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

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POSTED BY: Patrik Ekenberg
4 Replies
POSTED BY: Micah Lindley
Posted 8 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] -> (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

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.

POSTED BY: Brian Winkel

enter image description here - Congratulations! This post is now Staff Pick! Thank you for your wonderful contributions. Please, keep them coming!

POSTED BY: EDITORIAL BOARD
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