# Theory Of The Permafrost Theory

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Permafrost theory

The third medium explored as a heat sink for the heat exchanger is permafrost. Permafrost is soil that is frozen year round. The top layer of permafrost experiences an active change in temperature over the year. However, the permafrost retains a constant annual temperature a couple meters below the surface. The constant below freezing temperature of the permafrost makes it a potential heat sink for the heat exchanger.
The permafrost is treated as a solid for our exploratory analysis of it as the heat sink. Therefore, for the purposes of our models, conduction is the primary mode of heat transfer out of the heat exchanger system when permafrost is used as the surrounding medium. Fourier’s Law is used as the fundamental equation used in all of the heat exchanger analysis.
Fourier’s Law: q"=-k∇T
Where:
q” = Heat flux k = Thermal conductivity
∇T = Temperature gradient

A basic model of the heat exchanger is a pipe carrying the CO2 through permafrost. The inlet temperature, outlet temperature, and heat rate out are all known variables. The dimensions of a simple tubular heat exchanger are found using the general heat exchanger equation.
General Heat Exchanger Equation: q=UA∆T
Where:
Q = Heat rate
U = Overall heat transfer coefficient
A = Outer surface area
ΔT = Change in temperature

The pipe experiences heat transfer by means of internal convection from the CO2, conduction through the pipes material, and conduction from the permafrost. The overall heat