AME HEAT TRANSFER. Technical Memo No. C1. Abstract: To better understand the thermal properties of a cup filled with beer, COMSOL was used to

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1 AME HEAT TRANSFER Technical Memo No. C1 Title: Computational Analysis of Beer Heat Transfer Submitted by: Aaron Stewart Date submitted: March Abstract: To better understand the thermal properties of a cup filled with beer, COMSOL was used to analyze the temperature of the cup over a period of time. The cup was modeled in COMSOL and assigned the appropriate material properties as well as initial temperatures. A study of the model, as it was sitting on a table for two hours, was performed to generate a plot of the average beer temperature, the temperature of the center of the beer, and the temperature just below the surface of the beer. This study was conducted for both a simple glass cup, and a glass cup containing an ice gel pack; both were plotted on the same graph for comparison. The results showed that the glass with the ice gel was colder over the analyzed period than the glass without the ice gel. A study was also performed to analyze and compare the cross section of the two mugs at three different times. From the thermal profile of the cross section, it was observed that the glass with the ice gel was cooler than the glass without the gel. Finally, the temperatures of the bases and center of the handle were plotted over a period of two hours. The results obtained from COMSOL s analysis closely matched analytical results assuming the handle was a fin. Computational procedure: The procedure for this lab began by modeling the cup with COMSOL s built in CAD software. After the cup was modeled, the appropriate material properties were assigned to the glass, gel pack, and beer along with the convective heat transfer coefficients, ambient temperature, and initial temperature conditions. A fine mesh was then added to the model to create enough data points to give accurate results. Next, cut points and cut planes were put in the model to locate specific positions to be analyzed. A study was conducted over the period of two hours, and the temperature results of the specified points were generated. The data from the results were exported and graphed using Matlab. Data specified: The data describing the geometry of the cup, initial temperature conditions, and material properties as they were entered into COMSOL [1], are listed below in Table 1:

2 Table 1 A list of the parameters entered into COMSOL Glass height 15 cm Height of base 5 mm Height of gel pack base 10 mm Height of base 5 mm Height of gel pack 13.4 cm Glass external radius 5.5 cm Ice gel external radius 5 cm Ice gel internal radius 4 cm Glass internal radius 3.5 cm Handle diameter 1 cm Handle radius 4 cm Beer volume 250 ml Initial beer temperature 4 Initial glass temperature -5 Initial gel temperature -5 Gel density 1026 kg/m 3 Ice gel thermal conductivity.46 W/(m K) Ice gel specific heat at constant pressure J/(kg K) Ice gel ratio of specific heats, =1 Air Temperature 20 Convection heat transfer coefficient 10 W/(m K) Analysis and results: The first part of this lab was to plot the temperature versus time of a point at the center of the glass, one centimeter below the surface of the glass, and the average of all the beer in the glass[2]. The results of the study for the first part of this lab can be seen in Figure 1. Figure 1 Temperature versus time of three points on the glass with and without gel Figure 2 shows a cross section of the glass with gel at three different times. Each time has a scale associated with it to determine the temperature from the corresponding shade.

3 Figure 2 Beer in glass with ice gel layer Figure 3 also shows the same cross section as shown in Figure 2 but for the glass without gel. Figure 3 Beer in glass without ice gel layer By observing figures 1, 2, and 3, it becomes apparent that the glass containing the ice gel indeed keeps the beer inside cooler than the simple glass without the gel pack. -

4 The second part of this lab was to plot three points; on the top of the handle, the bottom of the handle, and the middle of the handle. A plot of the temperature versus time for these three points can be observed in Figure 4 below. Figure 4 Temperature versus time plots of points at the top, bottom, and middle of the handle Discussion: From Figure 1 the data of the temperature versus time was plotted for both the glass with the ice gel pack, and the simple glass without the ice gel pack. The suspected results, that the ice gel pack keeps the beer cooler over time, are clearly shown in this plot. It is observed that the temperature at the center of the beer with the ice gel decreases for the first 1700 seconds but only decreases for the first 1100 seconds in the simple glass. Figures 2 and 3 also depict the results by looking at a cross section of the glass and displaying a thermal profile. These plots have scales associated with the time that the cup is being analyzed to determine the temperature from the shaded image. The second part of this lab is to determine the temperature versus time at specific points in the handle of the glass. This data can be observed in Figure 4. It is observed that the temperature at the center of the handle is cooler than that of the temperatures at the ends. This is because the temperatures at the ends are closer to the handle. The results obtained from COMSOL closely match the results expected if the handle was a treaded like a fin [3].

5 Conclusions: COMSOL was used to analyze the temperature of the cup over a period of time to better understand the thermal properties of a cup filled with beer. The cup was modeled using the COMSOL CAD software and assigning the appropriate material properties and initial temperatures. The average beer temperature, the temperature of the center of the beer, and the temperature just below the surface of the beer were plotted versus time in a two hour study. This study was performed for both the simple glass cup and the glass cup containing an insulating ice gel pack and then compared the two by plotting the temperature versus time on the same graph. The results showed the beer in the insulated glass was colder over the whole period than the glass without the gel back. The study was also performed to analyze and compare the cross section of the two mugs at three different times. A thermal profile of the cross section was generated and it was observed that the beer in the insulated glass was cooler than the glass without insulation. Finally, the temperatures of the bases and center of the handle were plotted over a period of two hours. The results obtained from COMSOL s analysis closely matched the results that an analytical solution of a fin will produce. References: [1] [2] cs.pdf [3] R.H.S.Winterton, Early study of heat transfer: Newton and Fourier, Heat Transfer Engineering, Vol. 22, No. 5, pp. 3 11, 2001.