Nusselt number vertical plate

Now let us consider the mixing time, t. This will be estimated by an order of magnitude estimate for diffusion to occur across the boundary layer thickness, <5Bl- If we have turbulent natural conditions, it is common to represent the heat transfer in terms of the Nusselt number for a vertical plate of height, , as... 

Comparison of measured and predicted Nusselt number variations for turbulent natural convective flow over a vertical plate. 

Use the computer program for two-dimensional laminar free convective flow to And the Nusselt number variation along a vertical plate whose surface temperature varies in such a way that Tw - r. is equal to 10°C over the lower half of the plate and equal to 30°C over the upper half of the plate. 

Numerically predicted variation of Nusselt number variation with Reynolds number in turbulent assisting mixed convective flow over a vertical plate. (Based on results obtained by Patel K., Armaly B.F., and Chen T.S., Transition from Turbulent Natural to Turbulent Forced Convection Adjacent to an Isothermal Vertical Plate , ASME HTD, Vol. 324, pp. 51-56, 1996. With permission.)... 

The characteristic dimension to be used in the Nusselt and Grashof numbers depends on the geometry of the problem. For a vertical plate it is the height of the plate L for a horizontal cylinder it is the diamter d and so forth. Experimental data for free-convection problems appear in a number of references, with some conflicting results. The purpose of the sections that follow is to give these results in a summary form that may be easily used for calculation purposes. The functional form of Eq. (7-25) is used for many of these prer sentations, with the values of the constants C and m specified for each case. 

For vertical surfaces, the Nusselt and Grashof numbers are formed with L, the height of the surface as the characteristic dimension. If the boundary-layer thickness is not large compared with the diameter of the cylinder, the heat transfer may be calculated with the same relations used for vertical plates. The general criterion is that a vertical cylinder may be treated as a vertical flat plate [13] when... 

Evaluate the Nusselt number for natural conveclion associated with vertical, horizontal, and inclined plates as well as cylinders and spheres,... 

When this criteria is met, the relations for vertical plates can also be used for vertical cylinders. Nusselt number relations for slender cylinders that do not meet this criteria are available in the literature [e.g., Cebeci (1974)]. 

When the boundary layer remains intact (tlie lower surface of a hot plate or the upper surface of a cold plate), the Nusselt number can be determined from the vertical plate relations provided that g in the Rayleigh number relation i.s replaced by g cos6 for d < 60°, Nusselt number relations for the other two surfaces (the. upper surface of a hot plate or the lower. surface of a cold plate) are available in the literature [e.g., Fujiii and Imura (1972)]. 

Kohsenow (1984) have compiled the available dala under various boundary conditions, and developed correlations for the Nusselt number and optimum spacing. The characteristic length for vertical parallel plates used as fins is usually taken to he the spacing between adjacent fins S, aliltough the n height h could also be used. The Rayleigh number is expressed as... 

The recommended relation for the average Nusselt number for vertical isothermal parallel plates is... 

Nusselt number relations for various surfaces are given in Table 9-1. All fluid properties are evaluated at the film temperature of Tf = 1(T, -T r ). The outer surface of a vertical cylinder can be treated as a vertical plate when the curvature effects are negligible. The characteristic length for a horizontal surface is Lg = AJp, where A, is the surface area and p is the perimeter. 

The average Nusselt number for vertical isolhermal parallel plates of spacing S and height L is given as... 

Find the local Nusselt number for free convection of a vertical plate subjected to a constant wall heat flux by using linear profiles for cases Pr > 1 (Fig. 5P-5). Compare the result with Eq. (5.104). 

Find the local Nusselt number for free convection of a vertical plate subjected to a constant... 

This is obtained from the average Nusselt number Nu defined in Fig. 4.6. A rough estimate of Nu can be obtained for Ra > 105 by using the equations in the section on vertical flat plates with uniform Tw and = 90°, with AT replaced by AT. For higher accuracy, and for convenience since Ra is used in place of Ra, use the following equation set ... 

Vertical Plates of Various Platforms. There is a class of vertical plates, such as shown in Fig. 4.9, for which any vertical line on the plate intersects the edge only twice. When such plates are isothermal, the thin-layer laminar Nusselt number Nur can be calculated [225] by dividing the surface into strips of width Ax and length S(x), applying Eq. 4.33a to compute the heat transfer from each strip, adding these to obtain the total (thin-layer) heat transfer, and using this heat transfer to calculate Nur. The result can be expressed as... 

For a wide isothermal plate at any angle of tilt, first compute the heat transfer from Eq. 4.33 (vertical plate) but with g replaced by g sin then compute the heat transfer from Eq. 4.40 (downward-facing plate) with g replaced by g(0, -cos Qmax, then compute the heat transfer from Eq. 4.39 (upward-facing plate) with g replaced by g(0, cos Qmax, and take the maximum of the three heat transfer rates. It is important to take maximum heat transfer rather than the maximum Nusselt number, because the Nusselt numbers are based on different length scales. 

For a vertical cylinder of length L and diameter D, first calculate the Nusselt number Nur and Nu, for a vertical flat plate of height L, using Eq. 4.33 if the cylinder is isothermal and Eq. 4.36 if it has uniform heat flux. These Nusselt numbers are based on the length L of the plate (see Fig. 4.6) and are renamed Nuplale and NufiPlate here. The laminar Nusselt number for the vertical cylinder (defined in Fig. 4.14), Nuf, is then calculated from... 

Uniform Heat Flux Parallel Plates. If the heat fluxes are specified as q" and q", respectively, on the surfaces of the vertical plates (where q" > q" and both q" and q" are positive, denoting heat transfer from the plate to the fluid), the Nusselt number for the fully developed regime for air is given by [11]... 

In the laminar boundary layer regime, the Nusselt number relation is of the form of that for a vertical flat plate... 

The intersection points of the pure natural convection and pure forced convection equation also provide valuable information on the conditions for which forced and natural convection are equally important. For example, for laminar flow along the heated isothermal vertical plate in Fig. 4.6 if Eq. 4.33a for NulV is equated to the forced convection Nusselt number given by... 

For vertical plates and natural convection, the Nusselt number is some empirical function of Prandtl and Rayleigh numbers, Nul = f (Pr,RaL), such as [1] ... 

Figure 6-6. Nusselt numbers for free convection from vertical plates. (Reproduced with permission from reference 23. Copyright I960, John Wiley Sons.)...

The second correlation was developed by the Oak Ridge National Laboratory (ORNL) for the Advanced Neutron Source Reactor (INEEL, 2003) for flat vertical plates with an aspect ratio of 68 11. The compact heat exchangers envisioned for Project Prometheus would best be characterized as finned plates with a high plate width to separation aspect ratio. The ORNL correlation is also a constant Nusselt number solution of the form ... 

Answer by Author Subsequent to pressurization the initial turbulence caused by the boiling decayed, as was evidenced by a time-wise decrease in the heat transfer coefficient at all longitudinal positions. These heat transfer coefficients were for nonboiling conditions and they decreased from a maximum value to a minimum, as indicated on our curves. The ratio of this minimum value of the nonboiling heat transfer coefficient to that which one would predict from a Nusselt — Grashof — Prandtl number relationship for natural convection over vertical flat plates for turbulent flow has the following values 2 in. above the bottom the ratio is 0.49 6 in. above the bottom the ratio is 0.59 10 in. above the bottom the ratio is 0.77. 

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