Cooling a cup of coffee
Cooling a cup of coffee
(OP)
Hi,
Id like to answer how much time does it take to the coffee to cool to the surrounding air?
I know the surface will cool from convection, but for example, what happens in the middle of the cup?
If someone could advice in how to make a mathematical model for this Id appreciate it.
Thanks
Id like to answer how much time does it take to the coffee to cool to the surrounding air?
I know the surface will cool from convection, but for example, what happens in the middle of the cup?
If someone could advice in how to make a mathematical model for this Id appreciate it.
Thanks





RE: Cooling a cup of coffee
1)Assuming the top to be insulated and the heat transfer rate thru the bottom is much less than along the wall of the cup, then, the flow will ascend in the middlle of the cup and descend along the wall of the cup, basically forming the shape of a toroid.
2)Assuming the heat transfer rate thru the top is equal to or greater than thru the wall, I believe that there will still be ascent thru the center until it reaches a strata below the fluid level where the flow divides mostly radially toward the wall and vertically to the surface where it will flow radially and downward along that level. That flow at the surface will reach the wall but most of the flow will be directed downward in that strata until it joins the radial flow at the bottom of that strata. At the wall the flow will descend to the bottom of the cup.
RE: Cooling a cup of coffee
RE: Cooling a cup of coffee
http://en.wikipedia.org/wiki/Marangoni_effect
and/or
http://en.wikipedia.org/wiki/Rayleigh%E2%80%93B%C3...
RE: Cooling a cup of coffee
Further, you put the hot coffee in the room, the room heats up and the cup cools, therefore it will meet somewhere in the middle. But what is a few 0.001 matter?
Best model needs convection from the top as a hot surface below a cylinder wall, evaporation out the top, radiation out on all sides, convection up the walls as a cylinder, and conduction from the bottom to the 'floor" (table ?)
RE: Cooling a cup of coffee
About 1 to 2 months into each new semester, the same physics I question comes up - how strange.
RE: Cooling a cup of coffee
RE: Cooling a cup of coffee