Viscous dissipation function

Table 5.6 Viscous Dissipation Function for Incompressible Newtonian Fluids...

The viscous dissipation function viscous, i e., which we have defined by T viscous = (—o Vv), represents the rate at which the shear and deviatoric... 

An obvious question that may occur to the reader is why the very simple method of integrating the viscous dissipation function has not been used earlier for calculation of the force on a solid body. The answer is that the method provides no real advantage except for the motion of a shear-stress-free bubble because the easily attained inviscid or potential-flow solution does not generally yield a correct first approximation to the dissipation. For the bubble, Vu T=0(l) everywhere to leading order, including the viscous boundary layer where the deviation from the inviscid solution yields only a correction of 0(Re x 2). For bodies with no-slip boundaries, on the other hand, Vu T is still 0(1) outside the boundary layer, but inside the boundary layer Vu T = O(Re). When integrated over the boundary layer, which is G(Re k2) in radial thickness, this produces an ()( / Re) contribution to the total dissipation,... 

Viscous dissipation function, Eq. (3.2.6) Electric potential in double layer,... 

Stresses and Viscous Dissipation Function, 463 Wall Effects, 465... 

The knowledge of the distribution of in the volume of the tank enables us to identify the zones where the energy dissipation is the most intense. Moreover, this parameter indicates which points in the tank are most at risk of local heating, if the heat transfer to outside is not sufficiently rapid. Figure 7d represents the distributions of ( ) (< ) = J(2n N D/T) ) in the same vertical plane as previously (0 = 3°). The maximum value of the viscous dissipation function is located at the impeller tip. It is clear that the distribution of < ) in the whole tank is more or less similar to the one of the normal and shear stresses x and x. Thus, only these stresses have to be considered in the case of a paddle agitator. 

This equation, when the thermal conductivity is constant and the viscous dissipation function is negligible, becomes... 

Viscous dissipation or shear heating is the conversion of mechanical energy into heat. For a fluid the, viscous dissipation function Gy relates the stress components rto the velocity gradients Vii by [8]... 

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