Nusselt number limit

TABLE 5-4 Values of Limiting Nusselt Number in Laminar Flow in Closed Ducts... 

Limiting Nusselt numbers for slug-flow annub may be predicted (for constant heat flux) from Trefethen (General Discu.s.sion.s on Heat Tran.sfer, London, ASME, New York, 1951, p. 436) ... 

Limiting Nusselt numbers for laminar flow in annuli have been calculated by Dwyer [Nucl. Set. Eng., 17, 336 (1963)]. In addition, theoretical analyses of laminar-flow heat transfer in concentric and eccentric annuh have been published by Reynolds, Lundberg, and McCuen [Jnt. J. Heat Ma.s.s Tran.sfer, 6, 483, 495 (1963)]. Lee fnt. J. Heat Ma.s.s Tran.sfer, 11,509 (1968)] presented an analysis of turbulent heat transfer in entrance regions of concentric annuh. Fully developed local Nusselt numbers were generally attained within a region of 30 equivalent diameters for 0.1 < Np < 30, lO < < 2 X 10, 1.01 <... 

Data are most frequently correlated by the Nusselt number (Nn )i or (NNu)om, the Graetz number Nc = (NReNpi-D/L), and the Grashof (natural-convection effects) number Ng,. Some correlations consider only the variation of viscosity with temperature, while others also consider density variation. Theoretical analyses indicate that for very long tubes approaches a limiting value. Limiting Nusselt numbers... 

Parallel Plates and Rectangular Ducts The limiting Nusselt number for parallel plates and flat rectangular ducts is given in Table 5-4. Norris and Streid [Trans, Am, Soc, Mech, Eng, 62, 525 (1940)] report for constant wall temperature... 

For electro-osmotic flow only the limiting Nusselt numbers for thermally fully-developed flow in parallel plate channel and circular tube are obtained as a special case from the solution for thermally developing flow. 

The integrals in eq. (75) have exact solutions and the limiting Nusselt number becomes 1 + 4 Kn)3v... 

The limiting Nusselt number is of great practical interest. For n=0 (parallel plate micro channel) and n=l (micro tube) the limiting Nusselt number depend on 2 parameters Kn/3v and /3. The Kn/3v control mainly the velocity slip and have influence on the temperature jump. The parameter /3 control only the temperature jump. The limiting Nusselt number is shown on Fig 6. 

Fig. 11 Limiting Nusselt number as function of heat generation due to resistance S and ratio of tube radius to Debye lengdi Z.

In the entire range of the Peclet number, the limit Nusselt number is nicely approximated by... 

From the temperature distribution (3.6.14) far from the input cross-section, one can find the limit Nusselt number... 

In the region of thermal stabilization of turbulent flow through a smooth tube, it is recommended to calculate the limiting Nusselt number by the formula [212,289]... 

Limit Nusselt Numbers for Tubes of Various Cross-Section... 

Heat exchange in fully developed laminar flow of fluids in tubes of various cross-sections was studied in many papers (e.g., see [80, 253, 341]). In what follows, we present some definitive results for the limit Nusselt numbers corresponding to the region of heat stabilization in the flow in the case of high Peclet numbers (when the molecular heat transfer can be neglected). 

At constant temperature on the wall of a tube whose cross-section is a regular W-gon, the limit Nusselt number is given by the approximate formula... 

The limiting Nusselt number for heat transfer from an isolated particle is given by Nu = 2/jryXj = 2.0 so that... 

The above results indicate that with an increase in temperature jump, Nu(cx>) decreases. It may be remembered that Kn x controls the velocity slip and y controls the temperature jump. The limiting Nusselt number (Nu(oo)) results as a function of Kn X at different values of Pt/Pv ratio has been shown in Figure 9.7. The heat transfer, that is, the Nusselt number, reduces with an increase in P /Pv that is, the temperature jump. The heat transfer also increases with an increase in velocity slip. Hence, the velocity slip and temperature jump have opposite influences on the heat transfer of a microchannel flow. 

Figure 9.7 The limiting Nusselt number as a function of velocity slip and temperature jump of a microchannel...

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