Nusselt number correlation

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... 

In the previous chapters on temperature variations in reactors, we needed heat transfer coefficients h to calculate rates of heat transfer within the reactor. For a more detailed examination of temperature variations, we must use Nusselt number correlations similar to those developed here for mass transfer. 

For Reynolds number greater than about 5, the Nusselt-number correlation depends on the square root of the Reynolds number... 

Consider now the heat-transfer coefficients that emerge from the Nusselt number correlations in the two cases. For the finite gap,... 

The inside film heat transfer coefficient (h ) can be calculated from the following Nusselt number correlation ... 

Velocity and temperature found by similarity method Also solved by use of the integral method Then heat transfer coefficient found in Nusselt number Correlation between Nusselt number and Grashof number. 

Estimates of the film thicknesses, 8j, needed to determine the gas-phase temperature and weight fraction profiles are based on the empirical Nusselt number correlations developed by Ranz and Marshall (23) for... 

Analysis For a tube with a known diameter and volume flow rate, the type of flow regime is determined before making any decision regarding which Nusselt. number correlation to use. The Reynolds number at the specified location is... 

For large-scale fermenters with multiple impellers, there are very few heat transfer correlations available. Most of the experimental investigations have been done with Newtonian liquids with a single, standard impeller. The following ungassed liquid phase Nusselt number correlation for heat transfer at the tank wall, in different vessel geometries with four standard baffles and a Rushton turbine, was developed by Strek.t ... 

A large number of empirical correlations is available for estimating the Nus-selt number in both packed- and fluidized beds. A Nusselt number correlation proposed by Gunn [60] was used. The Nusselt number parameterization represents a functional fit to experimental data for Reynolds number up to 10 in the porosity range 0.35 — 1 ... 

Let us now return to (11 33), which is valid for any arbitrary (no-slip) 2D body in the limit Re 1, /V 1. As noted earlier, the geometry of the body enters at this leading order of approximation only through the function X(x). The somewhat surprising fact is that we can solve (1133) for arbitrary X(x). Hence we can obtain a universal first approximation for 9 and for the Nusselt number correlation (11-36). 

Figure 11-7. A comparison of the asymptotic forms for the local Nusselt number correlation for Pr

For developing longitudinal laminar flow between a square array of cylinders with a uniform wall heat flux, the local Nusselt number correlations were made by Miyatake and Iwashita [256] as follows ... 

Corrections by Morgan [66] for the combined effects of free-stream turbulence and wind tunnel blockage on Nusselt numbers measured in air are shown in Fig. 6.27. Here, dldT is the ratio of the cylinder diameter to the wind tunnel height or diameter, 8 Nu<( is the increase in the Nusselt number over Hilpert s measurements (Fig. 6.26), and Tu is the intensity of the longitudinal turbulent fluctuations in the free stream. In addition to these corrections, Morgan also proposed the Nusselt number correlations shown in Table 6.7 that are applicable to an extremely wide range of Reynolds numbers in air. At the higher Reynolds numbers, these Nusselt numbers are quite consistent with those of Fig. 6.26. 

Note that T 0 = 1 on the fluid side, which does not have fins. For fully developed turbulent flow through constant cross-sectional ducts, the Nusselt number correlation is of the form... 

The transition flow and fully developed turbulent flow Nusselt number correlation for a circular tube is given by Gnielinski as reported in Bhatti and Shah [46] as... 

The friction factor and Nusselt number correlations for the circular duct are the most reliable and agree with a large amount of the experimental data within 2% and 10% respectively. The correlations for all other duct geometries are not as good as those for the circular duct on an absolute basis. 

The downstream jets are subjected to crossflow originating from the upstream jets. Average Nusselt number correlations appropriate for use in analyzing circular jet array impingement systems in which the flow is constrained to exit in a single direction along the channel formed by the jet plate and the impingement surface, have been developed by Florschuetz et al. [92], The correlation adopted is of the form... 

For fully turbulent jets issuing from a fully developed pipe-type nozzle at Hid < 4, Stevens and Webb [97] recommend the following stagnation zone Nusselt number correlation ... 

In these equations, Tj is the temperature at coordinates (r, t) in the macrograin, pcp is the average value of the heat capacity per unit volume of the macroparticle, is the effective thermal diffiisivity in the macrograin and (—Affr) the enthalpy of polymerization. In Equation 2.141, the parameter hp is the average convective heat transfer coefficient, usually calculated from a Nusselt number correlation. Early works tended to use the well-known Ranz-Marshall correlation for evaporation from a droplet however, it has been... 

Nusselt Number Correlations for Single-Phase Flows... 

The average Nusselt number has been found to have the fiinctional form Nu = C- Re "- Pr . The coefScient C depends on the Sow characteristics. For jet Sows with equivalent exit diameter D , C depends on the ratio of nozzle-to-plate distance and nozzle-diameter, L/D. For single round nozzles, Martin [15] and Beitelmal and Saad [16] suggested Nusselt number correlations proportional to Re and Re respectively. Mohanty and Tawfek [17] found Nusselt number dependences between Re and Re for different nozzle diameters. In the current study, for Re > 20,000, the foUowing correlation can be used to represent the data for single-phase Sow ... 

In turbulent flow, the boundary conditions constant wall temperature and constant heat flux lead to approximately the same mean Nusselt numbers. Correlations in the far turbulent regime (Re> 10 ) are noted here. The hydrodynamic entry length is approximately independent of Re, so that an approximation for fully turbulent flow after length x can be made for... 

If inlet effects, such as the simultaneous development of the flow profile, are found to be important, it is known [39] that Sherwood (or Nusselt) number correlations exhibit three distinct dependences in different ranges of the Graetz parameter. For Dirichlet boundary condition, these are given by... 

Further, these data provide evidence that the heat flux to the sidewalls is quite uniform. This again is in contrast to a frctor of two (peak-to-average) non-uniformity found in an aspect-ratio-one pool by Steinbemer and Reineke, even though their Nusselt number correlation, for the mean, was in reasonable agreement with the present data. 

---