## The HPC Behind the Product

*June 24, 2021*

The length of time that a beverage can stay hot or your ice doesn’t melt on a hot summer day is one characteristic that differentiates YETI tumblers from others on the market. From a customer perspective, a YETI tumbler *could* function just like any other insulated cup, but, as we delve into the design and functionality we get to appreciate the power of numerical analysis and *the Cloud* used to solve these everyday problems in a simulated environment.

Generally, a hot beverage in a tumbler starts cooling down because of heat exchange with the environment. As soon as a tumbler with hot liquid inside is exposed to ambient temperature, which is usually colder than the beverage, heat transfers from the liquid to the environment, a process called heat transfer or exchange.

In nature, there are three ways of transferring heat: conduction, convection, and radiation. Mathematically speaking, the total heat transferred from a system can be expressed as a combination of the three modes:

### Considering this equation we find the secret to the performance of the YETI tumbler, and we shed light on how they use physics to their advantage below.

To design and develop a product that is superior to other reusable tumblers, YETI developers minimized these three opportunities for heat loss through clever design and the help of computer simulations.

Within a solid wall, energy is transferred from the hot side to the cold side through atomic or molecular excitement, also known as conduction. In fluids, conduction is less dominant, but fluids move heat from hot to cold regions when they move along a hot wall. This process is called convection. Heat is also transferred from body to body through thermal radiation by means of electromagnetic waves. Radiation is different from conduction and convection as it does not require matter or medium to be present. Radiation will pass perfectly through a vacuum as well as air. Further expanding each of those heat transfer modes in the total heat loss mentioned above, we get the following equation:

### The science behind the material

Aluminum is generally the material of choice for reusable tumblers. It is durable, lightweight, and easy to maintain. It does have its drawbacks as it conducts heat better than most affordable metals. However, YETI tumblers are made of stainless steel. Using stainless steel versus aluminum decreases the tumbler’s thermal conductivity (*k*) by a factor of 5. Thermal conductivity is an intrinsic property of a material. Stainless steel has a low enough thermal conductivity and high enough structural strength to make it ideal for the task.

While stainless steel has a higher conductivity than plastic materials, YETI uses a double-wall construction with a vacuumed space between the steel outer and inner cup to further reduce the wall’s *effective *thermal conductivity*. *The vacuumed double-wall further reduces the conduction losses through the cup.

An example of a double wall cup model used in computer modeling and simulation

So, what about the effective thermal conductivity, the weighted average of thermal conductivities of the layers that make up the conducting wall? Cloud computing and advanced simulation software help with that too. Mathematically, for a layered, finite cylinder of length L, the thermal resistance of a layer can be computed as:

Total heat flow in a multilayered cylinder with constant hot and cold temperatures (

*T*

*hot*and

*T*

*cold*) is then:

The double-wall construction adds complexity to the mathematical problem to be solved. It also minimized the convective heat exchange with the environment.

### Is there another material that could improve the thermal performance?

Evaluating the thermal equations above tells us that using materials with lower thermal conductivity, titanium, for example, will help. It has a thermal conductivity of about half of stainless steel’s thermal conductivity. It is also lighter, easy to roll, and durable.

### The analysis behind YETI’s material decision

The answer can be found using thermal analysis. Thermal simulations in the cloud show the improvements between titanium casing versus stainless steel casing are not huge. Using computational analysis, one can conclude that YETI selected the materials used for their tumblers well. Other than a few degrees warmer and a lighter frame, titanium, for example, has little impact on the thermal performance of the Yeti tumbler due to the double-wall construction of the tumblers.

CFD analysis of a reusable tumbler with titanium dual wall

**Overall, radiation heat exchange does not need matter or relative motion in order to occur. Did YETI tumbler designers learn to live with the effect of radiation? The simple answer is no.**

Radiation heat exchange depends on the surface characteristics of the radiating bodies. Computer simulations are able to fully model body-to-body radiation heat exchange. A numerical method called the discrete ordinate method allowed the engineers to model different surface properties of the tumbler’s wall. To reduce the radiation heat exchange with the environment, the inner wall of the tumbler is coated with a shiny copper layer that reflects 97% of the incoming thermal radiation.

Heat transfer and computational fluid dynamics simulations on the cloud helped YETI designers select the materials, construct, and evaluate the performance of the tumbler virtually. Design experiments can be run in the cloud with little effort and relatively cheap. This is what most likely made YETI’s differentiating designs and functionality possible.

The cloud revolution is only in its infancy. Numerical analysis powered by clusters of computers and highly parallelized analysis software will help us continue to develop innovative new products. Tumblers, and other products like YETI coolers, are a prime example of how science is bringing those products to, in this case, our hands.

Read about the HPC involved in the design and development of other popular products including the Peloton bike, robot vacuum cleaners, and smokeless firepit stoves.

*Disclaimer: We are not affiliated, associated with, or in any way represent YETI.*

**Can cloud computing and simulation help us evaluate the performance of the YETI tumbler on, let’s say, Mars?**

It turns out that simulation is the easiest way to be on Mars. We are still waiting for a call from SpaceX to hitch a ride. Turning off gravitation, and removing the air from the equations, answers the question. Looking at side-by-side simulation results on a YETI tumbler shows us that the dual-wall vacuum seal helps us on Mars even better since there is no heat lost due to buoyancy and the temperature distribution in the volume of the coffee is more uniform and maintained at a higher value over a longer period of time.