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David J. Stevenson modeled a magnetic mechanism for hot-Jupiter radius inflation with Konstantin Batygin. Their calculation coupled winds, a planetary magnetic field and electrical conductivity to estimate how induced electric currents deposit Ohmic heating in a giant planet's interior.^[ref]

The location of the dissipated energy is crucial. Heating a thin upper atmospheric layer need not replace the deep energy lost as the planet contracts; a useful inflation model must connect atmospheric forcing to the interior heat budget.

Konstantin Batygin, with David J. Stevenson, proposed Ohmic heating of a giant planet as a mechanism for oversized hot Jupiters. Their model used the interaction between atmospheric winds and the planetary magnetic field to drive electric currents into deeper conducting material.^[ref]

In the simple resistive description, local irreversible heating is $q=J^2/\sigma$, with current density magnitude $J$ and electrical conductivity $\sigma$. Predicting a total power still requires the spatial current distribution and its closure; choosing a large wind speed alone is not a complete heating calculation.