# Heat equation advice for a small ice rink.

• Stevensam2009
In summary, the conversation discusses the feasibility of building a small ice rink for a Cybernetics project. The plan involves using a wooden frame, insulation, and a plastic sheet for the top. Suggestions were made to use dry ice and a brine system to keep the ice frozen. The student is seeking equations to determine the amount of dry ice needed and any design modifications or alternatives. One suggestion is to simply build the rink in a cold location such as Saskatoon. However, budget constraints may prevent this option.
Stevensam2009
Hi everyone,

I am a Cybernetics student and as part of a project I need to determine the feasability of building a small ice rink (approximately 2m x 4m)

The plan is to build a frame and exterior (the sides and bottom of a box) out of wood, and have a layer of internal insulation such as polystyrene. A plastic sheet will be the top of the box and the idea is that the water will freeze on top of this. I may also have an insulated lid for the system that is closed when freezing the water.

My lecturer has suggested putting dry ice in the bottom of the box and spraying on water gradually to create the ice, and running copper pipes through the system with cooled brine being pumped through them in order to keep the ice frozen.

I'm not really too sure how to go about determining whether this system will work or not. I would be very grateful if anyone could help me out by suggested what equations are suitable for calculating how much dry ice would be needed to freeze a particular amount of water when the system has insulation with a known thickness, and also some advice on how best to apply such equations. Also, any possible design modifications/alternatives would be welcome.

-Steve-

Forget the fancy stuff. You don't need any pipes or styrofoam. Just build it in Saskatoon. It was -34 C here this morning.

AM

I could suggest this to my lecturer, but somehow I don't think that he would let the budget stretch that far.

## 1. What is the heat equation and how does it apply to a small ice rink?

The heat equation is a mathematical equation that describes how heat energy is transferred in a system. In the case of a small ice rink, the heat equation helps us understand how the temperature of the ice surface changes over time due to factors such as air temperature, ice thickness, and the number of skaters on the rink.

## 2. How can the heat equation be used to maintain the ice quality in a small ice rink?

By understanding the heat equation, we can make informed decisions about how to manage the temperature of the ice surface in a small ice rink. For example, we can adjust the heating and cooling systems to maintain the ideal temperature for the ice to remain solid and smooth.

## 3. What factors influence the rate of heat transfer in a small ice rink?

The rate of heat transfer in a small ice rink is influenced by several factors, including the temperature difference between the air and the ice surface, the thermal conductivity of the ice, and the presence of any insulating materials such as a layer of snow on top of the ice.

## 4. How can the heat equation be used to predict the melting rate of ice in a small ice rink?

Using the heat equation, we can calculate the rate at which heat is being transferred to the ice surface and how quickly the ice will melt. This information can help us plan and adjust our maintenance schedule to ensure the ice remains in good condition for skaters.

## 5. What steps can be taken to ensure the ice surface remains at a consistent temperature in a small ice rink?

To maintain a consistent temperature on the ice surface, it is important to regularly monitor and adjust the temperature of the air and the ice. Additionally, minimizing the number of skaters on the ice and avoiding excessive snow accumulation can also help keep the ice temperature stable.

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