Dimensionless groups Rayleigh number

In the Rayleigh method of carrying out a dimensional analysis the dependent variable is assumed to be proportional to the product of the independent variables raised to different powers. By equating dimensions, the number of independent dimensionless groups and one set of their possible forms can be obtained. By way of illustration two examples may be considered. 

Important Dimensionless Groups. The average Nusselt number for steady-state heat transfer from the body shown in Fig. 4.1a depends on the dimensionless groups that arise in the nondimensionalized equations of motion and their boundary conditions [78]. With Tw and T constant, the only dimensionless groups that appear in the boundary conditions are those associated with the body shape. Provided the simplified equations (Eqs. 4.5 1.7) are valid, the only other dimensionless groups are the Rayleigh and Prandtl numbers. Thus, for a given body shape,... 

Dimensional analytical procedure was first introduced by Lord Rayleigh in 1915 (71). It is a process whereby the variables pertinent to a physical problem are systematically organized into dimensionless groups/numbers. Assuming the absence of chemical reaction and heat transfer, the following influencing and independent variables are pertinent to the wet-granulation process (72) ... 

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 ... 

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