Recently, I was fortunate enough to be recognized at a banquet for volunteering with the local engineering society. The token of appreciation was not a gold star, or a plaque, or one of those amusing but relatively short lived novelty gifts. No, this was much more sensible (this is a group of engineers after all). I graciously accepted my travel mug and smiled for the photographer. What a great gift! I mean this with all sincerity. After taking my seat I started to realize that I can use this at home, at work, and anywhere in between. The utility far outpaced that of a shelf dust collector. I brought the mug into work the next day and performed the proper cleaning regime. There is a fantastic amount of mechanical design that went into the two phase locking mechanism that also enables meticulous cleaning of the bacteria prone nooks and crannies.
With a giant smile across my face, I head over to the coffee machine. As it is filling, I scoff at the mere mortals who use those waxy-coated Styrofoam cups to consume their daily fix of caffeine. From there, I sit down at my desk and get to work. While my emails are loading up, I reach over for the maiden drink of my coffee. I push the button to release the lock and tilt the mug back. My mouth is instantly way too hot. See, I usually consume hot beverages at a cool 120 °F (in a previous life I was a barista and learned this to be true). Traditionally, coffee is dispensed at 160°C. To allow for the cool down, 10 minutes or so with an open top cup is usually requisite for me to enjoy my beverage. Well this darn travel mug was so well designed that I honestly had to wait several hours in order to not have a violent reaction to the littlest of sips.
Now time to put on my engineering hat and do something about it! On the bottom of the mug it actually listed the patents involved for the product. After some quick bedtime reading, I learned that there are two layers of metal with a vacuum in between. This is an excellent method of insulation that is now adopted by several manufacturers. Why? It all comes down to the three types of heat transfer:
1. Conduction — Conduction comes into play while going through the inner shell. From there the radiation takes over. Then again, we have conduction through the outer shell.
2. Radiation — The evacuated region between the inner and outer shells only allows radiation as a mode of heat transfer.
3. Convection — Working from the inside out, there are convective effects within the coffee. Finally, convection from the ambient air in my office removes heat from the outer shell.
It has been a while since I took Heat Transfer in undergrad, but I think Professor Williams would be proud that I remember the concepts. Luckily, I have SOLIDWORKS Flow Simulation to handle all the physics and hide the equations out of sight. Firing up my project wizard, this is definitely going to be an External Analysis so I can model the coffee inside as well as the air around the mug. All three modes of heat transfer should be considered, so we will activate Radiation and Conduction in Solids.
FOURTH ORDER EQUATIONS
I want to find out how long it takes for my coffee to cool down and how long it will be in an acceptable range, so the simulation needs to be Time-Dependent. From here, we add aluminum as our solid material and air as our ambient fluid. Coffee is not in the default database, but that is okay because I found a white paper online outlining the necessary properties to enter (grad students have fun sometimes). The model will need to have radiative surfaces selected for the outside of the inner shell as well as the inside of the outer shell (tongue twister but relatively simple to define). The initial condition will be a uniform temperature of the coffee. Now we sit back and relax while the software chugs through fourth order equations!
So what is to be gained from all of this? Well my self-induced constraints are that I want to be able to sip after 10 minutes (during my morning hellos) and enjoy for the next two hours or so. Sounds like a perfect application for optimization, but I do not have time to babysit the software. That’s okay because the Parametric Study saves the day. Now we simply enter in the acceptable values into a table and let the solver crank overnight. The perfect initial temperature of the coffee no longer being a mystery, I can now sneak away to the water cooler and add my dose of bio-friendly coolant.
If you haven’t already, be sure to read CFD for the Common Man Part One