Stagnation point region

Hence, in the stagnation point region, the heat flux is 56.5 W/m2. The heat flux is constant in this region, i.e., in this region qv does not vary with x. 

Because, this quantity is independent of x, the use of Eq. (10.02) implies that in the stagnation point region, SBISx = 0. Substituting Eq. (10.62) into Eq. (10.61) therefore gives ... 

Variation of 0 with 17 in boundary layer in stagnation point region. 

It will be seen from Fig. 10.18 that in the forward stagnation point region the heat transfer rate obtained is in agreement with that previously given for the stagnation point region, i.e., NuD/Pe] = 1.596. 

Because the right-hand side of this equation is independent of x, it follows that in the stagnation point region dbjldx = 0 and in this region therefore ... 

Note that the boundary layer thickness continues to grow in the stagnation point region (x = 0.82). Previous analytic solutions assumed that the boundary layer thickness was zero at the moving stagnation point. Figure 16 shows that this is clearly incorrect. 

Circular Stagnation point region r/d Attalla and Specht... 

In region III near the tube center, viscous stresses scale by the tube radius and for small capillary numbers do not significantly distort the bubble shape from a spherical segment. Thus, even though surfactant collects near the front stagnation point (and depletes near the rear stagnation point), the bubble ends are treated as spherical caps at the equilibrium tension, aQ. Region... 

Interestingly, the shape of the wake is similar to that developed behind a hypersonic blunt body where the flow converges to form a narrow recompression neck region several body diameters downstream of the rear stagnation point due to strong lateral pressure gradients. The liquid material, that is continuously stripped off from the droplet surface, is accelerated almost instantaneously to the particle velocity behind the wave front and follows the streamline pattern of the wake, suggesting that the droplet is reduced to a fine micromist. 

As indicated by Fig. 23 and Fig. 24, the source function can be highly asymmetrical. For the liquid droplet corresponding to Fig. 23, one would expect the internal temperature to be higher near the back and front of the sphere because of the spikes in the source function in those regions. As a result, the evaporation rate should be enhanced at the rear stagnation point and the front of the sphere. To calculate the evaporation rate when internal heating occurs, one must solve the full problem of conduction within the sphere coupled with convective heat and mass transport in the surrounding gas. 

Figure 5.15 shows streamlines and concentration contours calculated by Masliyah and Epstein (M6). Even in creeping flow, Fig. 5.15a, the concentration contours are not symmetrical. The concentration gradient at the surface, and thus Shjoc is largest at the front stagnation point and decreases with polar angle see also Fig. 3.11. The diffusing species is convected downstream forming a region of high concentration at the rear (often referred to as a concentration wake ) which becomes narrower at higher Peclet number.

Note also Ihe variation of Ihe profile near the surface of the plate. Skin friction has steadily decelerated the individual fluid particles, lire profile at n indicates that Ihe lower portion has come to rest. This is known as the stagnation point. Air-llow phenomena in this region arc important in many ways, especially when there is an intended rising downstream pressure gradient, as in diflfuser lubes or over the surface of airfoils. 

For X = 0.425, the stagnation point is at the contact point hence, for X > 0.425a circulatory flow develops in the entrance region. 

Therefore, near the stagnation point, u is proportional to x so that the similarity solution with m equal to 1 will apply in this region. 

Substituting this into Eq. (3.114) then gives the local heat transfer rate in the region of the stagnation point as... 

This relationship only applies for small values of x. D is the diameter of the cylinder. While this relation is strictly only applicable for flow over a cylinder, it closely describes the freestream velocity distribution in the region of the stagnation point for flow over any rounded body, D, then being twice the radius of curvature of the leading edge. Substituting this value of u into Eq. (3.116) then gives ... 

The values of Nud predicted by this equation are in good agreement with measured heat transfer rates in the region of the stagnation point on rounded bodies. 

As another example of a situation in which a similarity-type solution can be obtained, consider flow in the region of a stagnation point of an isothermal body as shown in Fig. 10.13. 

Using these equations, the numerical procedure outlined above can be used to find the variation of the local heat transfer rate in the form of Nup/Pe 2 around the cylinder. The solution procedure does not really apply near the rear stagnation point (R in Fig. 10.17) because the effective boundary thickness becomes very large in this area as indicated in Fig. 10.17. This is however, of little practical importance because the heat transfer rate is very low in the region of the rear stagnation point. 

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