conductive walls are shown in Eig. 6.10. 

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. 

Effectively what Barnett (B3) did was to confirm the validity of Eq. (18) using burn-out data for water in round tubes. Subsequently, Eq. (18) was applied to more extensive round-tube data (M3, Tl), to annuli (B6), rectangular channels (M3), and rod-bundle arrangements (M4), using simple mathematical expressions for A and C, and a consistently high accuracy was achieved. Details of the respective correlations obtained are given in Section VIII. 

Comparatively few burn-out data have been published for rectangular channel geometries most of these were produced before 1958, and have been compiled by De Bortoli (D2). The limited range of the system parameters are shown in Table III, indicating that they mostly refer to a pressure of 2000 psia. 

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,... 

Range of System Parameters for Burn-Out in Rectangular Channels Uniformly Heated (Lengthwise) with Liquid Water Inlet ... 

D2. De Bortoli, R. A., Green, S. J., Le Tourneau, B. W., Troy, M., and Weiss, A., Forced convection heat transfer burnout studies for water in rectangular channels and round tubes at pressure above 500 psia, WAPD-188 (1958). 

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. 

M3. Macbeth, R. V., Burnout analysis. 4. Application of a local conditions hypothesis to world data for uniformly heated round tubes and rectangular channels, AEEW-R.267 (1963). 

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. 

The heat transfer and pressure drop in a rectangular channel with sintered porous inserts, made of stainless steels of different porosity, were investigated. The experimental set-up is shown in Fig. 2.9. Heat fluxes up to 6MW/m were removed by using samples with a porosity of 32% and an average pore diameter of 20 pm. Under these experimental conditions, the temperature difference between the wall and the bulk water did not exceed AT = 55 K at a pressure drop of AP = 4.5 bars (Hetsroni et al. 2006a). 

Figure 2.48 compares the predictions of this correlation with the flow boiling CHF data for water both in the rectangular micro-channel heat sink (Qu and Mudawar 2004) and in the circular mini/micro-channel heat sinks (Bowers and Mudawar 1994). The overall mean absolute error of 4% demonstrates its predictive capability for different fluids, circumferential heating conditions, channel geometries, channel sizes, and length-to-diameter ratios. 

Pfund et al. (2000) studied the friction factor and Poiseuille number for 128-521 pm rectangular channels with smooth bottom plate. Water moved in the channels at Re = 60—3,450. In all cases corresponding to Re < 2,000 the friction factor was inversely proportional to the Reynolds number. A deviation of Poiseuille number from the value corresponding to theoretical prediction was observed. The deviation increased with a decrease in the channel depth. The ratio of experimental to theoretical Poiseuille number was 1.08 0.06 and 1.12 zb 0.12 for micro-channels with depths 531 and 263 pm, respectively. 

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. 

It appears that the Poiseuille number in a rectangular channel depends on the aspect ratio, e. In order to reveal an explicit form of the dependence (p e), it is necessary to solve the problem defined by Eqs. (3.8) and (3.9) to obtain... 

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. 

Qu and Mudawar (2002) Rectangular channel 0.231x0.713 130-1,440 De-ionized water 200-2,000 0.12... 

The thermal balance equation for rectangular channels with four or three heated walls shown in Fig. 6.10 are ... 

Fig. 6.10 Rectangular channels (a) four heated walls, (b) three heated walls...

If the value of rB,oNB Ts, (D -c 1) the integral characteristics for the circular channels, the rectangular channels with four and three heated walls, respectively,... 

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