# Model the Coffee cooling problem with WSM?

Posted 1 year ago
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 Greetings while I am new to WSM I have a few years physics experience.It seems to me that a the classic 'when do I add milk/cream? is a perfect opportunity for illustrating the modelling capabilities of WSM. However, I am yet to see this application..Too simple perhaps?I have plenty of examples of mathematical modelling. this conference article covers all the possibilities with 5 models, each more complex to allow for fat globules on surface insulation radiation, colour of surface of cup, material of cup, volume of cup, surface area etc..I am hoping experienced WSM guru will not find this too trivial and apply their talents to develop an all tim classic WSM model..regards Gary high school physics/IT teacher melbourne Australia** the need for this? we have just licensed every high school teacher (20k)and their students (200k) on whatever OS they have for the entire wolfram suite Wolfram Alpha PRO Mathematica Wolfram SystemModeler Wolfram Cloud... Attachments:
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Posted 1 year ago
 This doesn't answer your question but I couldn't resist posting that a classmate of mine at Reed College, Andrew Case, wrote a B.A. dissertation modelling the behaviour of milk drops falling into a cup of coffee, and if I recall correctly, even did some of the work in Mathematica http://catalog.library.reed.edu/REED:local:CP71102917680001451
Posted 1 year ago
 BTW why not Mathematica? See: The Coffee Cooling Problem. You can download the code freely there.
Posted 1 year ago
 Greetings Vitally i was aware of the Demonstration, however the differential equation and approximate exponential over estimates higher temperatures and underestimates lower temperatures. if you 'stand back' far enough observation data and the calculated data points are close, but a not very good fit.an 'ideal' cooling curve does not represent real behaviour of a container. e.g.. radiation, convection, convection, insulation of milk fat layer http://demonstrations.wolfram.com/NewtonsLawOfCooling/Better than a quadratic or quartic approximation however, not an accurate predictor of behaviour as the model does not take into account colour, container or surface interface (i.e. insulated with milk fat).The demonstration is good as far as it goes.I was after something like the kettle WSM example which calibrates the theory with real data to achieve a far better fit (~ 2%) http://www.wolfram.com/system-modeler/examples/consumer-products/electric-kettle-fluid-heat-transfer.htmlregards Gary (39˚C here today!)
Posted 1 year ago
 WSM can do this easily and is perfect for that type of system. I would start with one of the heat transfer examples and modify it. You can even add some of the thermal components if you want to model circulating air (i.e. someone turns on a fan!). Look at the thermal examples to see how to do that. The basic case is very much like the examples.If you have problems you can post your example for some more help. Regards
Posted 1 year ago
Posted 1 year ago
 Greetings Patriki follow the development of your model..so far.I get stuck on the next step.where an amount of cold milk/cream is added to the coffee(assuming black) after a specified time usually t=0 and t=300seconds volume ~10ml Cp will be different to water . skim milk 3.97; 'regular' milk 3.77 compared to water 4.18 kJ/˚C/kgthe total volume changes from 200ml to 210ml assuming complete mixing the 'new' temperature will decrease , however the mixed Cp is unknown so the standard calculation of ratios is difficult to use.the contrasting treatments are to add milk at the beginning, or to wait 5 minutes (300 seconds) and add milk after allowing the coffee to cool and the milk to warm(!) ambient is 20˚Conce a working model has been achieved, can the details be calibrated using 'real' data? similar to the WSM example of the cooling kettle? http://www.wolfram.com/system-modeler/examples/consumer-products/electric-kettle-fluid-heat-transfer.htmlLooking good, so far!My approach for High school would be to research the history of Newton and differential equations. Identifying the scope and constraints on the 'ideal' solution.Then introduce the concept of modelling and calibration. the main idea to highlight the benefits of theory and experience, where there is 'never the ideal', however there can be very close approximations.in physics anything better than 5% is considered a 'good fit', 2% a 'close' fit and <1% always the goal.Gary
Posted 1 year ago
Posted 1 year ago
 Patrik, your detailed reply is very helpful.In high school the purpose of the exercise is exploration within limits. These examples provide alternatives which can usefully be explored and verified by direct experiment.limits of theory and limits of experiment (accuracy and errors) are all important lessons which can be reinforced with open ended exploration.Comparison of different coffee pouring strategies can easily be measured and now modelled. Different cup materials and configurations can now also be accounted for. surface area, covered/uncovered, material glass, ceramic, metal, colour, double walled, vacuum insulated..I appreciate your comment about 'over fitting the model' however in physics this is a constant temptation because we can.. Knowing when to stop is an important skill. regards Gary Melbourne (ambient air temp = 32˚C today..)