Ranz and Marshall correlation

O. For liquids and gases, Ranz and Marshall correlation Nsh = - = 2.0 + 0.eNgNg AT dpVt uperP i-yRe R [E] Based on freely falling, evaporating spheres (see 5-20-C). Has been applied to packed beds, prediction is low compared to experimental data. Limit of 2.0 at low is too high. Not corrected for axial dispersion. [121][128] p. 214 [155] [110]... 

Bt = Cp(Tg,p — 7 )/(A/tv), where FFg.p is the fuel vapor mass fraction interpolated to the droplet location. For 7 > Jb, By is set equal to Bj. The Clausius-Qapeyron equilibrium vapor-pressure relationship is used to compute the fuel mass fraction at the droplet surface. In addition, convective correction actors (based on Ranz and Marshall correlations) are applied to obtain spray evaporation rates at high Reynolds numbers. Liquid properties are evaluated using the one third rule for reference mass fractions [28]. Advanced models for droplet evaporation accounting for nonequilibrium effects can also be incorporated in the above framework by altering the timescales associated with the droplet lifetime and the convective heating. 

The Sherwood nnmber, Shp, was correlated in the following variant of the Ranz and Marshall correlation (Eq. 6.4) ... 

Thus, the Ranz and Marshall correlations for heat transfer may be written... 

Ranz and Marshall 51 have carried out a comprehensive study of the evaporation of liquid drops and confirm that equation 10.231 correlates the results of a number of... 

Rate-process parameters estimation of kAg for spherical particle. The three rate-process parameters in the expressions for t(fB) (kAg,De, and jkAj),may each require experimental measurement for a particular situation. However, we consider one correlation for estimating kA for spherical particles given by Ranz and Marshall... 

Correlations for heat transfer coefficient between a single sphere and surrounding gas have been proposed by many researchers (Table 5.2), for example, Whitaker,1584 and Ranz and Marshall,15051 among others. The correlation recommended by Whitaker is accurate to within 30% for the range of parameter values listed. All properties except jus should be evaluated at Tm. For freely falling liquid droplets, the Ranz-Marshall correlation 505 is often used. The correlations may be applied to mass transfer processes simply by replacing Nu and Pr with Sh and Sc, respectively, where Sh and Sc are the Sherwood number and Schmidt number, respectively. Modifications to the Ranz-Marshall correlation have been made by researchers to account... 

In a supersonic gas flow, the convective heat transfer coefficient is not only a function of the Reynolds and Prandtl numbers, but also depends on the droplet surface temperature and the Mach number (compressibility of gas). 154 156 However, the effects of the surface temperature and the Mach number may be substantially eliminated if all properties are evaluated at a film temperature defined in Ref. 623. Thus, the convective heat transfer coefficient may still be estimated using the experimental correlation proposed by Ranz and Marshall 505 with appropriate modifications to account for various effects such as turbulence,[587] droplet oscillation and distortion,[5851 and droplet vaporization and mass transfer. 555 It has been demonstrated 1561 that using the modified Newton s law of cooling and evaluating the heat transfer coefficient at the film temperature allow numerical calculations of droplet cooling and solidification histories in both subsonic and supersonic gas flows in the spray. 

Most of the data available to substantiate Equations 1 to 4 pertain to single droplets in still air. Therefore, in most cases, the Nusselt number is 2, and Froessling s correlation for the Nusselt number in terms of the Reynolds and Schmidt numbers is neither verified nor cast in doubt. Data of Ranz and Marshall (102) do afford substantiation in particular, they verify Equation 4. 

Although some controversy exists on the correlation of Sherwood Number applicable to fluidized beds, well-defined combustion experiments support the use of the Ranz and Marshall (35) or Frossling (36) correlation with an approximate correction of mf to allow for the obstruction to diffusion by the inert particles surrounding the burning char particles (37). Thus... 

Ranz and Marshall (13) carefully studied the evaporation of water droplets in still and moving air. They found that the steady-state temperature at the surface of a small evaporating drop was the wet bulb temperature of the surrounding air. Marshall considered the dependence of the effective mass transfer coefficient on air velocity to be determined largely by the boundary layer of less mobile air at the droplet surface, and he reported correlations which show that varied linearly with v1/2. Ranz and Marshall s data clearly show this relation, which we may write as Equation 5. 

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... 

A standard correlation for heat transfer to a sphere is given by (Ranz and Marshall, 1952)... 

Based on FYosslings development, Ranz and Marshall [121] came to the well established conclusion that the heat transfer correlation can be expressed in an analogous manner ... 

Investigator Type of correlation Phases involved Correlation equation Range of applicability Ranz and Marshall [26] Particle-to-fluid heat transfer (single-particle system) Fluid-solid Nu = 2 + 0.6Rep 2 Pr1/3 Re, > 50... 

The heat-transfer coefficient is evaluated using the correlation of Ranz and Marshall (1952a,b) ... 

The mass-transfer coefficient in Equation 4.18 is calculated from the Sherwood correlation (Ranz and Marshall 1952a,b) ... 

For spray dryers, the popular equation of Ranz and Marshall [132] is presented in Table 4.9 (Equations T9.13 and T9.14). They correlated data obtained for suspended drops evaporating in air. 

There are various expressions for the Sherwood and Nusselt numbers if the relative drop-gas velocity is nonzero, i.e., for forced convection. Widely used correlations are those by Ranz and Marshall [20]. These were obtained from experiments of vaporizing single-component drops at atmospheric pressure and moderate ambient temperatures with low transfer rates, that is, when B = B kQ and, therefore, Nmo = 5/jo = 2. These correlations are given by... 

On the other hand, for very small particles (Rep<< lor 0), mass transfer can be depicted by diffusion in an infinite quiescent medium. For such a situation, the limit of Shp=2 implicit in Ranz and Marshall s correlation suggests that with decreasing particle diameter, must increase in a hnearly reciprocal manner. 

Harriott s data on in stirred tanks were found to be 1.5-8 times higher as compared to those estimated from the steady-state correlations of Ranz and Marshall (1952b) and Friedlander (1957) using the particle Reynolds number based on in Equations 6.14 and 6.15, respectively. In view of the complex procedure for calculating the true slip velocity of a particle suspended in stirred tank from Equation 6.16, Harriott (1962a) suggested a modified, simple procedure to estimate (i) compute... 

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