Nusselt number stagnation

The heat flux between the gas and the stagnation surface can be correlated in terms of a relationship between the Reynolds number and the Nusselt number. The heat flux is... 

Fig. 6.9 Correlation of the Nusselt number with the Reynolds number for the axisymmetric stagnation flow in a finite gap. The Prandtl number is Pr = 0.7.

Recall that in the semi-infinite stagnation flow, the Reynolds number does not appear in the governing flow equations. As a result the Nusselt number is simply a constant for... 

The Sherwood number is a nondimensional mass-transfer coefficient that is analogous to the Nusselt number for heat transfer. For the situation of A being dilute in B, the mass transfer at the stagnation surface is derived from the solution to the species equation by... 

As seen in Section 6.4.3, the Nusselt number in finite-gap stagnation flow is proportional to the square root of the flow Reynolds number. For Pr = 0.7,... 

B12 Cell B12 contains the value of the Nusselt number, which is the nondimen-sional temperature gradient evaluated at the stagnation surface. The contents of B12 is computed as =(E48-E47) /dz. 

For each regime involving separation, the characteristics of the downstream flow separated from the cylinder are quite different from the characteristics of the upstream flow that is attached to the cylinder. This difference is also reflected in the upstream and downstream heat transfers. Figure 6.8 shows, for free-stream Reynolds numbers between 70,000 and 220,000, the change in the local Nusselt number, as a function of angular distance from the stagnation point. Note the difference between the maximum and minimum Nusselt number, as well as the location of maximum heat transfer. 

Local heat transfer rates from the surface of a cylinder in cross flow in air were measured by Schmidt and Wenner [68] and are shown in Fig. 6.28. The local Nusselt number is based on the local heat transfer coefficient and the cylinder diameter. Note that for subcritical Reynolds numbers (Red < 170,000), the local Nusselt number decreases initially along the surface from the forward stagnation point to a minimum at the separation point and subsequently reaches high values again in the separated portion of the flow on the back surface. For... 

In the above equations, x is the distance along the condensate film measured from the top of the body or from the upper stagnation point, g(x) is the local component of gravity along the flow direction, and R(x) is the local radius of curvature about the vertical axis. Once the local Nusselt number is known, the result may be integrated to get an average expression for the whole body. Some examples follow. 

For fully turbulent jets issuing from a fully developed pipe-type nozzle at Hid < 4, Stevens and Webb [97] recommend the following stagnation zone Nusselt number correlation ... 

For higher Reynolds numbers, other investigators [101, 102] report stronger dependence of stagnation Nusselt number on Reynolds number. Gabour and Lienhard [102] find, for 25,000 < Re < 85,000,... 

Using a long parallel-plate nozzle to produce fully developed turbulent jets, Wolf et al. [103] correlated their stagnation zone Nusselt number data to an accuracy of 10 percent by the equation... 

The correlation is based on Re . from 17,000 to 79,000 and Pr between 2.8 and 5.0. Vader et al. [104] used a converging nozzle to produce uniform velocity profile water jets. These nozzles were intended to suppress but not to eliminate turbulence. The stagnation zone Nusselt numbers were correlated by an equation... 

The Nusselt numbers found earlier by other investigators are lower than those found in the present study. This discrepancy is attributed primarily to the uniform plate temperatures used in this study which resulted from the choice of flow field and heat arrangement. The shorter L/D distance and smaller test plate to jet diameter ratio used in the cmrent study resulted in uniform plate temperatures that more accurately simulate uniform flow approaching from infinity forming a stagnation point. The... 

Figure 3.2.10 Variation of local Nusselt number along the circumference of a cylinder for cross flow of air (Pr=0.7) for low Reynolds numbers Re = ud< /v [Sucker and Brauer, 1976, short-dash line values of Khan, Culham, and Yovanovich (2005) for0 (front stagnation point)

A laboratory study of convective heat transfer to a cylinder in cross-flow was conducted in a small wind tunnel. The sensor was located at the forward stagnation line and tests were performed over a range of air speeds. For each test were the Reynolds NgJ and Nusselt numbers were calculated based on fluid, flow, and geometrical properties. 

The Nusselt functions specified in the literature deviate from each other particularly with regard to the exponent of the Reynolds number this is because the exponent depends on the radial distance. At the stagnation point the flow is always laminar, and the exponent is therefore 0.5. Turbulence fully develops only at a considerable distance from the stagnation point, and as a result the exponent must be 0.8. Figure 1.6 shows the increase of the exponent related to the radius (Adler, 2004). At a distance of r/d = 3, the exponent has reached a value of only about 0.62. Different exponents are obtained depending on the size of the area considered in averaging. 

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