Nu-number

Fig. 11.7 Runaway boundary as a function of Nu number. [Reprinted by permission from D. H. Sebastian, Non-Isothermal Effects in Polymer Reaction Engineering, in Temperature Control Principles for Process Engineers, E. P. Dougherty, Ed., Hanser, Munich, 1993.]...

Henriksen A, Kesler RB (1970) The Nu-number, a measure of lignin in pulp Tappi 53 1131-1140... 

An interesting point is the dependence of the turbulent Nu numbers on the boundary condition. For laminar flow it was shown that the dependence of Nu on the boundary condition rapidly fades away when the relative pitch is increased The difference in Nu between the two limiting boundary conditions is less than 30% for relative pitches larger than 1.1. Because of the flatter velocity profile in turbulent flow, the dependence on the boundary conditions is weak in turbulent flow, except for small relative pitches. An estimate of the maximum influence of the boundary condition on the turbulent Nu number can be obtained from the respective values for laminar flow. 

For the ease of the uniform wall heat flux boundary eondition, we again apply the integral transform teehnique using a method similar to the eylindrieal solution. The Nu number is given as ... 

Nu number of trays above the feed tray P pressure or perimeter... 

The effect of (T on the performance index of the reactor is important since it affects Sherwood (Sh) and Nusselt (Nu) numbers. The values of kg and h are computed from the j-factor correlations given by Aris... 

Nu number of moles of 1 chemical species adsorbed in the solid phase moles... 

Various studies have been undertaken to resolve experimentally the problem of a fluid circulating in a tube [2]. The other problem of heat convection between the external surface of a cylinder and the fluid is quite different. The method to be followed is based on the relationship between two dimensionless numbers, the Niisselt (Nu) number and the Reynold (Re) number. 

For a partially ionized gas, dimensional analysis leads to the following expression for the Nu number... 

The Nu number is determined from empirical correlations between the Reynolds number. Re, and the Prandtl number, Pr. 

In the definition of the Nu -number, the characteristic length is chosen to be a function of the dynamic viscosity til gravitational acceleration g, because the... 

Nc = number of peaks common to both pyrograms Nu = number of unique peaks in both pyrograms... 

Figure 9.3 Nu number predictions from the literature for microchannels and macrochannels. The Reynolds number range covers laminar and turbulent flows.

This varies in many cases in the rangebetween 3 and 7 for straight channels involving gaseous medium at low pressure drop. Despite these relatively low numbers, the small diffusion paths allow for fest heat transfer. For liquids much higher Nu numbers are achievable owing to the higher heat conductivity of the medium. 

Another measure of dispersion is the Abbe number or nu-number, denoted Vj, which is the ratio of the refractivity divided by the dispersion as follows ... 

For fully developed laminar flow (Section 3.2.2.1), the average Nu number for the heat transfer to the internal surface of the tube with uniform temperature, length L, and diameter dt is (Schluender, 1970 VDI, 1997, see Example 3.2.1) ... 

Example 3.2.1 Local and average Nu number for laminar flow in a circular tube... 

For pure heat transfer problems, the value of the Nu is not needed, and knowledge of an average Nu number is sufficient. However, Nu may be important for a heated or cooled tube if a chemical reaction takes place in the tube. Then the behavior (and the modeling) of the reactor depends on /Vu ,asthe (local) reaction rate r strongly depends... 

The Nu number determined by Eq. (3.2.18) or by the two other equations given in Figure 3.2.9 represents the average heat transfer that is required for heat transfer calculations. The local heat transfer along the circumference of a cylinder is not needed in practical applications, but discussion of the local Nusselt number is insightful (Example 3.2.2). 

Figure 3.2.9 Average Nu number for the cross-flow of a gas (Pr= 0.7) over a cylinder according to Eq. (3.2.18). For comparison, two other equations proposed by Churchill and Bernstein (for Rex Pr>0.2,dotted-dashed line,Cengel,2002) and by Collis and Williams (for 0.02 < Re < 44, dotted line,...

The variation of the local Nu number along the circumference of a cylinder in cross flow of air (Pr= 0.7) for low and high Reynolds number is shown in Figures 3.2.10 and 3.2.11, respectively. The reason for the local variation of Nu is that the cross flow over a cylinder (and also over other bodies) exhibits complex flow characteristics. The fluid approaching the cylinder at the front stagnation point (angle y = 0) branches out and... 

Inspection of the heat transfer (and of the local Nusselt number] along the circumference of a cylinder leads to the following conclusion. The overall heat transfer from cylinders (and other bodies] consists of three parts (i) the convective heat transfer in the laminar boundary layer of the front part, (ii) heat transfer from the rear part, where — depending on Re — separation and turbulences occur, and (Mi) a constant and small part representing the limit case of minimum heat loss to a stagnant surrounding [Re = 0, see text below Eq. (3.2.3)]. Hence, the mean Nu number can be expressed by a correlation equation of the form ... 

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