Per unit area, is there more heat transfer through the open top of a mug or the side walls?

Question

I had a mug of hot coffee cool too rapidly for my liking the other day, which made me wonder what was the greater contributor to heat loss for a typical open-top ceramic mug: the open top, the walls, or the base?

The open top allows the coffee to radiate to the room, free convection with the ambient air, and heat loss through evaporation.

The side walls have conduction to the mug walls, free convection between the air and the mug, radiation, and the thermal capacitance of the mug itself (assuming room temperature when filled).

The bottom is similar to the sides, but a thin ring is in direct contact with the table and there is a pocket of trapped air between most of the bottom and the table.

Per unit area (which should normalize the contribution of the various cmponents) where is more heat lost?

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I can't determine where convective heat transfer will be greater. The air in the top of the mug is relatively stagnant, but evaporating steam might stir things up. The mug wall temperature will be lower than the coffee because of the temperature drop across the mug wall.

Answer 1

I'm sure it depends on the mug and the temperature of the coffee, but most of the time I bet that evaporative cooling from the top is the dominant source of heat loss. That's just based on experience--like it stays hot much longer when you cover the top, and much shorter when you blow on the top. I also think that it cools at a similar rate in my ceramic mug versus my well-insulated thermal mug when I don't cover either.

My experience suggests that the heat capacity of the ceramic mug itself is much smaller than the liquid inside, so that the warming-the-mug cooling makes little difference. That's something that could be easily calculated though.