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Heat Transfer problem

  1. Jun 5, 2010 #1
    I am currently faced with a problem. I am trying to design a cooling system that uses Geo-Thermal energy to cool water. From my research I have found that 12 feet below the earth in the month of August the temperature is maintained at approximately 62-65 degrees Fahrenheit.

    I would like to utilize this natural energy to cool water. Right now I am trying to determine the best type of material that can be placed 12 feet below the surface of the earth to maximize heat dissipation from the water into the soil.

    My goal is to come up with the right material to achieve timely cooling (I am thinking of using PVC its thermal conduction is low but on the upside it does not rot or corrode).

    Secondly I would like to come up with a mathematical equation for the system, so that I can tell exactly what the temperature of the water would be at a given time (here is where I am having difficulties)

    At the moment I am aware of 2 formulas

    1) Newtons law of cooling: T(t) = Ta + (To - Ta)*e^(-kt)

    2) Conduction Law: Q = [(K)(A)(Tw-Tc)(t)]/L

    Where K = thermal conductance of material; units : J/(s m degree Celsius)
    A = Cross sectional Area; units : m^2
    Tw = Warm temperature
    Tc = Cool temperature
    t = time in seconds
    L = length; units: m

    The first formula will give me the temperature at a given time however I would need to determine the time constant "k" for the material that I am using (not sure how to to that unless I do a physical test first to find values for T(t), Ta, To and t then solve for k).

    The seconds formula gives me the amount of heat transferred in Joules (how does heat transferred in joules correlate to temperature transferred?)

    I would appreciate some advice because I feel I am not quite understanding the dynamics of how to approach this problem or even if I am using the right formulas to do so.

  2. jcsd
  3. Jun 5, 2010 #2
  4. Jun 6, 2010 #3
    Ummmm....he is trying to cool the water. Sooooo he is heating the earth...why would it freeze?
  5. Jun 6, 2010 #4
    your problem is that it is dynamic.... First, you are heating the soil, this requires knowing the rate of recovery of the soil,, (the heat transfer rate of your plumbing is insignificant by comparison, although copper is best). The variables here are, conductivity, Exposed surface area, water saturation and rate of replenishment (this is where experimentation is your best option..).
  6. Jun 6, 2010 #5
    Sorry, I was thinking about a heat pump system, in the winter. The point I attempted to make is that the local volume of earth you are heating is limited, and once you heat it up too much, that volume will need to cool back down before you can get the same cooling performance as at initial conditions. You not only lose the delta Temp needed to get your heat transfered, but you have to rely on conduction of heat in the soil, which is slow.
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