Diagrams, I like the ambiance plus converse of https://demonstrations.wolfram.com/TheCoffeeCoolingProblem/#more to be quite honest if you see them you'll understand what it means to calculate the area of a rectangle, which is reminiscent of the logistic map bifurcation diagrams.
acc = {};
Subscript[f, r_][x_] := (1 - x) x r;
Do[{Do[orbit[r][n] = {r,
NestList[Subscript[f, r], 0.25 r, 100][[n]]}, {n, 100}];
acc = Join[acc, Table[orbit[r][n], {n, 100}]]}, {r, -2, 4, .005}]
Graphics[{PointSize[.0001], Point[acc]}]
The thicker the cream, the smaller the thermal conductivity. Are you sure you want to make a coffee cooler? Wouldn't it be cool to see this but for the linear amplification, the heat coefficient of pure coffee and coffee (with cream) such as dT/dt = hâ‹…(0 - T), h = 0.4, instantaneously with a small amount of coffee and a massive amount of cream.
It reminds me of pouring the cream in the coffee immediately. The cream's already at room temperature right?
f[h_, T_] =
h (0 - T); StreamPlot[{1, f[h, T]}, {h, -3, 3}, {T, -3, 3},
Frame -> False, Axes -> True, AspectRatio -> 1/GoldenRatio]
If you put it in it's like a buffer against the rate of heat loss, but butter and cream affect the coffee's temperature differently; butter's thermal conductivity is much less than that of water, and creams would be better mixed into the hot coffee so butter's warmth-keeping mechanism is totally different from that of cream's.
