Natural convection Nusselt number

The natural convection Nusselt number in this case can be determined from Eq. 9-25 to be... 

Data are most frequently correlated by the Nusselt number (Nn )i or (NNu)om, the Graetz number Nc = (NReNpi-D/L), and the Grashof (natural-convection effects) number Ng,. Some correlations consider only the variation of viscosity with temperature, while others also consider density variation. Theoretical analyses indicate that for very long tubes approaches a limiting value. Limiting Nusselt numbers... 

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... 

Sparrow and Gregg [260] established by a perturbation analysis that the forced convection Nusselt number was altered by less than 5 percent by either an assisting or opposing natural convection if... 

Horizontal Flow. For laminar flow over the upper surface of a horizontal heated plate (or over the bottom surface of a cooled plate), the center of the mixed convection regime can again be estimated by equating the forced convection Nusselt number from Eq. 4.154 to that for natural convection from Eq. 4.39c (for detached turbulent convection). This results in... 

Flemeon is the first standard reference book that presents the equations for calculating thermal updrafts. These equations are repeated and expanded in other standard reference books, including Heinsohn, Goodfellow, and the ACGIFl Industrial Ventilation Manual.These equations are derived from the more accurate formulas for heat transfer (Nusselt number) at natural convection (where density differences, due to temperature differences, provide the body force required to move the fluid) and both the detailed and the simplified formulas can be found in handbooks on thermodynamics (e.g., Perry--, and ASHRAE -). 

Coefficients of heat transfer by natural convection from bodies of various shapes, chiefly plates and cylinders, are correlated in terms of Grashof, Prandtl, and Nusselt numbers. Table 8.9 covers the... 

The correlations cited in Tables 17.16 and 17.18 are of the Nusselt number in terms of the Reynolds and Prandtl numbers, or of the Reynolds alone. They are applicable only above specified Reynolds numbers, about 40 in most cases clearly they do not predict correctly the coefficient of natural convection, at Re = 0. 

It can be seen that the expression for the average Nusselt number for Pr 1 is closer in form to the case where Pr — oo, than the case where Pr —> 0. The reason for this is that in natural convection, the driving force is caused by the temperature gradients, and thus defined by the thermal boundary layer. When Pr 1 and when Pr — co, the thermal boundary layer is thicker than the velocity boundary layer. Hence, the behavior of the Nusselt number would be similar in form for both cases. When Pr — 0, the behavior of the kinematic viscosity relative to the thermal diffusivity is going to be different from that of the other two cases. In addition, the right-hand side of the expression for Pr — 0 is independent of o, as one would expect for this case where the effects of the kinematic viscosity are very small or negligible. 

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

Nuxn being the local Nusselt number in purely free or natural convection. 

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.)... 

Sparrow. E.M. Chrysler. G.M., and Azevedo. L.F.. Observed Flow Reversals and Measured-Predicted Nusselt Numbers for Natural Convection in a One-Sided Heated Vertical Channel . J. Heat Transfer Vol. 106, No. 2. pp. 325-332. 1984. 

Natural convection occurs when a fluid is in contact with a solid surface of different temperature. Temperature differences create the density gradients that drive natural or free convection. In addition to the Nusselt number mentioned above, the key dimensionless parameters for natural convection include the Rayleigh number Ra = p AT gx3/ va and the Prandtl number Pr = v/a. The properties appearing in Ra and Pr include the volumetric coefficient of expansion p (K-1) the difference AT between the surface (Ts) and free stream (Te) temperatures (K or °C) the acceleration of gravity g(m/s2) a characteristic dimension x of the surface (m) the kinematic viscosity v(m2/s) and the thermal diffusivity a(m2/s). The volumetric coefficient of expansion for an ideal gas is p = 1/T, where T is absolute temperature. For a given geometry,... 

From (5-35) with Pr = 0.707, the Nusselt number is 240 and the average heat-transfer coefficient due to natural convection is... 

The simple empirical correlations for the average Nusselt number Nu in natural convection are of the form (Fig. 9-9)... 

When the average Nusselt number and thus (he average convection coefficient is known, the rate of heat transfer by natural convection from a solid surface at a uniform temperature T, to the surrounding fluid is expressed by Newton s law of cooling as... 

Natural convection heat transfer in enclosed spaces has been the subjec of many experimental and numerical studies, and numerous correlations fo the Nusselt number exist. Simple power-law type relations in the form o... 

Discussion Recall that a Nusselt number of Nu = 1 for an enclosure corresponds to pure conduction heat transfer through the enclosure. The air in the enclosure in this case remains still, and no natural convection currents occur in the enclosure. The Nusselt number in our case is 1.40, which indicates that heat transfer through the enclosure is 1.40 limes that by pure conduction. The increase in heat transfer is due to the natural convection currents that develop in (he enclosure. 

To determine llie Rayleigh number, we need to know the surface temperature of the glass, which is not available. Therefore, it is clear lhat the soiulion will require a trial-and-error approach. Assuming the glass cover temperature to be 40°C, the Rayleigh number, the Nusselt number, the convection heat transfer coefficteniy and the rate of natural convection heat tiansfer from the glass cover to th e ambient air are determined to be... 

In natural convection mass transfer, the analogy betsveen the Nusselt and Sherwood numbers still holds, and thus Sh =y(Gr, Sc). But the Grashof number in this case should be determined directly from... 

Coefficients of heat transfer by natural convection from bodies of various shapes, chiefly plates and cylinders, are correlated in terms of Grashof, Prandtl, and Nusselt numbers. Table 8.9 covers the most usual situations, of which heat losses to ambient air are the most common process. Simplified equations are shown for air. Transfer of heat by radiation is appreciable even at modest temperatures such data are presented in combination with convective coefficients in item 16 of this table. 

Consider the natural convection from a horizontal cylinder rotating with an angular frequency to (Fig. 5P-9). The peripheral surface temperature of the cylinder is Tm and the ambient temperature is To,. The diameter of the cylinder is D. Assuming that the natural convection resulting from rotation and that from gravity can be superimposed, express the Nusselt number in terras of the appropriate dimensionless numbers. 

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