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?
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.