
Team Number: 037 School Name: Clayton High School Area of Science: Botany, Zoology, Behavior and Social Sciences Project Title: A New Developement for Agriculture Project Abstract: http://mode.lanl.k12.nm.us/97.98/abstracts/037.html Interim Report: http://mode.lanl.k12.nm.us/97.98/interims/037.html Final Report: http://mode.lanl.k12.nm.us/97.98/finalreports/037/finalreport.html
First we will calculate the amount of energy required to raise a variable temperature to the cows normal body temperature. We will then calculate how much feed is needed for that conversion. This will later give us a calculation for the cost of the feed. The equation Q=mc t, will be used to find the heat required to raise a variable temperature of water up to normal temperature. In the formula Q=mc t, the variable Q equals the number of calories it takes to raise the temperature 1 degree Celsius. M is the mass of the water consumed by the animal. C equals the specific heat of the water, and t is the change in temperature from the outside temperature up to body temperature.
After we find the calories of the water, then we will convert it into a cost of feed. After we do this, we are ready to move on to figure the information to run the water heater.
The heater will work by convection, conduction, and radiation to transfer heat throughout the tank. Convection is when the motion of a fluid enhances or increases the amount of heat that is transferred. On a still, calm night, when the air is really cold, the air around the tank is a little warmer than the air far away. So since warm air rises, the warmer air is replaced by the colder air. This air then is slowly heated by the water and convection takes place.
Conduction is where heat is conducted or transferred by contact from a warmer to a colder body. Heat always flows from the warmer body to the colder one. An example of conduction is when you touch something cold and the heat flows from your hand into the cold thing that is being touched. The third form of heat transfer is radiation, which is energy that is emitted by everything in the form of photons. This is when you are standing next to a radiator and you feel the heat that is being radiated from the radiator to your body.
The equation that we will use to describe our heat transfer is: delta (q) = k Area (T1 T2)/length. Delta(q) equals the amount of heat that is exchanged per unit time. This can be expressed in terms of calories/hr, joules/sec, or any other form of unit per time. Area is the surface area of contact, or the area of the water exposed to the air on top plus the area of the sides of the tank. K is the conduction coefficient. It tells how well the material gives up its heat. (T1  T2) equals the difference in the temperatures of the two bodies. Length is the distance that the temperatures vary along.
The minus sign in front of the equation is to make known that heat flows from the warm side to the cold side therefore, if T1 is the temperature of the water and T2 is the temperature of the air, the result would be negative. This would mean that the amount of heat in the water is decreasing in time. If it is looked at from the air's point of view, then the result would be that the heat in the air is increasing.
Once we find how heat is transferred throughout the tank, then we can find the temperature of water that the cow will be drinking. Next we will calculate the calories to raise that temperature up to normal body temperature. This will give us a cost which we will add to the cost of running the heater 24 hours a day.
With this information, we can find out if the cost of not having a heater is greater than the cost of running a heater. We know that it probably won't be a big difference, but we hope to have some good results, and hope that it will be somewhat helpful to other farmers in the business.