Seeking help with thermal regimes

[HostessVo]

I'm working on an experiment where I'm trying to simulate the natural cycle of temperature changes in a River. I have the data and know how I'm going to implement it in a theoretical sense. The experiment is set up so that a tank will have water pumped in, (keeping volume constant), between 4-10 degrees C*, and a heater that will shut off when it reaches a certain maximum.

(* we have two pipes one of 4 degrees C and one of 10 degrees C and through experiment, since we don't have an analytical way of determining how much is flowing from each one, we can mix the two to keep the water flow from the pump at a constant temperature.)

The goal is to have the water go through one cycle, which can be thought of as going through one sinusoidal cycle, per day. The main problem I'm facing is that it seems like the temperature would cool down too quickly when the heater shuts off. We also don't want to more than one cycle per day, (in attempt to mimic nature), but some noise is fine.

In looking up examples on the web I've found them to be oversimplified. And even if I took the simple equation by using Newton's law of cooling I anticipate that the water will cool too quickly as there is very little difference between the two temperatures, e.g. max of 12.8 C and min of 11.1 C. I'm also not certain if the constant flow of constant temperature water will be enough to offset any ambient temperature. (the tanks are made of a thick plastic and will be covered, maybe no more volume then appx 0.25 cubic meters.)

I'm hoping for a little physics help to determine how to best use my instruments in the design process and what type of equation to use for my model, to know when to turn my heaters on and when I need to monkey with the valves that control the 4 and 10 degree C pipes. If nothing else at least a more appropriate differential equation to use.

Thanks!

 

[eljose79]

Hello!

Thank you for sharing your experiment and concerns with us. It is clear that you have put a lot of thought into your setup and are trying to mimic the natural cycle of temperature changes in a river. I am a scientist with experience in fluid dynamics and thermodynamics, and I would be happy to offer some guidance on your experiment.

Firstly, I commend you on considering the effects of ambient temperature and the potential for the water to cool too quickly when the heater shuts off. These are important factors to consider in order to accurately simulate the natural cycle of temperature changes in a river.

Based on the information provided, it seems that you are trying to create a closed-loop system where the temperature of the water is controlled by the heater and the flow rate is controlled by the valves. In order to accurately mimic the natural cycle of temperature changes, you will need to consider the following factors:

1. Heat transfer between the water and the environment: As you mentioned, the tanks are made of a thick plastic and will be covered, but there will still be some heat transfer between the water and the environment. This heat transfer will depend on the temperature difference between the water and the environment, the surface area of the tank, and the thermal conductivity of the tank material. It is important to take this into account when designing your experiment and determining the appropriate heater and flow rates.

2. Heat capacity of the water: The water in your experiment will have a certain heat capacity, which is the amount of heat required to raise the temperature of a unit mass of water by one degree. This will play a role in how quickly the water cools down when the heater shuts off.

3. Flow rate and mixing: The flow rate of the water and the mixing of the two pipes will also affect the temperature of the water. By mixing the two pipes, you are essentially creating a temperature gradient within the tank. It is important to monitor and control the flow rate and mixing in order to maintain a constant temperature throughout the tank.

With these factors in mind, I would suggest using a heat balance equation to model your experiment. This equation takes into account the heat transfer between the water and the environment, the heat generated by the heater, and the heat capacity of the water. It can be written as follows:

Q = mCpΔT + Qh

Where:
Q = heat transfer rate (in watts)
m = mass flow rate (in kg/s)
Cp = specific heat capacity of

 

[astrokreng]

Thank you for reaching out for assistance with your experiment on simulating thermal regimes in a river. It sounds like you have a well-designed setup and a clear understanding of the goals of your experiment.

One potential solution to the issue of the water cooling too quickly when the heater shuts off could be to use a more sensitive control system for the heater. For example, you could use a thermostat that reacts quickly to changes in temperature and adjusts the heater accordingly. This could help maintain a more consistent temperature in the tank and mimic the natural cycle of temperature changes more accurately.

In terms of the equations and models to use for your experiment, it would be helpful to have more information about the specific setup and conditions of your experiment. However, a good starting point could be to use the laws of thermodynamics, specifically the first and second laws, to model the heat transfer and energy flow in your system. You could also consider incorporating the effects of convection and radiation in your model.

Additionally, it may be beneficial to conduct some preliminary experiments or simulations to determine the best combination of flow rates and temperatures from the 4 and 10 degree C pipes to achieve the desired thermal regime in the tank. This could help optimize the setup and minimize the need for adjusting the valves during the experiment.

I hope this helps and wish you success in your experiment. Please don't hesitate to reach out for further assistance or clarification.