Dimensionless groups Grashof number

N, IVc, IVnu IVp. K, IVh. IVs. N Proportionality coefficient, dimensionless group Grashof number, L p P Af/)U Nusselt number, hD/k or hL/k Peclet number, DGc/k Prandtl number, c A/k Reynolds number, DG/ l Stanton number, Number of sealing strips Dimensionless Dimensionless... 

American engineers are probably more familiar with the magnitude of physical entities in U.S. customary units than in SI units. Consequently, errors made in the conversion from one set of units to the other may go undetected. The following six examples will show how to convert the elements in six dimensionless groups. Proper conversions will result in the same numerical value for the dimensionless number. The dimensionless numbers used as examples are the Reynolds, Prandtl, Nusselt, Grashof, Schmidt, and Archimedes numbers. 

Several dimensionless groups characterize these equations. The Reynolds number Re = f O/Poo indicates the ratio of centrifugal forces to viscous forces. The ratio of the Grashof number and the Reynolds number to the 3/2 power,... 

The other governing equations—the overall eontinuity equation, the speeies eontinuity equation, and the energy equation—are identieal to the dimensionless forms presented in Chapter 1. Two new dimensionless groups, a thermal Grashof number... 

The Grashof number may be interpreted physically as a dimensionless group representing the ratio of the buoyancy forces to the viscous forces in the free-convection flow system. It has a role similar to that played by the Reynolds number in forced-convection systems and is the primary variable used as a criterion for transition from laminar to turbulent boundary-layer flow. For air in free convection on a vertical flat plate, the critical Grashof number has been observed by Eckert and Soehngen [1] to be approximately 4 x 10". Values ranging between 10" and 109 may be observed for different fluids and environment turbulence levels. ... 

There are many well-known dimensionless groups that are used in transport phenomena. Earlier, the Reynolds number was used to correlate data on pressure drop in pipe flow. For correlating data on heat transfer, often the dimensionless groups Nus-selt (Nu), Reynolds (Re), Prandtl (Pr), and Grashof (Gr) are used. They are defined as ... 

Heat transfer by free convection can thus be presented as a relation between three dimensionless groups Cpt]/k is known as the Prandtl number, the combination l ATagp /tf as the Grashof number, and ql/AT, the Nusselt number may also be written hl/k. 

The functional dependence expressed in Equations 4.29 and 4.31 governs the behavior of convective heat transfer. In some cases the functionality can be determined analytically, but in most cases it can be determined only as a statistical correlation of experimental data. Dimensionless groups are used to generalize empirical correlations for convective heat transfer. These groups can be determined from the parameters in Equations 4.29 and 4.31. They are the Reynolds, Nusselt, Grashof, and Prandtl numbers, respectively, defined as ... 

Since the effect of j5 is through buoyancy in a gravitational field, the product gP AT acts as a single factor, and the last two groups fuse into a dimensionless group called the Grashof number Nq,. 

For single horizontal cylinders, the heat-transfer coefficient can be correlated by an equation containing three dimensionless groups, the Nusselt number, the Prandtl number, and the Grashof number, or specifically. 

As we have seen, the critical dimensionless groups for free or natural convection are the Grashof and Prandtl numbers. In general (the h will be a mean value). 

For gravity driven free convection the velocity v is not known a priori therefore one has to use relations with a dimensionless group containing the acceleration of gravity. This is expressed by the Grashof number Gr, or by the Rayleigh number Ra ... 

Dimensionless groups are as follows — and f jav are Reynolds numbers vjD is the Schmidt number d g( is the Grashof number, kdjD is... 

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