## Solution Library

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

**Question**

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. **Summary**

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**

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