Number Graetz

Circular Tubes For horizontal tubes and constant wall temperature, several relationships are available, depending on the Graetz number. For 0.1 < Ngz < 10 Hausens [A//g. Waermetech., 9, 75 (1959)], the following equation is recommended. 

For flow inside helical coils, Reynolds number less than 10,000, substitute the term DJDjY for (L/Di) where the latter appears in the apphcable equation for straight tubes (frequently as part of the Graetz number). 

Convective heat transfer to fluid inside circular tubes depends on three dimensionless groups the Reynolds number. Re = pdtu/ii, the Prandtl number, Pr = Cpiilk where k is the thermal conductivity, and the length-to-diameter ratio, L/D. These groups can be combined into the Graetz number, Gz = RePr4/L. The most commonly used correlations for the inside heat transfer coefficient are... 

Assuming an initially fully developed parabolic velocity profile. Re = 1000, and Pr = 5, calculate and plot the Nusselt number as a function of the inverse Graetz number,... 

The Peclet number, DGC/k = GC/(k/D) and its modification, the Graetz number wC/kL, are ratios of sensible heat change of the flowing fluid to the rate of heat conduction through a film of thickness D or L. 

Analysis of the various stages in mold filling is based on two dimensionless criteria the Graetz Number, Gz, which is a measure of the ratio of convective to conductive heat exchange ... 

A typical estimate of the critical value Gcr is discussed in Ref. 47 it was shown that if Gz > 10, then gelation happens at G > 0.17 if the Graetz number lies between 2 and 10, Gcr = 0.06. These results apply only to the specific system investigated47 but since the viscosity changes in a similar manner for other reactive mixes the authors of the cited publication believe that analogous conclusions are valid for other systems. 

For known values of the parameters in the kinetic equation for a specific reactive mix, it is easy to calculate the dimensionless factors y and v. Then the flow pattern in the mold filling process is completely determined by the dimensionless Da and Gz Numbers and the boundary conditions. The Damkohler Number characterizes the ratio of the rates of chemical reaction and convective heat transfer and the Graetz Number is a measure of the ratio of the convective heat flux due to a moving liquid to the heat flux due to the conductivity of the liquid. 

Figure 4.69. Nature of dependences of the gelation criterion G on the reciprocal Graetz Number at different mold temperatures. The arrow shows the direction of increasing wall temperature. To = const. [Adapted, by permission from S. R. Esevez, J. M. Castro, Potym. Eng. Sd., 24 (1984), 431.]...

Kays [36] and Sellars, Tribus, and Klein (Ref. 3, Chap. 5) have calculated the local and average Nusselt numbers for laminar entrance regions of circular tubes for the case of a fully developed velocity profile. Results of these analyses are shown in Fig. 6-5 in terms of the inverse Graetz number, where... 

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