Frossling number

Kato and Wen (5) found, for the case of packed beds,that there was a dependency of the Sherwood and Nusselt numbers with the ratio dp/L. They proposed that the fall of the heat and mass transfer coefficients at low Reynolds numbers is due to an overlapping of the boundary layers surrounding the particles which produces a reduction of the available effective area for transfer of mass and heat. Nelson and Galloway W proposed a new model in terms of the Frossling number, to explain the fall of the heat and mass transfer coefficients in the zone of low Reynolds numbers. 

In other works (, ), Galloway and Sage state that the Frossling number (a) varies in the turbulent regimes(900model predict in the range of our experimental values. 

Fig. 5.19 Local Sherwood number for a sphere Solid lines are the numerical results of Woo (W9) and Hatim (Hll) at the values of Re and Sc indicated. Points are the data of Frossling (F3) for sublimation of naphthalene into air.

The case of combustion of an entire spherical surface with forced convection has not yet been solved. Frossling (4) originally proposed a semi-empirical relation for the low-temperature evaporation of droplets in motion. Spalding (60) has applied the equation to his heterogeneous combustion data with some success by including the term containing the transfer number ... 

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... 

A. Solid particles suspended in agitated vessel containing vertical baffles, continuous phase coefficient A = 2 + 0.6N tNS Replace vz [p with uT = terminal velocity. Calculate Stokes law terminal velocity c d lp,-pjg K 18 ic and correct 1 10 100 1,000 10,000 100,000 [S] Use log mean concentration difference. Modified Frossling equation = Vn "P ° Re (Reynolds number based on Stokes law.) V -vTdrP° A Re,r — (terminal velocity Reynolds number.) kl almost independent of dp. Harriott suggests different correction procedures. Range ki/k is 1.5 to 8.0. [74] [ 138] p. 220-222 [110] [74]... 

Frossling studied vaporizing droplets without combustion and found that KjK = 1 + 0.276 Re Sc, where Sc is the Schmidt number (Appendix E), Re is the Reynolds number, and is the value of K for evaporation in the same atmosphere without forced convection. Here... 

Case 2 Shear between Particles and the Fluid If the particles are sheared by the fluid motion, one can neglect the 2 in the Frossling correlation between the Slherwood number and Reynolds number, and... 

Keywords Dufour effect Evaporation Frossling correlation Heat transfer Fatent heat Mass transfer Nusselt number Ranz-Marshall correlation Soret effect Stefan flow... 

The polymer particles/aqueous phase mass-transfer coefficient can be determined through the Frossling equation [73], where Sh is the Sherwood number. Re the Reynolds number, and Sc the Schmidt number. 

Frossling [6] had earlier presented an almost identical equation and showed theoretically that the Sherwood number should take on a value of 2 in a stagnant fluid moreover, there were theoretical grounds for expecting the square root dependence on the Reynolds number that he had observed experimentally. Frossling s experiments concerned the evaporation of nitrobenzene, aniline, water, and napthalene into a hot air stream, within the Reynolds number range 2 < < 1300. 

The subject of mass transfer from solid spheres has recently been examined by Keey and Glen [11], who maintained that the exponent of the Reynolds number in an equation of the Frossling type should increase with increasing Reynolds number due to the changing importance of wake transfer with Reynolds number and due to the onset of turbulence in the boundary layer. Keey and Glen recommended a different correlation for each Reynolds number region. 

The reader may find the number of correlations presented here for the mass transfer coefficients somewhat confusing. It is to be stressed that the expressions proposed by Frossling, Rantz and Marshall, and Rowe and Claxton give virtually identical results for the range of Reynolds and Schmidt numbers usually encountered in gas-solid reaction systems of practical interest. Indeed the ""rate expressions"" for gas-solid mass transfer constitute an area where most investigators appear to be in quite good agreement. 

---