where we have assumed that the convective motion is isotropic in the three directions of space with typical speed wc. Using our equation of state for water, Eq. 4-4, we may simplify this to:
where AT is the difference in temperature between the upwelling and downwelling parcels that are exchanged over a height Iz = z2 - z1. Using Eq. 4-9 in Eq. 4-8 yields the following "law" of vertical heat transfer for the convection in our tank:
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