When will the hot cup of tea cool faster?

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TSN79
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I just sat with a cup of tea, and started wondering about this. If the cup just sits there, the tea will cool slowly. Will it cool faster if I repeatedly clench and let go of the cup? The difference between the cup surface temp and the surrounding air is higher than than between the cup and my hand, but then again I sense that the heat will have an easier time transfering to my hand than to the air...and so I sit here wondering :) What do you think?
 
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The root question is; is conduction at T_coffee times Flux_mass coffee less T_hand more effective than convection at T_coffee less T_air times Flux_mass air
 
You could actually make two cups and do the experiement. Drop a thermometer in each, and clench only one. My hunch is that the clenched one cools faster.