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

Patrik Ekenberg

Patrik Ekenberg, Wolfram MathCore

Posted 7 years ago

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POSTED BY: Patrik Ekenberg

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Micah Lindley

Micah Lindley, Wolfram Alpha LLC

Posted 6 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 6 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

POSTED BY: garyb AU

Brian Winkel

Brian Winkel, SIMIODE

Posted 7 years ago

Hi - we really enjoyed your modeling of coffee cooling et al. We invite you to consider writing up a Modeling Scenario for use by students who use materials from SIMIODE at www.simiode.org - a FREE source of modeling scenarios for teaching and learning differential equations through the use of modeling and technology. We suggest offering up two versions, Student Version in which you state the modeling situation and ask students questions while making modeling activities for them and Teacher Version in which you do, much like you do here, offer ideas and extensions on solution strategies. You can see how to do this at https://www.simiode.org/about-peer-review where we offer a double-blind, peer-reviewed system for online publication at www.simiode.org. Thank you. Brian Winkel, Director SIMIODE, Director@simiode.org.