Can the TdS(adsbygoogle = window.adsbygoogle || []).push({}); by a systembe calculated by taking the area, time double integral of the heat flux density?

If so, is it possible that this double-integral would take on an opposite sign if inside there was a dominating, growing black hole, where, I would presume, heat flows inwards, and not outwards? The divergence of the field inside the surface would therefore have an opposite sign, so would a growingblackhole therefore be a TdS reducer?

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# Can TdS be computed using an area, time double integral of heat flux density?

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