Abstract
where the integrals are taken over the Earth's core. F. J . Lowes has pointed out that (1) also holds when the integral on the right-hand side is taken over V + V' , the whole of space, and includes the external magnetic field. This form of the inequality furnishes better bounds on the heat flux, which are derived below. Paper 1 contains some algebraic errors which are corrected. The Ohmic heat flux was bounded in 1 by minimizing the integral:
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