Ohmic dissipation term

The last term in (5.45) accounts for quantum corrections to the classical escape rate (5.32) [Dakhnovskii and Ovchinnikov 1985 Grabert and Weiss, 1984 Melnikov and Meshkov, 1983 Wolynes, 1981]. In the case of ohmic dissipation the product in (5.45) can be calculated explicitly and one obtains for the quantum correction factor... 

The formal similitude between Eq. (30) and Ohm s law in an electrical circuit justifies the term of Ohmic model given to the dissipation model as defined by the spectral density (23). 

It is important to emphasize that the terms due to the Ohmic conductivity appear as a contribution to the dielectric loss, which decays at low frequency with 1/ft). Fitting the calculated e" curve with a l/o) fimction, therefore, one can calculate the Ohmic conductivity. Both the dielectric and Ohmic loss contribute to the dissipation, which is defined as... 

Here, K and Cp are, respectively, the thermal conductivity and specific heat capacity of the fluid. The viscous dissipation

strain rate tensor, e = i(V + (Vm) ). The second term of equation (7.59) is the ohmic heating due to the passage of the current. 

As current density increases (corresponding also to reduced cell voltage), the thermal energy dissipation flux will increase. The first term on the right-hand side of Eq. (5.110) represents Peltier heating. The second term on the right-hand side represents the sum of the activation (kinetic), concentration, ohmic, and crossover contributions to the heat generation. 

It is evident from the previous discussion that significantly sim-phfied modeling of the current distribution can often be achieved once scaling analysis has identified the controlling dissipative mechanisms in the cell. It has been shown that the current distribution in most common systems can be characterized in terms of three major dissipative processes ohmic (within the electrolyte across the cell), mass transport (across the concentration bmmdary layer), and surface activation (on the electrode). These are designated in terms of the corresponding resistances R q,R q, and R. The Wa number characterizes the cmrent distribution in terms of the relative importance of two of the three resistances the surface (Jfg)and the ohmic (Rq ) resistances.Clearly,more complete characterization of the system requires the comparison of two additional resistance ratios and the formulation of two additional dimensionless parameters. ... 

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