Uniform heat flux

NUh2 is the Nusselt number for uniform heat flux boundary condition along the flow direction and periphery. 

Cracking reactions are endothermic, 1.6—2.8 MJ/kg (700—1200 BTU/lb) of hydrocarbon converted, with heat supplied by firing fuel gas and/or fuel oil in side-wall or floor burners. Side-wall burners usually give uniform heat distribution, but the capacity of each burner is limited (0.1—1 MW) and hence 40 to 200 burners are required in a single furnace. With modem floor burners, also called hearth burners, uniform heat flux distribution can be obtained for coils as high as 10 m, and these are extensively used in newer designs. The capacity of these burners vary considerably (1—10 MW), and hence only a few burners are required. The selection of burners depends on the type of fuel (gas and/or liquid), source of combustion air (ambient, preheated, or gas turbine exhaust), and required NO levels. 

The surface of ultra large-scale integrated circuits (ULSI), from which the heat should be transferred, may be heated by a uniform heat flux, and more often by a non-uniform one. Even in the former case the temperature of the cooled surface is not uniform, but is determined by the heat transfer coefficients along the surface and in the span wise direction. 

We have designed, manufactured and tested a prototype that may be applied in thermal control of electronic devices. It was fabricated from a silicon substrate and a Pyrex cover, serving as both an insulator and a window through which flow patterns and boiling phenomena could be observed. A number of parallel triangular micro-channels were etched in the substrate. The heat transferred from the device was simulated by different types of electrical heaters that provided uniform and non-uniform heat fluxes, defined here respectively as constant and non-constant values... 

Fig. 2.61 Type of heater providing non-uniform heat flux. Reprinted from Hetsroni et al. (2001a) with permission...

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. 

One particular characteristic of conduction heat transfer in micro-channel heat sinks is the strong three-dimensional character of the phenomenon. The smaller the hydraulic diameter, the more important the coupling between wall and bulk fluid temperatures, because the heat transfer coefficient becomes high. Even though the thermal wall boundary conditions at the inlet and outlet of the solid wall are adiabatic, for small Reynolds numbers the heat flux can become strongly non-uniform most of the flux is transferred to the fluid at the entrance of the micro-channel. Maranzana et al. (2004) analyzed this type of problem and proposed the model of channel flow heat transfer between parallel plates. The geometry shown in Fig. 4.15 corresponds to a flow between parallel plates, the uniform heat flux is imposed on the upper face of block 1 the lower face of block 0 and the side faces of both blocks... 

The local heat transfer coefficients on the surface of the pipe may not be uniform, though the surface is heated by uniform heat flux. This irregularity is due to the distribution of the air and liquid phase in the pipe. The temperature distribution along the pipe perimeter shows a maximum at the top and a minimum at the bottom of the pipe. In Fig. 5.36a-c, the heat transfer coefficients are plotted versus angle 0. These results were compared to simultaneous visual observations of the flow pat-... 

By comparing Eq. (5-11) with existing flow boiling crisis data obtained in water at 1,000-2,000 psia (6.9-13.8 MPa) inside a single tube test section with uniform heat flux, Tong (1968) reported that C, is a function of the bulk quality and Eq. (5-11) becomes... 

The values of C, , n, and m were determined by plotting the CHF data of high-pressure water flowing in circular tubes with uniform heat flux as shown in Figure 5.15, and in one-side-heating annuli as shown in Figure 5.16. Based on the above plots, Eq. (5-13) becomes... 

The critical pressure, pc, for water is 3,206 psia (22 MPa). The product of constants CaC is 0.23, which was evaluated from existing water DNB data for circular tubes. As Eq. (5-20) was developed from a uniform heat flux distribution, a shape factor Fc (Tong et al., 1966a) should be applied to the correlation in a case with nonuniform heat flux distribution. 

For the approximately 1,500 points in this range of uniform heat flux CHF experiments, the root-mean-square error was -10%. 

In a uniform heat flux test section, the CHF cannot vary by one variable without affecting another accompanying variable. Figure 5.40 is reproduced from an article by Aladyev et al. (1961). This figure actually indicates the combined effects of pressure and inlet subcooling at a constant exit quality. The CHF occurs at the exit, and the exit enthalpy is kept at saturation. Because the critical flux varies with pressure, the inlet temperature must also vary. Hence the high CHF at low pressure is achieved by means of a low inlet temperature and the favorable physical properties of water and steam under low pressures also help the heat transfer at the corebubble layer interface. 

The dryout heat flux from a uniform heat flux distribution can be correlated as a function of p, X, and (DU2G) but is not generally valid for a nonuniform heat flux distribution. 

DNB EU — axial location at which DNB occurs for uniform heat flux (in.), starting from inception of local boiling... 

Predictions of a nonuniform heat flux, DNB non obtained by using <7dNB(W.3), f°r uniform heat flux in a single tube and the shape factor, Fc, agree very well with the measured nonuniform flux condition, DNB non of Biancone et al. (1965), Judd et al. (1965), and Lee and Obertelli (1963), as shown in Figure 5.70. 

Correlation for uniform heat flux. The correlation for uniform heat flux, in specified units, is... 

Bowring CHF correlation for uniform heat flux (Bowring, 1972). For water in round tubes with uniform heat flux, the CHF can be expressed as... 

Local quality method Dryout occurs when the local nonuniform heat flux equals the uniform heat flux dryout value at the same local conditions (quality, etc.). 

The correlation predicts the source data of 3,607 CHF data points under axially uniform heat flux condition from 65 test sections with an average ratio of 0.995 and RMS deviation of 7.2%. 

Bowring, R. W., 1972, A Simple but Accurate Round Tube, Uniform Heat Flux, Dryout Correlation over Pressure Range 0.7—17 MN/m2 (100-2500 psia), Rep. AEEW-R-789, UK Atomic Energy Authority, Winfrith, England. (5)... 

Cermak, J. O., R. Rosal, L. S. Tong, J. E. Casterline, S. Kokolis, and B. Matzner, 1971, High Pressure Rod-Bundle DNB Data with Axial Non-Uniform Heat Fluxes, Rep. WCAP-5727, Westinghouse Electric Corporation, Pittsburgh, PA. (5)... 

Nylund, O., et al., 1969, The Influence of Non-Uniform Heat Flux Distribution on the Thermodynamic Behavior of a BHWR 36-Rod Cluster, European Two-Phase Group Meeting, Karlsruhe, Germany. (3)... 

Smith, O. G., W. M. Rohrer, Jr., and L. S. Tong, 1965, Burnout in Steam-Water Flows with Axially Non-uniform Heat Flux, ASME Paper 65-WA/HT-33, ASME, New York. (5)... 

Tong, L. S., 1967a, Prediction of Departure from Nucleate Boiling for an Axially Non-uniform Heat Flux Distribution, J. Nuclear Energy 21. 241-248. (3)... 

Tong, L. S., H. B. Currin, P. S. Larsen, andO. G. Smith, 1966a, Influence of Axially Non-uniform Heat Flux on DNB, AIChE Chem. Eng. Prog. Symp. Ser. [Pg.556]

Heat fluxes in fire conditions have commonly been measured by steady state (fast time response) devices namely a Schmidt-Boelter heat flux meter or a Gordon heat flux meter. The former uses a thermopile over a thin film of known conductivity, with a controlled back-face temperature the latter uses a suspended foil with a fixed edge temperature. The temperature difference between the center of the foil and its edge is directly proportional to an imposed uniform heat flux. Because the Gordon meter does not have a uniform temperature over its surface, convective heat flux may not be accurately measured. 

The temperature at the comer edge of a thick wood element exposed to a uniform heat flux can be expressed, in terms of time, by the approximate equation given below for small time ... 

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