Nahme number

Knudsen number Nahme number Nusselt number... 

The Nahme number can be considered to be the ratio of viscous dissipation to ther-mai conduction in the direction perpendicular to flow. Large values of the Nahme number (>1) indicate that the temperature non-uniformities created by the viscous dissipation have a substantiai effect on the resulting velocity profile. Thus, if the Nahme number is iarge, a non-isothermal flow analysis has to be made in order to maintain sufficient accuracy. If the Nahme number is small, an isothermal analysis can yieid reiativeiy accurate resuits. The Nahme number is also referred to as the Griffith number. 

The effect of barrel temperature on melting performance can be predicted in a quantitative way. Figure 7.42 shows how the melting rate changes with barrel temperature for two values of the Nahme number as expressed by Eq. 7.f43. Low Nahme numbers indicate little viscous dissipation, while high Nahme numbers correspond to high levels of viscous dissipation. 

At low Nahme numbers the melting rate increases with barrel temperature. However, at high values of the Nahme number the melting rate reduces with increasing barrel temperature. There is a critical Nahme number above which increasing barrel temperature results in reduced melting rate. At a power law index of n = 0.5 the critical Nahme number is about 4.5. The critical Nahme number increases with the power law index as shown in Fig. 7.43. 

Critical Nahme number versus power law index... 

Equation 7.356 shows that the value of constant A depends on the Nahme number NNa, the power law index n, and wall temperatures 0,5 and 0,. ... 

There does not appear to be a general, explicit solution for constant A. Thus, in most cases a numerical scheme has to be used to determine the value of A. A simple solution can be found for the special case of a Newtonian fluid with equal wall temperatures. In this case, A depends only on the Nahme number with the following linear... 

The Nahme number Na is the critical parameter for estimating the importance of shear heating in rheometry. It determines how... 

Shear heating can also affect slit data. Again the Nahme number can be used to estimate when significant viscosity errors will occur. For a rectangular charmel... 

The Nahme number is a measure of viscous dissipation effects compared to conduction hence, it is an indicator of coupling of the energy and momentum equations. For values of Na > 0.1-0.5 (depending on geometry and thermal boundary conditions), the viscous dissipation leads to considerable coupling of the conservation equations, and a nonisothermal analysis is necessary. 

Equation (6.245) is the well known Nahme-Griffith number... 

Note that they use the Nahme-Griffith number Na = l>Br. Na is a ratio of temperature rise due to viscous heating to the temperature change necessary to alter the viscosity. Thus since... 

Table 14.1 Ionic conductivity and transference number of PEO-based composite polymer electrolyte systems (Stephan and Nahm, 2006)...

---