Nusselt number

In a quiescent fluid, the dimensionless mass-transfer coefficient, or the Nusselt number, djkj for a sphere is two. In fluidized beds the Nusselt... 

Nusse/t Number. Empidcal correlations can be obtained for a particular size of tube diameter and particular flow conditions. To generalize such results and to apply the correlations to different sizes of equipment and different flow conditions, the heat-transfer coefficient, Z, is traditionally nondimensionalized by the use of the Nusselt number, Nu named after Wilhelm Nusselt,... 

Correlations for Convective Heat Transfer. In the design or sizing of a heat exchanger, the heat-transfer coefficients on the inner and outer walls of the tube and the friction coefficient in the tube must be calculated. Summaries of the various correlations for convective heat-transfer coefficients for internal and external flows are given in Tables 3 and 4, respectively, in terms of the Nusselt number. In addition, the friction coefficient is given for the deterrnination of the pumping requirement. 

The convective heat-transfer coefficient and friction factor for laminar flow in noncircular ducts can be calculated from empirically or analytically determined Nusselt numbers, as given in Table 5. For turbulent flow, the circular duct data with the use of the hydrauhc diameter, defined in equation 10, may be used. 

NUh2 is the Nusselt number for uniform heat flux boundary condition along the flow direction and periphery. 

Heat transfer in static mixers is intensified by turbulence causing inserts. For the Kenics mixer, the heat-transfer coefficient b is two to three times greater, whereas for Sulzer mixers it is five times greater, and for polymer appHcations it is 15 times greater than the coefficient for low viscosity flow in an open pipe. The heat-transfer coefficient is expressed in the form of Nusselt number Nu = hD /k as a function of system properties and flow conditions. 

The dimensionless group hD/k is called the Nusselt number, Nn , and the group Cp i./k is the Prandtl number, Np. . The group DVp/ i is the familiar Reynolds number, encountered in fluid-friction problems. These three... 

The classical (and perhaps more famihar) form of dimensionless expressions relates, primarily, the Nusselt number hD/k, the Prandtl number c l//c, and the Reynolds number DG/ I. The L/D and viscosity-ratio modifications (for Reynolds number <10,000) also apply. 

TABLE 5-4 Values of Limiting Nusselt Number in Laminar Flow in Closed Ducts... 

Limiting Nusselt numbers for slug-flow annub may be predicted (for constant heat flux) from Trefethen (General Discu.s.sion.s on Heat Tran.sfer, London, ASME, New York, 1951, p. 436) ... 

Limiting Nusselt numbers for laminar flow in annuli have been calculated by Dwyer [Nucl. Set. Eng., 17, 336 (1963)]. In addition, theoretical analyses of laminar-flow heat transfer in concentric and eccentric annuh have been published by Reynolds, Lundberg, and McCuen [Jnt. J. Heat Ma.s.s Tran.sfer, 6, 483, 495 (1963)]. Lee fnt. J. Heat Ma.s.s Tran.sfer, 11,509 (1968)] presented an analysis of turbulent heat transfer in entrance regions of concentric annuh. Fully developed local Nusselt numbers were generally attained within a region of 30 equivalent diameters for 0.1 < Np < 30, lO < < 2 X 10, 1.01 <... 

Parallel Plates and Rectangular Ducts The limidng Nusselt number for parallel plates and flat rectangular ducts is given in Table 5-4. Norris and Streid [Tran.s. Am. Soe. Meeh. Eng., 62, 525 (1940)] report for constant wall temperature... 

A droplet Nusselt number = 2, corresponding to pure conduction (Reynolds number = 0) to infinity, is employed for evaluating the coefficient of heat transfer. 

For low values of the Reynolds number, such as 10, where sn eamline flow should certainly apply, the Nusselt number has a value of about 2, and a typical value of the average heat transfer coefficient is 10 ". For a Reynolds number of 104, where the gas is certainly in turbulent flow, the value of the Nusselt number is typically 20. Hence there is only a difference of a factor of ten in the heat transfer coefficient between tlrese two extreme cases. 

The Nusselt number for the heat transfer between a gas and a solid particle of radius d, is given by the Ranz-Marshall equation... 

This yields a value of 4 for die Nusselt number in a situation where Nrs is about 10, which is typical of a small laboratoty study. 

The inside film heat transfer eoeffieient (h ) ean be ealeulated from the following Nusselt number eorrelation ... 

Agitator type Baffled Reynolds number (Np ) Nusselt number Remarks... 

Other dimensionless parameters, namely the Reynolds number, Prandtl number, and Nusselt number ean be represented as follows ... 

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... 

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