Analytical Update

During the development of the concept design, different engineering analyses, are currently being used, to mitigate any error that the group might encounter throughout the remainder of the design process. The conduction cup plays an important part in the operation of the device. The beverage will be placed in the cavity of the conduction cup where heat transfer will take place. Therefore, cooling the beverage. A transient thermal analysis will be done on the Peltier module and the cup to see how the temperature acts throughout the cup over for the given time period. In addition, we have to take into consideration, the densities of different beverages, and volume as well. For instance, cooling a drink at 500 milliliters versus 380 milliliters by one degree at constant temperature. The drink that has 500 milliliters will take a longer time than the drink that has 380 milliliters to drop one degree. However, for now, water properties will be used as a reference point. (See Figure 1).

Figure 1. Peltier Module & Conduction Cup

Heat Transfer Analysis – Stage 1

Assumptions:

• • Steady state 

  • Delta T = 5 K 

  • Uniform thickness for the conduction cup, and the beverage container 

  • Neglect thermal contact resistance since # is small 

  • Same material, therefore same thermal conductivity

  • Uniform thermal conductivity

  • L1 = 0.003175 m

  • L2 = 9.7 x 10-5 m

  • Specific heat is 4.182 kJ/kg-K

  • Mass of the conduction cup is 3 kg

Figure 2. Device Thermal Schematics

Figure 3. Thermal Resistance Model

R is the total amount of resistance from both materials.

𝑅_𝑡𝑜𝑡 = 0.003772 𝐾⁄𝑊

UA is 1 divided by the summation of the total about of thermal resistance 

𝑞 = 𝑈𝐴(𝑇2 − 𝑇1)

𝑞 = 1368 W

The required time it takes to change the temperature of an object is given by the formula below [1].

T=(m*Cp*∆T)q

If the mass of the conduction cup is 3kg, and using the specific heat at room temperature. The time it would take to change to temperature by 5 degrees, given the calculated heat rate, is,

T= (3kg*4182jkg*K*(296-291)K)1368 W=45 s 

Should the walls of the conduction cup modified with a larger (L), the rate of q will be lower, and it would take a longer time to change to a temperature difference of 5-degree K.

L = 0.006985 

q=625W and T = 100.33s

Therefore, it would take 100.33 seconds to get a temperature difference of 5-degree K

Heat Transfer Analysis – Stage 2

    Furthermore, a more in depth analysis was performed. We wanted to know how much heat that would be transferred to this can sitting in an open setting, with a beverage temperature of 0⁰C and an air temperature of 20⁰C. For water, we calculated the Rayleigh number and the Prandtl number, in order to determine the Nusselt number, and thus the convective heat transfer coefficient for this 20K temperature difference from the following equations [1] (Using a 24oz beverage can: L = h = .157m, Source: Ball Corp.)

    For this, we can infer to our analysis that our system would need to add approximately 375 W/m2 to maintain the beverage at its current temperature. This is a very useful parameter because the can will not directly be in contact with the surface of the aluminum conduction cup, thus, some of the cooling energy will be lost into the ambient air also due to free convection. The amount of cooling energy lost however will not be constant, and will vary dependent upon the diameter of the beverage placed in the cup holder.

    Figure 4 references a proof of concept experiment we plan to perform upon receiving our purchased parts. This experiment would be very simple and would only involve placing a cup of cool water atop the cold side of the Peltier module and the heatsink / fan setup below on the cold side.

Figure 4. Proof of Concept – Design of Experiment

Environmental & Economic Impacts

In relation to the analyses done on our design concept, another important aspect to consider is the environmental and economic impact of the parts and materials being used.  With regards to our design, more analyses need to be done in order to solidify the amount of time to manufacture the product. Additionally, machining and engineering cost seem to have the largest impact in the total production cost. However, this is using very conservative assumptions in pay, overtime and production time. Other materials and possible assembly types should be explored in order to reduce cost of production. Data shows that only 68 units are necessary in order to break even (recover the investment), however, even giving it a conservative estimate of plus or minus 20 units, this number could be fulfilled with two or three stadium sells (A private section of 20 to 40 seats equipped with a cooling beverage holder would satisfy this requirement.  Another way of satisfying this requirement would be selling the coasters in bundles, which would forcefully make sells of the required numbers, increasing the amount of revenue. Finally, facility requirements should be further investigated, as the cost of electricity and real estate were estimated.  With regards to the environmental side of things; the manufacturing of our prototype requires a multitude of materials, means of transportation of these materials and components, energy to be used in the fabrication stage, and disposal of the materials after use.  All of the requirements have impacts on the environment.  As the developers of our prototype, it is extremely beneficial to understand the impacts on the environment.  Our group took many steps to ensure that the products purchased were transported from the closest facility to the SUNY Buffalo North Campus to eliminate the energy usage associated with transportation.  Another step taken, was to ensure that most of the components had some degree of recyclability associated with them.  That is, after the lifespan of the system, the components can be reused or salvaged to be used as other components.   As far as steps we can take moving forward, we can eliminate time wasted in the machine shop operating equipment that have a high energy usage.  Another step is to ensure that our tests of the device are accurate and precise which eliminates the use of the lab and specialized equipment to take readings and visually represent the workings of the device.