Charge Transport by Convection

The mass charge flux owing to convection mode is given as 

The convection velocity, u, in the porous electrolyte structure is given either by Darcy s law equation (Equation 6.17) or by Brinkman s equation (Equation 6.18) as discussed in Chapter 6. 

Considering the convection velocity given by Darcy s law, the pressure-driven mass flux is given as 

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In this model, the current due to convective motion of the melt has been neglected, because the magnetic Reynolds number for this system is of the order of 10, which means that the charge transported by convection is much smaller than the diffusive current. The electric field intensity, E, can be used to calculate the local heat release rate in the slag or bullion by Joule heating according to the equation ... 

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