Heat loss and thermal equilibrium of underground aquifer

[Ortix]

Homework Statement

I am working on a project where I have to design and size an aquifer. There are two which either store hot or cold water for 6 months which is then pumped up to be used in either the summer or winter.

The aquifer is going to be 80 meters under the ground. The rest is basically variable. I made the assumption that it's a rectangular cube with (HxWxL) 10x40x20.

The equation I am using is q=λ*A*ΔT/s (i will learn LaTeX eventually ;) )

where lambda is the thermal conductivity of the soil which is 3.44. The temperature difference is 4K where the soil is 11C (constant over time) and the water is 15C. "s" is the thickness.. well the top soil layer is 80m and assumed to be homogeneous with the same thermal conductivity throughout.

But this obviously can't work because the temperature of the water decreases over time so I would need a differential equation but I have no idea how to set this up.

So the question basically boils down to the following two:
1. How do I calculate the end temperature of the water after 6 months
2. When is temperature equilibrium reached

Thing is that all this soil crap is not in my curriculum but my project group ended up with an aquifer to design so we have to do these calculations.

EDIT:

I found this:
http://ec.pathways-news.com/Text-PDF/Part B-6.pdf

And figured I could use equation 6.9
Is that correct? If so what are V and c in that equation?

 

[member 553083]

Homework Equations q=λ*A*ΔT/s The Attempt at a SolutionFor the first part of the question, you can use a differential equation to find the end temperature of the water after 6 months. The equation would look something like this:dT/dt = -(q/(V*c))Where q is the heat transfer rate, V is the volume of the aquifer, and c is the specific heat capacity of the water. This equation can then be solved using standard numerical methods, such as Euler's method or Runge-Kutta integration.For the second part of the question, temperature equilibrium is reached when the rate of heat transfer is equal to zero, which can be determined by setting the left side of the differential equation equal to 0 and solving for T.