Estimate the Cooling Down of a Standard Ceramic Coffee Cup left on the Desktop


Cooling down of a cup of coffee sitting on a desk in an office

You are an avid coffee drinker. You drink your coffee with milk. If you order coffee at the beginning of a meal but want to drink it at the end and still have the coffee be as hot as possible: Do you

A. add the milk to your coffee as soon as the waiter pours it? Or
B. add the milk to your coffee only seconds before your first sip at the end of your meal? Thus your challenge is to analyze the cool down of a standard ceramic coffee cup left out on an open desk.  

1. Write and numerically model the theoretical rate of cool down of a full coffee cup answering the following questions:
a. What are the fundamental modes of heat transfer using characteristic values from your text (show calculations),
b. numerically estimate the heat rates of each of  following modes(showing all your work):
a. Natural convection off the sides and top of the liquid surface
b. Radiation heat transfer from the sides and top of the cup
c. Conduction through the liquid to the air surrounding
d. Conduction heat rates through the cup into  the surface below
e. Evaluate the evaporation cooling rate assuming a stagnant mass of extremely dry air above the cup.  How does that calculation vary with some relative humidity in the air above the cup?

2. create a table of order of magnitude heat transfer rates for each of the 4 modes above

3. how do you model the evaporative heat transfer process

4. what is the equation describing the heat transfer rates and the change of temperature of the coffee in the cup

5. graph the T(t) for the problem

6. Conduct a simple experiment measuring the coffee temperature as a function of time and superimpose it on your theoretical data. There should be a curve with only one modality active at a time, that is do 1experiment where conduction and convection are minimized and evaporation clearly dominates. Do 1 cool down where evaporation is minimized and the other modes are present so that you can compare the relative effects of each mode on the overall cool down rate.


The question belongs to Chemical Engineering and it is about calculating the heat transfer happening from a coffee cup. The heat given off by an average sized coffee cup with hot coffee in it eventually has been calculated and answers to various questions have been answered in the solution.

Total Word Count 1351


Download Full Solution


  • HWA

    this is a very good website

  • HWA

    I have 50 questions for the same test your page is showing only 28

  • HWA

    hi can you please help or guide me to answer my assignments. thanks

  • HWA

    hi can anyone help or guide me to my assignments. thanks

  • HWA

  • HWA

    This solution is perfect ...thanks

  • HWA

    Hello Allison,I love the 2nd image that you did! I also, had never heard of SumoPaint, is something that I will have to exolpre a bit! I understand completely the 52 (or so) youtube videos that you probably watched. Sometimes they have what you want, sometimes they don't! However, it is always satisfying when you are able to produce something that you have taught yourself. Great job!Debra 0 likes

  • HWA

    Perfect bank of solution. 

  • HWA

    great !

  • HWA
    Paul Brandon-Fritzius

    thanks for the quick response. the solution looks good. :)

  • HWA
    tina Johnson

    thnx for the answer. it was perfect. just the way i wanted it. 

  • HWA

    works fine.