Nusselt number forced convection

Each of these is a ratio of a convective transfer rate to the corresponding diffusion rate of transfer. Dimensionless analysis indicates that, for fixed geometry and constant properties, the Nusselt number and the Sherwood number depend on the Reynolds number (forced convection), Rayleigh number (natural convection), flow characteristics, Prandtl number (heat transfer), and Schmidt number (mass transfer). 

First the dimensionless characteristics such as Re and Pr in forced convection, or Gr and Pr in free convection, have to be determined. Depending on the range of validity of the equations, an appropriate correlation is chosen and the Nu value calculated. The equation defining the Nusselt number is... 

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 -). 

Adams et al. (1998) investigated turbulent, single-phase forced convection of water in circular micro-channels with diameters of 0.76 and 1.09 mm. The Nusselt numbers determined experimentally were higher than those predicted by traditional Nusselt number correlations such as the Gnielinski correlation (1976). The data suggest that the extent of enhancement (deviation) increases as the channel diameter decreases. Owhaib and Palm (2004) investigated the heat transfer characteristics... 

Warrier et al. (2002) conducted experiments of forced convection in small rectangular channels using FC-84 as the test fluid. The test section consisted of five parallel channels with hydraulic diameter = 0.75 mm and length-to-diameter ratio Lh/r/h = 433.5 (Fig. 4.5d and Table 4.4). The experiments were performed with uniform heat fluxes applied to the top and bottom surfaces. The wall heat flux was calculated using the total surface area of the flow channels. Variation of single-phase Nusselt number with dimensionless axial distance is shown in Fig. 4.6b. The numerical results presented by Kays and Crawford (1993) are also shown in Fig. 4.6b. The measured values agree quite well with the numerical results. 

The heat transfer coefficient to the vessel wall can be estimated using the correlations for forced convection in conduits, such as equation 12.11. The fluid velocity and the path length can be calculated from the geometry of the jacket arrangement. The hydraulic mean diameter (equivalent diameter, de) of the channel or half-pipe should be used as the characteristic dimension in the Reynolds and Nusselt numbers see Section 12.8.1. 

No and Kazimi (1982) derived the wall heat transfer coefficient for the forced-convective two-phase flow of sodium by using the momentum-heat transfer analogy and a logarithmic velocity distribution in the liquid film. The final form of their correlation is expressed in terms of the Nusselt number based on the bulk liquid temperature, Nuft ... 

For a straight tube immersed in a well-stirred fluid, the inside film coefficient, h, may be calculated from the Nusselt number given by the general relationship applying to forced convection in tubes when Re > 10 and0.7[Pg.30]

For the prediction of the Nusselt number in ducts of non-circular-cross section (like concentric annular ducts) the same equations can be used for forced convection in the turbulent regime. In this case, the inside diameter should be replaced in evaluating Nu, Re, and (D/L) by the hydraulic diameter defined as,... 

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. 

If a flat plate is inclined with an angle p from the body force direction, show that the Nusselt number for free convection on this inclined plate is a function of Pr and Grcosp. 

In some forced convective flows it has been found that the Nusselt number is approximately proportional to the square root of the Reynolds number. If, in such a flow, it is found that h has a value of 15 W/m2K when the forced velocity has a magnitude of 5 m/s, find the heat transfer coefficient if the forced velocity is increased to 40 m/s. 

The surface tension unit length. Consider a convective heat transfer situation in which surface tension is important Show that the additional quantity pU2Ha, termed the Weber number, We, is required to determine the Nusselt number. 

The flows over a series of bodies of the same geometrical shape will be similar, i.e., will differ from each other only in scale, if the Reynolds and Prandtl numbers are the same in all the flows. From this it follows that the Nusselt number in forced convection will depend only on the Reynolds and Prandtl numbers. 

Nuxf being the local Nusselt number in forced convection. Dividing the above two equations then gives ... 

At low Reynolds numbers, the Nusselt number will tend to the constant value that would exist in purely free convection, this being designated as Afa.v, whereas at high Reynolds numbers, when the effects of the buoyancy forces are small, the Nusselt numbers will tend to the values that would exist in purely forced convection at the same Reynolds number as that being considered. These forced convection Nusselt numbers are here designated as Nur- In the combined convection regions between these two limits, the Nusselt number variation can be approximately... 

Because, for flow over a heated surface. r>ulc>x is positive and ST/ y is negative. S will normally be a negative. Hence, in assisting flow, the buoyancy forces will tend to decrease e and e, i.e., to damp the turbulence, and thus to decrease the heat transfer rate below the purely forced convective flow value. However, the buoyancy force in the momentum equation tends to increase thle mean velocity and, therefore, to increase the heat transfer rate. In turbulent assisting flow over a flat plate, this can lead to a Nusselt number variation with Reynolds number that resembles that shown in Fig. 9.22. 

At higher Reynolds numbers, i.e., between points A and B in Fig. 9.22, the effect of the buoyancy forces on the turbulence quantities is the dominant effect and the Nusselt number is, therefore, decreased below its forced convective value. At the lower Reynolds number, i.e., between B and C in Fig. 9.22, the direct effect of the buoyancy forces on the mean momentum balance becomes the dominant effect and the Nusselt number rises above its forced convective value. The changes are displayed by the numerical results shown in Fig. 9.23. These results were obtained using a more advanced turbulence model than that discussed here. 

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.)... 

This chapter has been concerned with flows in wb ch the buoyancy forces that arise due to the temperature difference have an influence on the flow and heat transfer values despite the presence of a forced velocity. In extemai flows it was shown that the deviation of the heat transfer rate from that which would exist in purely forced convection was dependent on the ratio of the Grashof number to the square of the Reynolds number. It was also shown that in such flows the Nusselt number can often be expressed in terms of the Nusselt numbers that would exist under the same conditions in purely forced and purely free convective flows. It was also shown that in turbulent flows, the buoyancy forces can affect the turbulence structure as well as the momentum balance and that in turbulent flows the heat transfer rate can be decreased by the buoyancy forces in assisting flows whereas in laminar flows the buoyancy forces essentially always increase the heat transfer rate in assisting flow. Some consideration was also given to the effect of buoyancy forces on internal flows. 

Figure 4 Normalised mass G(a), energy H(a), average enthalpy increase K(a) and transition mass flux g(a) of a droplet for the cases of (a) enthalpy improved 3EM and (b) for standard 3EM. Ambient temperature dFiame = 900°C, initial temperature 910 = 270°C, transition temperature STrans = 420 °C, initial droplet diameter di,0= 400mm, Nusselt number 18 and amplification factor of the heat conduction coefficient due to internal forced convection IWkmoiec = 2.72 (Beer [5]), residence time t=30 ms.

Flow In Round Tubes In addition to the Nusselt (NuD = hD/k) and Prandtl (Pr = v/a) numbers introduced above, the key dimensionless parameter for forced convection in round tubes of diameter D is the Reynolds number Re = (.7 ) u where G is the mass velocity G = m/Ac and Ac is the cross-sectional area Ac = kD2I4. For internal flow in a tube or duct, the heat-transfer coefficient is defined as... 

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

For a given geometry, the average Nusselt number in forced convection depends on the Reynolds and Prandtl numbers, whereas the average Sherwood number depends on the Reynolds and Schmidt numbers. That is. 

For forced convection, the heat transfer coefficient is normally correlated in terms of tliree dimensionless groups the Nusselt number, Nu, the Reynolds number, Re, and the Prandtl number, Pr. For the single spherical pellets discussed here, Nu and Re take the following forms ... 

This relation is analogous to the expression for the heat transfer by forced convection given earlier. The dimensionless group kd/D corresponds to the Nusselt group in heat transfer. The parameter rj/pD is known as the Schmidt number and is the mass-transfer counterpart of the Prandtl number. For example, the evaporation of a thin liquid film at the wall of a pipe into a turbulent gas is described by the equation... 

According to (1.56) and (1.57) the Nusselt number depends on the temperature difference (i w — t F). Although the heat transfer coefficient a is found by dividing the heat flux qw by this temperature difference, cf. (1.24), in free convection a is not independent of (i9w — dF). In other words the transferred heat flux, qw, does not increase proportionally to w — dF. This is because w — F is not only the driving force for the heat flow but also for the buoyancy, and therefore the velocity field in free convection. In contrast, the heat transfer coefficient for forced convection is not expected to show any dependence on the temperature difference. 

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