Heat Capacity Experiment Tool

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Introduction

The purpose of this tool is to quantify heat exchange within an underground site to help scale a temperature-cooling intervention. The Heat Capacity Experiment Tool will provide the equations to calculate your system's effective heat-transfer behavior (often summarized as UA, the overall heat conductance) and an initial estimate of the system's effective thermal capacitance (C, or "thermal mass") over the timescale relevant to cooling interventions.

The tool is designed to calculate UA and C from a pilot experiment in which a fan blows air into a portion of a subterranean site and measures how the temperature within that portion changes due to the influx of heat.

Step 1

Begin by constructing an experimental area (treatment room) inside a test hibernaculum. Limiting the test to a defined space reduces the required power and increases interpretability. We constructed an insulated wall (Figure 1) at one end of our treatment room, and the other end was defined by an existing cement wall, as shown in Figure 3. The treatment boundary does not need to be airtight, but it should meaningfully restrict mixing with the rest of the hibernaculum.

Step 2

Install multiple temperature loggers throughout the treatment room to measure the temperature over time, and one logger at the entrance to measure the temperature of the air being pulled in. Use a short logging interval (1 minute) to record initial responses. Start recording the temperature before the experience begins to establish a baseline.

Record the airspeed and, if using ducting, the duct diameter, as these will all affect airflow. We used a Kestrel to measure the airspeed in MPH exiting the duct.

Step 3

Apply a controlled temperature disturbance. It does not matter whether this experiment is conducted in winter or summer, as long as the external temperature differs measurably from the internal temperature. We just want to quantify the rate of change at the initial point, since it is fastest when the temperature difference is largest and slows as internal temperatures reach a new equilibrium.

Operate the fan long enough to observe a clear temperature response curve (1 to 2 hours). When the system is turned off, avoid entering the treatment room for about an hour or so, as we want to measure how the system returns to normal after the heat flow is stopped.

Step 4: Setup

After completing the experiment, order your temperature logger responses in the following format.

Step 5: Open the Heat Capacity Experiment Tool In a New Tab

https://tannermbarnes.github.io/climate-tool/

Step 6: The Heat Capacity Experiment Tool

Step 1 - Direct UA Steady-State (cooling) of the heat capacity tool provides a theoretical baseline for exploring mine cooling capacities by treatment area. These results provide a table of achievable temperatures based on the air's external temperature and the treatment room area.

U is the heat transfer coefficient (sometimes available in the literature), but it is highly dependent on the airflow rate between the rock/air interface. We are estimating this using the experiment, but based on the literature, this value is typically between 1 and 5 W/m-2K-1. For conservative estimates, we set this number to 5.

Now input the area to be cooled in m2, the typical internal temperature of the site in ºC, a typical external winter temperature for your area in ºC, and the approximate amount of airflow in CFM.

The results show new steady-state potentials based on different airflow rates and external temperatures. For our 240 m2 area, we would need to increase the airflow rate to 720 CFM to cool and maintain an internal temperature of 3.5ºC, or reduce the treatment room area.

Step 7: Paste in data from your experiment

Instead of using a theoretical U and an approximate area, we can empirically quantify both of these (UA) from the fan experiment.

In Step 2 - paste your date/time stamps and temperatures from the temperature loggers into the space provided (don't add headers, names, just the data).

Enter either the duct diameter size (inches) and airspeed (measured coming out of the duct), OR if known, the cubic feet per minute (CFM) airflow rate.

Then select the external temperature column and all the internal temperature columns (if using multiple loggers).

This creates a graph of the different columns' temperature over time and creates an internal average (solid blue line). We can see the initial rates of change when the fan was turned on (around 25) and when the fan was turned off (around 175).

Step 8: Calculate C and UA

Next, hover over the graph and drag your mouse over these initial changes. The first line will calculate the initial rate of heating (red dashed line) from the input of warm air (we ran this in the summer), and the second line will calculate the initial rate of cooling (blue dashed line) when the fan was turned off, and the mine returned to ambient temperature. These two values will automatically calculate the space's thermal mass (Croom) and the effective heat-transfer rate UA (between the air and the rock) for your area.

Step 9: Local Simulation

Step 3 of the Heat Capacity Experimental Tool uses the numbers from step 2 and the ambient temperature you enter (the average winter temperature for your area) to calculate how cool your treatment room will get at a constant airflow rate, given the external ambient temperature.

Based on our experiment, this site can cool from 7.8ºC to 5.7ºC when the external temperature is -4ºC and the fan airflow is 480 CFM.

Step 10: Weather Simulation

However, we know the outside temperature changes drastically throughout the winter, so we can use our results from step 2 to see how the internal temperature of our site will change based on the external temperatures from a weather station near our site from a previous winter.

In step 4, we can enter a ZIP code for a city near our site and past start and end dates to pull real weather data from a local weather station and see how the internal temperature of our site will change based on the external temperature from a previous winter.

Just need to enter a zip code, start and end dates, the ambient temperature of your site at time 0, the rock temperature, and your suggested airflow rate.

We can see from our experiment that if we increase the airflow rate to 720 CFM, our treatment area will approach 0 during a really cold spell in January 2025, so we will want to install thermostats to stop the fan from running when it's that cold.

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