My Math Forum Thermos flask construction.

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 April 17th, 2017, 10:04 AM #1 Banned Camp   Joined: Aug 2011 Posts: 534 Thanks: 2 Thermos flask construction. 1 Can the Geometrical shapes changes in the Thermos flask design can improve the Hot or Cooling property of the Thermos flask? 2 Can we trace for how much duration do the beverages remain hot or Cold drinks remain cool in the Thermos flask? Thanks & Regards, Prashant S Akerkar
 April 17th, 2017, 10:09 AM #2 Senior Member   Joined: Aug 2012 Posts: 2,342 Thanks: 731 I always make ice cubes with hot water. That way any time I need hot water I can just defrost them. (Joke credit: The great Gracie Allen)
 April 17th, 2017, 10:16 AM #3 Banned Camp   Joined: Aug 2011 Posts: 534 Thanks: 2 Thanks. 1 Can the changes in Geometrical shapes of the Thermos flask increase the Hot or Cooling property of the Beverages kept inside? 2 Can we trace the duration as how much time the beverages remain hot or cool inside ? Any Mathematical equation can be derived ? Thanks & Regards, Prashant S Akerkar
 April 17th, 2017, 12:03 PM #4 Math Team     Joined: Jul 2011 From: Texas Posts: 2,980 Thanks: 1573 The Thermos is a great invention. It keeps hot things hot and cold things cold, but the amazing thing is ... how do it know? Thanks from Benit13
 April 17th, 2017, 11:09 PM #5 Banned Camp   Joined: Aug 2011 Posts: 534 Thanks: 2 Thanks. Experiment -------------------- We boiled 500 ml water with Boiling point reached as 100 ° Celsius, and then kept it inside the Thermos flask device. 1 For how much duration the water will remain hot in the Thermos flask ? Any Mathematical equation derived for the same? 2 Can different Geometrical shapes of the Thermos flask device can impact the duration increase of water remaining hot in the Thermos flask device? Thanks & Regards, Prashant S Akerkar Last edited by prashantakerkar; April 17th, 2017 at 11:12 PM.
April 18th, 2017, 07:25 AM   #6
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Quote:
 Originally Posted by prashantakerkar Can the Geometrical shapes changes in the Thermos flask design can improve the Hot or Cooling property of the Thermos flask?
Minimise surface area.

April 24th, 2017, 01:30 AM   #7
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Quote:
 Originally Posted by prashantakerkar Thanks. Experiment -------------------- We boiled 500 ml water with Boiling point reached as 100 ° Celsius, and then kept it inside the Thermos flask device. 1 For how much duration the water will remain hot in the Thermos flask ? Any Mathematical equation derived for the same? 2 Can different Geometrical shapes of the Thermos flask device can impact the duration increase of water remaining hot in the Thermos flask device? Thanks & Regards, Prashant S Akerkar
It's always good (and fun!) to perform an experiment, but you might want to read a bit about the basic processes of heat transport first, namely conduction, convection and radiation. The design of the thermos flask is to reduce all three of these.

As for the points...

1. The surface area is probably the most important parameter, although if you choose a wacky geometry the theoretical calculations get harder and the choice of convective heat transfer coefficient, which is geometry dependent, might become important.

As for the mathematics, there are equations that describe conduction, convection and radiation and can be combined to create a heat transfer formula for any desired situation. It's basically the conservation of energy formula applied to a control volume:

$\displaystyle \dot{E_{cond}} + \dot{E_{conv}} + \dot{E_{rad}} + \dot{E_{stored}} = \dot{E_{out}} - \dot{E_{in}}$

where each of the terms can be replaced by an equation relevant for that process. There's also the electricity analogy method for solving heat transfer problems.

2. Yes. Presumably the spherical volume is the one with the best volume to heat loss ratio, but no one wants to put a spherical thermos in their bag on the way to work!

April 24th, 2017, 06:36 AM   #8
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Quote:
 Originally Posted by Benit13 but you might want to read a bit about the basic processes of heat transport first, namely conduction, convection and radiation.
Let's face it, never going to happen

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