Team:Cornell NY/Model
Modeling
Cold Shock Module
The cold shock module is used to reduce the temperature of the tip of the teat to a level which would expedite the closing of the teat post-milking. The teat remaining open for over 30 minutes after milking was cited as the biggest reason mastitis was developed. The cold shock concept was developed using the observation that the areolas of mammals shrivel when exposed to colder temperatures, due to the need to reduce surface area to maintain homeostasis. The purpose of this analysis is to determine the feasibility of the temperature reducing to a safe yet effective level for teat size reduction in a reasonable amount of time.
- Assumptions:
- • Heat transfer must occur across the liner
- • Liners are made of silicone rubber (k=0.2 W/mK, cp=1050 J/kgK)
- • Liners are long thin-walled cylinder geometry of OD 25mm and ID 23mm
- • No heat generation from teat
- • Teat is pressed up against ID of liner
- • Cold shock is applied to OD of liner
- • No convection or radiation - only conduction
- • Symmetrical heat transfer
- • Peltier Device used to create cold temperatures (-30°C)
- • Teat and the liner initial temperature is 30°C
Methods: Using COMSOL Multiphysics 5.2, the geometry and material properties as stated in the assumptions were input. Boundary condition of T = -30°C (temperature of Peltier device) at the OD and an initial condition of 30°C initial temperature were used. A heat transfer analysis over 200 seconds (temperature change with time at the ID) was computed using the software and exported as a plot and animation.
Results: The temperature with respect to time at the inner diameter is displayed in Figure 1. The temperature approaches steady state after approximately 100 seconds. The temperature arrives at 0°C at approximately 17 seconds. The temperature change can be seen in the animation (Figure 2).
Figure 1: Temperature with respect to time at the inner diameter of the liner, where the teat is expected to be. Temperature decreases to levels which can safely stimulate a teat closure response between 10 and 17 seconds.
Figure 2: An animation of the temperature change throughout the liner with time. Cold temperature spreads from the outside of the liner, where the cold shock is applied, to the inside, where the teat is.
Discussion: Farmers were extremely concerned with safety and cow comfort. Thus, they were not comfortable with cooling the teat to below 0°C. Since the temperature of the teat will reach 0°C after 17 seconds, we must expose the teat to cold shock for less than 17 seconds, and this will allow the teat to reach colder temperatures but still above the safety threshold. Below 17 seconds is also an acceptable time scale over which to expose to cold shock, since it does not considerably add to the time needed to complete milking. How cold teats must become to experience considerable shrinkage has yet to be determined, and more extensive research into this must be completed to fully optimize the cold shock module. The cold shock module, nonetheless, is a feasible technology for development.
Temperature Sensor Module
The temperature sensor module is used to monitor temperature in the udder. The temperature of mastitis infected udders has been shown to be higher than normal udder temperature, as well as directly correlated to the severity of infection. Because of this, it would be advantageous to detect the temperature of the udder at each milking session in order to catch infections early and prevent further damage. The purpose of this analysis is to assess the feasibility of containing the temperature sensor between the liner and the shell of the milking machine. This design was ultimately not chosen, and a design where the temperature sensor would be external to the milking shell and pressed up against the udder of the cow was chosen.
- Assumptions:
- • Heat transfer must occur across the liner
- • Liners are made of silicone rubber (k=0.2 W/mK, cp=1050 J/kgK)
- • Liners are long thin-walled cylinder geometry of OD 25mm and ID 23mm
- • Teat is pressed up against ID of liner
- • Temperature sensor is applied to OD of liner
- • No convection or radiation - only conduction
- • Symmetrical heat transfer
- • Initial temperature of 20C throughout
- • Boundary condition of teat at 35°C at ID
- • Temperature sensor located at OD
Methods: Using COMSOL Multiphysics 5.2, the geometry and material properties as stated in the assumptions were input. Boundary condition of Ti = 35°C (temperature of the teat) at the ID and an initial condition of 20°C initial temperature were used. A heat transfer analysis over 200 seconds (temperature change with time at the ID) was computed using the software and exported as a plot and animation.
Results: The temperature with respect to time at the inner diameter is displayed in Figure 3.The temperature sensor approaches teat temperature at approximately 200 seconds. The temperature change throughout the liner can be seen in the animation (Figure 4).
Figure 3: Temperature with respect to time at the OD of the liner, where the temperature sensor is expected to be. Temperature increases at the location of the temperature sensor and approaches the cow temperature after over 200 seconds
Figure 4: An animation of the temperature change throughout the liner with time. Hot temperatures spread from the cow’s teat, at the inner diameter, to the outer diameter, where the temperature sensor is.
Discussion: The temperature at the temperature sensor approaches the temperature of the teat at a reasonable time (200 seconds). This would be able to be reasonably achieved through the normal milking cycle, which lasts for longer than 200 seconds. However, this is using the incredibly strong assumption that there would be no convective heat transfer, which would add significant resistance to the heat transfer. Thus, we decided that the design analyzed here, where the temperature sensor is located between the shell and the liner, pressed up against the liner, was not an ideal design choice. We opted instead to mount the temperature sensor to the external side of the shell, and have the temperature sensor press up against the bottom of the udder, thus making the temperature sensor more accurate.
Automatic Post-Dip Module
The iodine module consists of a sponge that holds about 10 mL of iodine at a time without being oversaturated. A pump can be used to transport the iodine from a container to the sponge. Using Bernoulli’s Energy Equation to find the head loss of the pump, we can then calculate the corresponding power needed to pump a certain amount of iodine at a time using a peristaltic pump. From there we can also calculate how long the pump would need to be run.
- Assumptions:
- • Iodine is a Newtonian, incompressible fluid
- • Iodine has laminar flow
- • Iodine is held in an open container
- • For this example calculation, a Jersey cow was used as the model, with an average height of 117 cm [1].
- • Assume that the udder is ⅓ of the total cow’s height from the ground
- • Rubber tubing with length of 130 cm connecting the sponge to the container of iodine has 1 inch diameter and equivalent roughness of 0.025 mm [2]
- • Average teat diameter is 2.75 cm and average teat length is 5.9 cm [3]
- • Machine pumps 0.5 mL/s of iodine
- • Teat is coated with a 0.5 mm thick layer of iodine
- • Density of Iodine is 4.93 g/cm3 [4]
Energy Equation:
Heat Loss:
Power Equation:
The power needed to run the pump when it starts is 0.00721 Watts, and as time increases, the more iodine is pumped, and the larger amount of power that is needed. The maximum amount of power that this pump would run at is 0.0178 J/s. The time needed to run the pump is 0.256 seconds in order to coat one teat in iodine.
