Please post the problems you developed for Part 3 of Assignment 12. The posting should include a brief statement of the problem, along with a description of the results using text, figures, and possibly, video. Details are up to you.

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Matt Beren

I ran a simulation showing the heating of a fluid inside of a can due to holding it. I set the initial temperature of the fluid inside the can to be 280 K (cold beer or soda) and I set the temperature on the side boundary to 303.15 K (roughly hand temperature). I ran the simulation for 5 min. The fluid material was set to be water and the solid material was set to be aluminum. The dimensions of can were measured and the geometry was altered to simulate a can.

Results: Figures 1-6 show the heat distributions throughout the can at various times. The sides of the can initially begin to heat up and flow upward due to the decreased density of the fluid (Figure 2). As the warm fluid moves upward, the cooler more dense fluid begins to flow downward as it is being slowly warmed (Figures 3 & 4). As the simulation runs, this process continues until the fluid in the can has become fairly well mixed and the temperatures have equilibrated throughout (Figure 6).

Dalton Weinstein

For this model I wanted to show how water gets heated up in a cermaic mug by a hot plate. I changed the material of the contianer to SiO₂ to make it more similar to a cermaic mug. I then changed the temperature of the water inside the mug to 293.15 K. I then changed the temperature of the top of the mug and the side of the mug to 293.15 K to be around room temperature. I then changed the temperature of the bottom of the mug to 368.15 K to resemble a hot plate. I ran the model for 2 minutes and as you can see the model heats from the bottom with the less dense water flowing up and the cooler more dense water flowing down. If the model were to run longer the temperature change would have been greater but it took 90 minutes for the model to run for a two minute model.

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N. Burak Akar

In this model, I wanted to illustrate a cooling system. The temperature of the water inside the system is set up to 293.15 K. Convective cooling boundary is set up to the left pipeline as it is seen on figures and T_external is the function of “293.15[K]+del_T*sin(2*pi*t/period) [K]” expression where del_T is set to the value of 3. The simulation is run for approximately 2 days (1.8E5 seconds). At the beginning of the simulation "T-293" was equal to 0.15 K (Figure 1), but at the end of the simulation, the value decreases down to approximately -0.05 at the right side of the system (Figure 4).

Figure 1. Temperature distribution at t=0 s.

t=20000.png Figure 2. Temperature distribution at t=20000 s.

t=40000.png Figure 3. Temperature distribution at t=40000 s.

t_1.8E5.png Figure 4. Temperature distribution at t=1.8E5 s.

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I set up a model to simulate natural convection that can occur during startup in a low power nuclear research reactor. The reactor core is simulated just as a 1m by 1m square 0.5m above the bottom of the reactor pool that is 12m deep and 10m wide. The initial water temperature is set at 293.15K and the “core” is set at 393.15K. At very early times the flow path of the heated less dense water is simple and symmetric, rising to the top of the pool and beginning to circulate back down as it cools and becomes less dense. As the heat flux from the reactor continues to heat the water a more erratic flow path develops a the system pushing the flow of hot water to one side and eventually creating a counter clockwise flow path toward the end of the simulation. At this point the bulk of the water is 30-40+ K degrees above the ambient or about 150°F. In reality the primary pumps would have already been initiated before this to remove the heat generated via forced circulation so that the reactor could continue to operate since there is a negative temperature coefficient of reactivity.

Dawn





Figure 1. Temperature distribution and flow (arrows) for various times.

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Zhenghsou Lai

I ran a simulation to see how will the boiled water get cooled naturally. The dimension of the geometry is got from a cup of 80mm in diameter and 150mm in height, and a 1mm thick layer is build to simulate the glass. The initial temperature of the boiled water is set as 293.15[K]+75[K], roughly boiled. The bottom of the cup is set insulated and the other boundary temperature is 293.15[K]. I ran the simulation for 300s. The effects of the ambient air heated up by the water is not considered.

Vedio. Temperature distribution of naturally cooling process of boiled water in glass cup as time going on.

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Viviana Heim

My model simulates a grill with a base of 0.3 m and a radius of 0.15 m, being heated from the bottom surface. This model shows the thermal convection generated previously to a barbecue, when the bottom surface is steadily heated from 293.15 K to 298.15 (an increment of 5 K) during 200 seconds. The fluid inside of the grill is of course air, with an initial temperature of 293.15 K, and the external temperature is fixed at T=293.15 K.

The Rayleigh-Bernard convection cells mixing the fluid can be appreciated.

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Yirui Chen

I simulated the hot pot of iron boiling the water inside by the 2D symmertic geometry of 10 cm raduis and 10 cm height. The initial temperature is of the room temperature about 293.15K. And the temperature of the bottom surface is 273.15+100[K]. Running the model for 2 minutes. And then, the results shows that the water temperature inside the hot pot is about 273.15+70[K].

Fig. The temperature distribution within 120s.

Jessica Denison

I simulated the heating of air inside a house due to the sun rising and heating the side of the house. I set the initial temperature to 293.15 K. To keep the simulation time down, I created a square geometry that was only 0.2m by 0.2 meters. I ran the simulation for 2 hours since this is about the time it would take the sun to rise. The air inside the house heated up very quickly which can be seen in the video of the increase in temperature. This created a convection cell. This can be observed in the video simulating the particle trajectories. From this analysis, it can be observed that air heats up faster than water which creates a larger degree of convection. This effectively mixes the particles. In the same manner, the air also quickly cools down, once heating has ended.

Question 3 Temperature.gif

Figure 1: The heating of air inside a house.

Question 3 Particle Trajectories.gif

Figure 2: The particle trajectories for air heated inside a house.

Chunyan Li

I set up a simulation of boiled water cooling in a acrylic plastic cup naturally. The dimension of the geometry is got from a cup of 90 mm in top diameter, 70 mm in bottom diameter and 100mm in height, and a 1.3 mm thick layer. The initial temperature of the boiled water is set as 293.15[K]+75[K]. The bottom and body of the cup is set to 293.15[K].

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In this model, ice cubes were added to hot coffee (80^oC) to make a Baileys and Cream Iced Coffee beverage. The ice cubes are the orange squares in the larger rectangle, which represents the plastic coffee cup. The top, left, and right boundaries were exposed to ambient room temperature of 20^oC. As the ice cooled the coffee, small vortices distributed the cooler temperature from the ice cubes into the coffee. As the top surface cooled, convection vortices generated at the surface, cycled hot coffee from the top to the bottom. If convection did not occur at the top boundary, then the coffee would have a stratified temperature with chilled coffee at the top and hot coffee at the bottom. The convection vortices formed at the surface promote mixing and accelerate the rate at which the ice cubes chill the coffee.

Geometry

Video showing chilling of hot coffee beverage

https://www.youtube.com/watch?v=TyfbExZACw0&feature=youtu.be

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Linlin Mu

We usually put cans or bottles of beverage into ice container to cool down them.

I do analysis of one can of coke and put it into ice container. The can’s sides and bottom are contact with ice. Assume that the coke’s original temperature is 298.15K, the ice’s temperature is 273.15K.

These figure and player below shows how the coke cools down by the ice.

Figure 1 Heat flux of coke can’s bottom, wall and top