Stagnation point heat transfer

In calculating stagnation point heat transfer rates, it is more convenient to use a Reynolds number based on the undisturbed freestream velocity ahead of the body, U, rather than one that is based on the local freestream velocity, u. The actual relation between u and U will depend on the body shape. For the case of flow over a cylinder... 

A. Pallone and W. Van Tassell, Stagnation Point Heat Transfer for Air in the Ionization Regime, ARSJ. (32) 436-437,1962. 

J. S. Gruszczynski and W. R. Warren, Measurements of Hypervelocity Stagnation Point Heat Transfer in Simulated Planetary Atmospheres, General Electric Space Sci. Lab. R63SD29, 1963. 

L. Yee, H. E. Bailey, and H. T. Woodward, Ballistic Range Measurements of Stagnation-Point Heat Transfer in Air and Carbon Dioxide at Velocities up to 18,000 feet per second, NASA Tech. Note D-777, 1961. 

R. M. Nerem, C. J. Morgan, and B. C. Graber, Hypervelocity Stagnation Point Heat Transfer in a Carbon Dioxide Atmosphere, AIAA J. (1) 2173-2175,1963. 

L. A. Gabour and J. H. Lienhard V, Wall Roughness Effects of Stagnation Point Heat Transfer Beneath an Impinging Jet, J. Heat Transfer, 116, pp. 81-87,1994. 

Fairweather, M., Kilham, J. K., and Nawaz, S. "Stagnation Point Heat Transfer from Laminar, High Temperature Methane Flames." International Journal of Heat and Fluid Flow 5, no. 1 (1984) 21-27. 

Chander, S., and Ray, A. "An Experimental and Numerical Study of Stagnation Point Heat Transfer for Methane/Air Laminar Flame Impinging on a Flat... 

Van der Meer, T. H. "Stagnation Point Heat Transfer from Turbulent Low Reynolds Number Jets and Flame Jets." Experimental Thermal and Fluid Science 4 (1991) 115-26. 

For our earlier example with water on a 0.5-m-diameter disc, Eq. (21) implies that the heat transfer him coefficient at the periphery is 43 kW/m2k, with the predicted him thickness of 28 microns. For this estimate to be realistic it is essential that the him wet the disc and not break up into rivulets. This depends upon a force balance at an incipient dry-out point, as indicated in Figure 9. At the him stagnation point the him momentum is potentially destroyed by the action of the component of the surface forces parallel to the disc. Thus for an average him velocity Uav we must satisfy the following condition for rivulet maintenance ... 

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

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. 

Air flows at a velocity of 2 m/s normal to the axis of a circular cylinder with a diameter of 2.5 cm. The surface of the cylinder is kept at a uniform surface temperature of 50°C and the temperature in the air stream ahead of the cylinder is 10°C. Assuming that the flow is two-dimensional. And the heat transfer rate in the vicinity of the stagnation point. 

Consider two-dimensional air flow normal to a plane surface. If the initial air temperature is 20°C, the surface temperature 80°C. and the air velocity in the free stream ahead of the plate is 1 m/s, plot the variation of heat transfer rate in the vicinity of the stagnation point. 

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. 

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. 

Assume that one-half the heat transfer from a cylinder in cross flow occurs on the front half of the cylinder. On this assumption, compare the heat transfer from a cylinder in cross flow with the heat transfer from a flat plate having a length equal to the distance from the stagnation point on the cylinder. Discuss this comparison. 

An airflow at 540°C and l atm impinges on the front side of a porous horizontal cylinder 7.5 cm in diameter at a velocity of 600 m/s. Air is injected through the porous material to maintain the surface temperature at 150°C. Calculate the heat-transfer rate at a distance of 0.75 cm from the stagnation point and with an injection parameter of 0.5. 

Problem 11-6. Mass and Heat Transfer for Chemical Vapor Deposition. Consider the following model for chemical vapor deposition (CVD) on a surface. A reactive species is transported toward the surface by a 2D flow near a stagnation point, as illustrated in the figure. Far away from the surface the flow is given by... 

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. 

For stagnation point flow between a pair of parallel disk electrodes with the gas uniformly distributed through the area of one of the disks (see Fig. 3a), the hydrodynamics is well defined to the point that an analytic solution is possible for low Re [160]. The corresponding heat transfer coefficient can be shown to be... 

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... 

Sibulkin, M. "Heat Transfer Near the Forward Stagnation Point of a Body of Revolution." Journal of Aeronautical Science and Technologies 19 (1952) 570-71. 

Savino, J.M. et al, 1970, Experimental study of freezing and melting of flowing warm water at a stagnation point on a cold plate. 4th Int. Heat Transfer Conf 1, 2- 11. 

The maximum possible continuous-phase heat transfer coefficient obtainable for nonoscillating drops was suggested by Elzinga and Banchero (E2). Their equation is based on the maximum heat transfer to a solid sphere, calculated in the vicinity of the front stagnation point. Applying it to drops with internal circulation they obtained... 

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