Now that’s a different way to look at it!

Today started off like any other Thursday.  Math class painfully early in the day – at 9:45AM.  (OK, you can judge me).  My roomie preferred to sleep at home instead.  I half thought of doing the same, but grudgingly went for class.  Thankfully so!

As I was travelling on the bus, I was thinking about something funny which was on one of the question papers.  ‘Hot tomato sauce at 80C is poured onto meatballs which are at 20C.  The meatballs are cooked when their surface temperature reaches 50C.  Assuming the meatballs to be spherical balls with a conductivity k, estimate how long it takes for them to be cooked.’  🙂

This wouldn’t even hold a candle to what was about to transpire in the math class…  About 45 minutes into the class when most people had switched off, the professor suddenly wrote this on the board:

“HOW LONG DOES IT TAKE TO COOK A POTATO?”

She then proceeded to outline the steps:

1) Heat equation with initial and boundary data.

2) Write problem at steady state + transient part.

3) Separation of variables – solve ODEs.

4) Put it together and expand in eigen functions to satisfy initial conditions.

Assume that it is a 1-D problem.  L/D << 1.

Potato starts at room temperature = 20C.

Throw them into boiling water = 100C.

The potato is cooked when all pieces are at 75C atleast.

Given:  Heat diffusivity, k = 0.0025, L = 1.5

By this time, most of us were FULLY awake. 🙂  We were thinking about all the time we had eaten French fries and realized what all went into making them… 😛  Some people were also hotly debating whether this problem could be applied for French fries.  ‘Hey the potatoes are being thrown into hot water here, not oil!  So it is French Blanches!’  Some others were wondering how accurate the modeling of a potato as a perfect ellipse was.  Some others really academic types started thinking about how to model a more complex case like potato wedges, where L/D << 1 didn’t hold.  Someone’s phone rang to the ringtone ‘baahon ke darmiyan! do pyaar mil rahe hain…‘.

Meanwhile, I was in splits!  I mean, if you want to know if a potato is cooked, stick a fork into it!  Stick a fork in me, I am done with math! 😀