How Can I Keep My Coffee Hot on a Cold Day?

I am a person who likes to get coffee from bakeries rather than making it myself. I think the walk to the bakery and the interaction with the bakery staff make it worth the money. Especially during winter, I like to take a few sips of my coffee as I walk back home. This makes me feel warmer, and I get to enjoy my morning walk more. However, there is one thing that ruins the experience-the coffee getting colder in absolutely no time. 

I usually do not bring a thermos with me; I use disposable paper cups from the bakery. I have always wondered, if I wrap my hands around the coffee cup, would it slow down the cooling? Or is it better to hold the coffee cup such that my hands minimally touch the cup? To answer this question, I did a CHT simulation of a cup of coffee. On this page, I will go step by step through how I set up the simulation and present my results. 

TL;DR: To keep the coffee hot for longer, it is better to minimize contact between your hands and the cup.

Creating the Mesh 

I exported the geometry from SolidWorks to ANSYS ICEM for meshing. Both the solid domain (the cup) and the fluid domain (the coffee) have circular cross-sections. For this reason, I preferred to use O-grids. Different regions were meshed in different files. I did 3D blocking, assignment, and part labelling as usual. For the solid domain only, I deleted the block in the middle, as it corresponded to the fluid region. I merged the meshes into one project file and then exported the combined mesh to ANSYS Fluent.

Setting Up and Running the Simulation 

I will mention only the important settings I used in order to avoid overcrowding of the page. I ran transient simulations with constant timestep size. I enabled the energy equation and used k-omega as my turbulence model. I did not allow for phase change. Using a trial simulation, I ensured that the y+ values at the boundaries were approximately 1. For the fluid material, I used liquid water. For the solid material, I used cellulose-based paper. I enabled gravity to capture the buoyancy-driven movement of the liquid within the cup due to temperature differences. I set the initial temperature of the entire computational domain to 373.15 K.  

The boundary conditions were different for the two simulations. For the case with minimal hand contact with the cup, I applied a convective boundary condition, with the free-stream temperature set to 273.15 K (I assumed a very cold day), to all external surfaces of the cup.  For the other simulation, the external cup surface was divided into two regions using a horizontal plane. The lower part of the surface was kept at a constant temperature of 307.15 K, representing the assumed hand-skin temperature, while the upper part retained the convective boundary condition.

I monitored the residuals as the simulation was running. After a couple of time steps, they decreased to values below 1e-06.  

Results 

I analyzed the results using CFD-Post. As shown in the GIFs, the initial temperature profiles match the intended conditions and the heat transfer appears physically reasonable. The boundary between the solid and the liquid domains is also visible in the temperature profiles as inner lines.  

In order to see the cooling rate more quantitatively, I included a temperature-versus-time graph. One can clearly see that the conductive heat transfer caused by hand contact makes the temperature of the coffee decrease faster. The curves meet approximately near the end of the simulation. This is due to the fact that the coffee gets cooler than the assumed hand temperature. So the hand becomes the heat source. However, although the hand begins to act as a heat source once the coffee falls below approximately 34 degrees C, the curves meet only when the coffee is around 30 degrees C. By then, the coffee has already gone cold. For me, enjoyable coffee is definitely above 45 degrees C. 

To conclude this study: from now on, I will always hold my coffee like a piece of artwork between my hands, touching it as little as possible.