Cylinders in cross-flow

The limited work on heat and mass transfer between power-law fluids and cylinders with their axis normal to the flow has been summarised recently by Ghosh et al. [1994] who proposed the following correlation for heat and mass transfer  

A polymer solution at 25°C flows at 1.8m/s over a heated hollow copper sphere of diameter of 30 mm, maintained at a constant temperature of 55°C (by steam condensing inside the sphere). Estimate the rate of heat loss from the sphere. The thermophysical properties of the polymer solution may be approximated by those of water, the power-law constants in the temperature interval 25 J 55°C are given below n = 0.26 and m = 26 — 0.0566 T where J is in K. What wiU be the rate of heat loss from a cylinder 30 mm in diameter and 60 mm long, oriented normal to flow  

For a cylinder, the Reynolds number of the flow is still the same and therefore equation (7.72b) applies. 

Note that the drop in the value of the heat transfer coefihcient in this case has been compensated by the increase in surface area resulting in higher rate of heat loss. Also, the heat loss from the flat ends has been neglected. 

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While the engineer may frequently be interested in the heat-transfer characteristics of flow systems inside tubes or over flat plates, equal importance must be placed on the heat transfer which may be achieved by a cylinder in cross flow, as shown in Fig. 6-7. As would be expected, the boundary-layer development on the cylinder determines the heat-transfer characteristics. As long as the boundary layer remains laminar and well behaved, it is possible to compute the heat transfer by a method similar to the boundary-layer analysis of Chap. 5. It is necessary, however, to include the pressure gradient in the analysis because this influences the boundary-layer velocity profile to an appreciable extent. In fact, it is this pressure gradient which causes a separated-flow region to develop on the back side of the cylinder when the free-stream velocity is sufficiently large. 

Fig. 6-8 Velocity distributions indicating flow separation on a cylinder in cross flow.

Fand [21] has shown that the heat-transfer coefficients from liquids to cylinders in cross flow may be better represented by the relation... 

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. 

External Flows For a single cylinder in cross flow, Churchill and Bernstein recommend [ /. Heat Transfer, 99, 300 (1977)]... 

More recently, Henry and Epstein (H3) reported data on psychrometric ratios for cylinders in cross-flow and spheres. Their experimental results, which covered the Lewis number range of 3.7 to 7.2, were identical for spheres and cylinders. Furthermore, their results could best be represented by an equation similar to that of Bedingfield and Drew (Bl) as follows ... 

Variation of the local heal transfer coefficient along the circumference of a circular cylinder in cross flow of air (from Giedl, 1949). 

Empirical correlations for the average Nusselt number for forced convection over circular and noncircular cylinders in cross flow (from Zukauskas, 1972 and Jakob, 1949)... 

S. W, Churchill and M. Bernstein. A Correlating Equation for Forced Convection from Gases and I.iquids to a Circular Cylinder in Cross Flow." Journal of Heat Transfer 99 (1977), pp. 300 -306. 

Zukauskas, A.A. Zingzda J. Heat transfer of a cylinder in cross flow. Washington Hemisphere Publ. Comp. 1986, p. 162... 

Similar results are given by Schlicting (12) for the heat transfer to a circular cylinder in cross-flow at varying degrees of turbulence. At the highest turbulence value. 

Zukauskas A. and Ziugzda J., Heat Transfer at Cylinder in Cross Flow of Fluid, Mokslas, Vilnius, 1979 [in Russian],... 

Figure 6.9 Average heat transfer coefficient versus Reynolds number for a circular cylinder in cross flow with air (from McAdams [25]).

Single Cylinder. The classic experiments on the average heat transfer rates from a cylinder in cross flow were performed by Hilpert [64] for a wide range of Reynolds numbers in air. Hilpert s results are shown in Fig. 6.26 as average Nusselt number versus the cross flow Reynolds number. 

In Ref. 66, Morgan made an extensive review of more recent heat transfer data obtained on a cylinder in cross flow. He found that the average Nusselt number could be correlated as... 

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... 

FIGURE 6.28 Distribution of local heat transfer on the surface of a circular cylinder in cross flow in air [66]. (Reprinted from Ref. 65 by permission of McGraw-Hill.)... 

Free-Stream Turbulence and Unsteadiness. It was shown in Fig. 6.27 that the free-stream turbulence level significantly affects local and overall heat transfer from single cylinders in cross flow. This is caused primarily by early transition of the laminar boundary layer on the forward portion of the cylinder and subsequently by delayed separation of the turbulent boundary layer from the surface of the cylinder. Free-stream turbulence and unsteadiness also affect, to varying degrees, the heat transfer behavior of a turbulent boundary layer in the absence of transition-point shift and separation. 

A. Zhukauskas, J. Ziugzda, and P Daujotas, Effects of Turbulence on the Heat Transfer of a Rough Surface Cylinder in Cross-Flow in the Critical Range of Re, in Heat Transfer 1978, vol. 4, pp. 231-236, Hemisphere, Washington, DC, 1978. 

J. Kami and R. J. Goldstein, Surface Injection Effect on Mass Transfer From a Cylinder in Cross-flow A Simulation of Film Cooling in the Leading Edge Region of a Turbine Blade, ASME J. of Turbomachinery, 112, pp. 418-427,1990. 

Figure 7.6 Overall correlation for heat and mass transfer from cylinders in cross flow...

Woods BG. Sonically enhanced heat transfer from a cylinder in cross flow and its impact on process power consumption. Inti. J Heat Mass Transfer 35(10) 2367-2376, 1992. 

Convection from a cylinder in cross flow has been widely investigated. The results for many liquids over a wide size range can be summarised as ... 

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... 

The heat transfer coefficient a. ex the side of the cooling medium can be calculated based on empirical equations, for example, those given in Section 3.2.1.2 for cylinders in cross flow or by more sophisticated correlations given in the literature (VDI, 2002 Cengel, 2002). 

The use of thermochromic liquid crystals in qualitative studies of heat transfer is relatively common [44—48] hot and cold regions are discriminated, but precise temperatures are not necessarily deduced from the results. Quantitative measurements were first made by Cooper et al. [49, 50], who evaluated the variation of the Nusselt number around a heated cylinder in cross-flow (the Nusselt number of a body, Nu=hl/KQ, where h is heat loss per unit area, / is a typical dimension, 0 the temperature difference between the body and surroundings and K is the thermal conductivity). Local heat transfer coefficients for plates in air jets have also been measured [51] and the temperature shift of the colour band due to the shearing action of the air flow determined [52] this is particularly important in making quantitative measurements from ex-... 

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. 

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