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Staff Picks Engineering Physics Modeling SystemModeler Materials and Manufacturing

Coffee optimization, how to get your cup of joe just right

Patrik Ekenberg

Patrik Ekenberg, Wolfram MathCore

Posted 10 years ago

POSTED BY: Patrik Ekenberg

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Micah Lindley

Micah Lindley, Wolfram Alpha LLC

Posted 9 years ago

What a cool use of System Modeler Patrik! Here's a link to an article by Nathan Myhrvold (former CTO of Microsoft) explaining why adding milk to your coffee immediately keeps the coffee warmer than adding the milk just prior to drinking the coffee: http://modernistcuisine.com/2012/12/the-physics-of-coffee-cream/

POSTED BY: Micah Lindley

garyb AU

garyb AU, Retired

Posted 9 years ago

Alternatively, drop it into Mathematica with manipulate. Manipulate[ { sols = NDSolve[{ D[Temp[t], t] == -0.1 (Temp[t] - ambient), Temp[0] == beginTemp, WhenEvent[ t > addMilk, Temp[t] -> (coffeeTemp[t] + milkmilkTemp)/(coffee + milk)]}, Temp, {t, 0, experimentTime} ]; Plot[ Temp[t] /. sols, {t, 0, experimentTime}, PlotRange -> {{0, experimentTime}, {0, beginTemp + 10}}, AxesLabel -> {"Time (minutes)", "Temperature ?C"}, LabelStyle -> Directive[Bold, Medium], ImageSize -> {{400, 600}}] }, {{ambient, 20, "Ambient temperature"}, 0, 30, 0.5, Appearance -> "Labeled"}, {{experimentTime, 30, "Time of Experiement(minutes)"}, 1, 100, 0.5, Appearance -> "Labeled"}, {{beginTemp, 80, "Coffee start temperature"}, 50, 100, 0.5, Appearance -> "Labeled"}, {{milkTemp, 5, "Milk start temperature"}, 1, ambient, 0.5, Appearance -> "Labeled"}, {{addMilk, 1, "Time to add milk(minutes)"}, 1, 100, 1, Appearance -> "Labeled"}, {{coffee, 200, "Coffee volume (ml)"}, 100, 500, 10, Appearance -> "Labeled"}, {{milk, 20, "Milk volume (ml)"}, 0, 50, 5, Appearance -> "Labeled"}, ControlPlacement -> Left ]

Alternatively, drop it into Mathematica with manipulate.

Manipulate[
 {
  sols = NDSolve[{
     D[Temp[t], t] == -0.1 (Temp[t] - ambient),
     Temp[0] == beginTemp,
     WhenEvent[
      t > addMilk,
      Temp[t] -> (coffee*Temp[t] + milk*milkTemp)/(coffee + milk)]},
    Temp,
    {t, 0, experimentTime}
    ];
  Plot[
   Temp[t] /. sols, {t, 0, experimentTime},
   PlotRange -> {{0, experimentTime}, {0, beginTemp + 10}},
   AxesLabel -> {"Time (minutes)", "Temperature  ?C"},
   LabelStyle -> Directive[Bold, Medium],
   ImageSize -> {{400, 600}}]
  },
 {{ambient, 20, "Ambient temperature"}, 0, 30, 0.5, 
  Appearance -> "Labeled"},
 {{experimentTime, 30, "Time of Experiement(minutes)"}, 1, 100, 0.5, 
  Appearance -> "Labeled"},
 {{beginTemp, 80, "Coffee start temperature"}, 50, 100, 0.5, 
  Appearance -> "Labeled"},
 {{milkTemp, 5, "Milk start temperature"}, 1, ambient, 0.5, 
  Appearance -> "Labeled"},
 {{addMilk, 1, "Time to add milk(minutes)"}, 1, 100, 1, 
  Appearance -> "Labeled"},
 {{coffee, 200, "Coffee volume (ml)"}, 100, 500, 10, 
  Appearance -> "Labeled"},
 {{milk, 20, "Milk volume (ml)"}, 0, 50, 5, Appearance -> "Labeled"},
 ControlPlacement -> Left
 ]

Manipulate parameters for coffee cup cooling