Prediction heat transfer

The heat-transfer coefficient depends on particle size distribution, bed voidage, tube size, etc. Thus a universal correlation to predict heat-transfer coefficients is not available. However, the correlation of Andeen and Ghcksman (22) is adequate for approximate predictions ... 

Transition Region Turbulent-flow equations for predicting heat transfer coefficients are usually vahd only at Reynolds numbers greater than 10,000. The transition region lies in the range 2000 < < 10,000. 

These high velocities occur at the bundle entrance and exit areas, in the baffle windows, through pass lanes and in the vicinity of tie rods, which secure the baffles in their proper position. In conjunction with this, the shell side fluid generally will take the path of least resistance and will travel at a greater velocity in the free areas or by-pass lanes, than it will through the bundle proper, where the tubes are on a closely spaced pitch. All factors considered, it appears a formidable task to accurately predict heat transfer characteristics of a shell and tube exchanger. 

The following equation can be used to predict heat transfer coefficients from coils to tank walls in agitated tanks. 

In the previous section we discussed wall functions, which are used to reduce the number of cells. However, we must be aware that this is an approximation that, if the flow near the boundary is important, can be rather crude. In many internal flows—where all boundaries are either walls, symmetry planes, inlets, or outlets—the boundary layer may not be that important, as the flow field is often pressure determined. However, when we are predicting heat transfer, it is generally not a good idea to use wall functions, because the convective heat transfer at the walls may be inaccurately predicted. The reason is that convective heat transfer is extremely sensitive to the near-wall flow and temperature field. 

This method for vertical thermosiphon reboilers is based on semi-empirical correlations of experimental data and is stated to predict heat transfer coefficients 30 percent, which is about the same range of accuracy for most boiling coefficient data. The advantage of this method is that it has had significant design experience in the industry to support it. It is also adaptable to other types of reboilers used in the industry. See Figures 10-110 and 10-111. 

In the correlations used to predict heat-transfer coefficients, the physical properties are usually evaluated at the mean stream temperature. This is satisfactory when the temperature change is small, but can cause a significant error when the change in temperature is large. In these circumstances, a simple, and safe, procedure is to evaluate the heat-transfer coefficients at the stream inlet and outlet temperatures and use the lowest of the two values. Alternatively, the method suggested by Frank (1978) can be used in which equations 12.1 and 12.3 are combined ... 

Optimizing the Geometry of the Encapsulation Besides predicting heat transfer it has to be improved in many cases. If the PCM is encapsulated, this can be done by optimizing the encapsulation. The optimization is done with respect to... 

Figure 3.7 Predicted heat transfer coefficient as a function of particle size.

Figures 5.22 and 5.23 present the result of combining the equations in Table 5.4 with the correlations of Table 5.3 to predict heat transfer for spheres falling in air at 20 C and mass transfer for spheres in water at 20 C with Sc = 10. The decrease in terminal velocity due to secondary motion has not been taken into account because the transfer rate depends on the overall relative velocity between the sphere and the fluid, not the vertical velocity component alone.

Most unfortunately, an incorrect correlation for heat-transfer coefficients for surface condensers has become widely disseminated in several books devoted to heat transfer. This correlation predicts heat-transfer coefficients, for clean condensers, of about 650, when the water-side velocity is about 6 ft/s. Use of this correlation has led to some extremely serious problems, with which your author is intimately acquainted. 

Numerical simulations that combine the details of the thermal-capillary models described previously with the calculation of convection in the melt should be able to predict heat transfer in the CZ system. Sackinger et al. (175) have added the calculation of steady-state, axisymmetric convection in the melt to the thermal-capillary model for quasi steady-state growth of a long cylindrical crystal. The calculations include melt motion driven by buoyancy, surface tension, and crucible and crystal rotation. Figure 24 shows sample calculations for growth of a 3-in. (7.6-cm)-diameter silicon crystal as a function of the depth of the melt in the crucible. 

In predicting heat transfer rates one of the first steps in creating a model of the flow is to decide whether it involves internal or external flow because there are different assumptions that can be conveniently adopted in the two types of flow. 

The present book is concerned with methods of predicting heat transfer rates. These methods basically utilize the continuity and momentum equations to obtain the velocity field which is then used with the energy equation to obtain the temperature field from which the heat transfer rate can then be deduced. If the variation of fluid properties with temperature is significant, the continuity and momentum equations... 

In predicting heat transfer rates it is important to know if the flow remains laminar or whether transition to turbulence occurs. If transition occurs, it is usually also... 

As discussed in the previous chapter, most early efforts at trying to theoretically predict heat transfer rates in turbulent flow concentrated on trying to relate the wall heat transfer rate to the wall shear stress [1],[2],[3],[41. The reason for this is that a considerable body of experimental and semi-theoretical knowledge concerning the shear stress in various flow situations is available and that the mechanism of heat transfer in turbulent flow is obviously similar to the mechanism of momentum transfer. In the present section an attempt will be made to outline some of the simpler such analogy solutions for boundary layer flows, attention mainly being restricted to flow over a flat plate. 

In the common types of baffled shell-and-tube exchangers, the shell-side fluid flows across the tubes. The equations for predicting heat-transfer coefficients under these conditions are not the same as those for flow of fluids inside pipes and tubes. An approximate value for shell-side coefficients in a cross-flow exchanger with segmental baffles and reasonable clearance between baffles, between tubes, and between baffles and shell can be obtained by using the following correlation ... 

The equations presented here can also be used to predict heat-transfer coefficients for the shell side of shell-and-tube heat exchangers in which the baffles have been designed to produce flow parallel to the axis of the tube. For such cases, the diameter that should be used is the equivalent diameter... 

Select the calculation method to be used. Condensation on the outside of banks of horizontal tubes can be predicted assuming two mechanisms. The first assumes laminar condensate flow the second assumes that vapor shear dominates the heat transfer. The following equations can be used to predict heat-transfer coefficients for condensation on banks of horizontal tubes For laminar-film condensation,... 

Select the calculation method to be used. A heat-transfer coefficient that predicts heat transfer when both sensible heat and latent heat are being transferred can be calculated using the equation... 

Transition Region Turbulent-flow equations for predicting heat transfer coefficients are usually valid only at Reynolds numbers greater than 10,000. The transition region lies in the range 2000 < Npe < 10,000. No simple equation exists for accomplishing a smooth mathematical transition from laminar flow to turbulent flow. Of the relationships proposed, Hausen s equation [Z Ver. EHsch. Ing. Beth. Verfahrenstech., No. 

Liquid metals constitute a class of heat-transfer media having Prandtl numbers generally below 0.01. Heat-transfer coefficients for liquid metals cannot be predicted by the usual design equations applicable to gases, water, and more viscous fluids with Prandtl numbers greater than 0.6. Relationships for predicting heat-transfer coefficients for liquid metals have been derived from solution of Eqs. (5-38a) and (5-38b). By the momentum-transfer-heat-transfer analogy, the eddy conductivity of heat is = k for small IVp,. Thus in the solu-... 

Figure 4. Comparison between experimental and predicted heat transfer coefficients in bubble columns (Equation 24) (analogy with mechanically agitated contactors) for symbol key, see Table II...

In some cases, even with correctly predicted heat-transfer coefficients, the unexpected AT loss can reduce the actual performance of the evaporator by as much as 200 percent below the predicted performance. The best approach is to maintain a high level of mixing of the ph ases through the heat exchanger near the heat-transfer surface. 

Three-dimensional analyses of heat transfer and cure in pultrusion of epoxy-resin composites have been examined by Chachad et al. (1995, 1996) and Liu et al. (2000). Carlone et al. (2006) review finite-difference and finite-element process models used for predicting heat transfer and cure in pultrusion. In this work they recommend the following empirical nth-order cure model for predicting cure kinetics of epoxy-resin composites, which is then coupled to the system s energy balance to predict thermal properties and cure conversion ... 

Heat transfer to a laminar flow in an annulus is complicated by the fact that both the velocity and thermal profiles are simultaneously developing near the entrance and, often, over the length of the heated channel. Natural convection may also be a factor. It is usually conservative (i.e., predicted heat-transfer coefficients are lower than those experienced) to use equations for the fully developed flow. 

The equation for thickness of a falling laminar film was first presented by Nusselt, who used the result to predict heat-transfer coefficients for condensing vapors. Measurements of film thickness on a vertical surface (cos = 1) show that Eq. (5.77) is approximately correct for x 1000, but the thickness actually varies with about 0.45 power of the Reynolds number, and the layers are thinner than predicted at low Nr and thicker than predicted above = 1000. The deviations may be due to ripples or waves in the films, which are apparent even at quite low Reynolds numbers. 

Compare Eqs. (15.22) and (15.23) with respect to the effect of the following variables on the predicted heat-transfer coefficient (a) thermal conductivity, (A) specific heat,... 

The Reynolds analogy, defined as the ratio of the Stanton number to the local skin friction coefficient St/(c//2) is a function of the Prandtl number and is extremely useful for estimating heat transfer. Pressure drop can be used to predict heat transfer in pipes, and the skin friction can be used to predict Stanton number for external flows. 

Annular. When the vapor velocity is high enough (j > 1.5), gravitational effects can be neglected, and the condensate collects as a thin annular film around the inside of the tube walls, with no stratification. A significant portion of most condensers operate in this flow regime. There are numerous predictive models described in the literature for annular flow. Laminar flow models predict heat transfer coefficients that are too low, and turbulent models must be used. The most commonly used models are listed in Table 14.1. All models have a form for the local Nusselt number... 

FIGURE 15.99 Comparison of experimental and predicted heat transfer coefficients for slug flow (from Wade-kar and Kenning [246], with permission from Taylor Francis, Washington, DC. All rights reserved). 

Last, a mathematical model was developed which accurately predicts heat transfer from the foam to a fluid flowing through the pores of the foam. 

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