Find steady state of constant heat application

In summary, a hobby beer brewer is seeking assistance with predicting the steady state temperature of water in a vessel being heated by an electric water heater element. The goal is to achieve precise temperature control within 1F. The temperature stabilizes at 127F after hours of heating with a 20% duty cycle, following a logarithmic curve. The question is how to predict the steady state with a few minutes of data instead of waiting for hours. One suggestion is to model it with a logistic curve using appropriate scaling.
  • #1
MTEXX
1
0
Hey all. I sure hope somebody can assist with this!

I am a hobby beer brewer and am writing my own heat control algorithms. Part of the process involves heating water to a desired temperature setpoint. I'm using an electric water heater element (5500W) inside the water vessel (~5-10 gal). I can pulse the heater element for a desired duty cycle (0 to 100%). The vessel is not well insulated as to allow quicker recovery from a temperature overshoot. Precise temperature control within about 1F is my goal.

Let's say that I apply 20% duty cycle. Over a VERY LONG time (hours) , the temperature stabilizes at say 127F. The curve is similar to a cooling curve but it rises toward an "asymptote" which is the steady state. I believe it is logarithmic.

My question is this- how can I predict the steady state with a few minutes of data instead of waiting hours upon hours?

Thanks in advance !
-Micah
 
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  • #2
MTEXX said:
Hey all. I sure hope somebody can assist with this!

I am a hobby beer brewer and am writing my own heat control algorithms. Part of the process involves heating water to a desired temperature setpoint. I'm using an electric water heater element (5500W) inside the water vessel (~5-10 gal). I can pulse the heater element for a desired duty cycle (0 to 100%). The vessel is not well insulated as to allow quicker recovery from a temperature overshoot. Precise temperature control within about 1F is my goal.

Let's say that I apply 20% duty cycle. Over a VERY LONG time (hours) , the temperature stabilizes at say 127F. The curve is similar to a cooling curve but it rises toward an "asymptote" which is the steady state. I believe it is logarithmic.

My question is this- how can I predict the steady state with a few minutes of data instead of waiting hours upon hours?

Thanks in advance !
-Micah

A logarithmic curve will not approach an asymptote. It just grows so slowly it might give that appearance. Perhaps you could model it with a logistic curve with appropriate scaling, the right side of which seems to fit your description. You might take a look at:
http://en.wikipedia.org/wiki/Logistic_function
 

FAQ: Find steady state of constant heat application

1. What is the steady state of constant heat application?

The steady state of constant heat application refers to a state in which the temperature of a system remains constant over time, despite a continuous supply of heat. This occurs when the heat input into the system is equal to the heat lost by the system to its surroundings.

2. How is the steady state of constant heat application achieved?

The steady state of constant heat application can be achieved by ensuring a balance between the heat input and heat output of a system. This can be done by controlling the rate of heat application and the rate of heat dissipation through insulation or other methods.

3. Why is finding the steady state of constant heat application important?

Finding the steady state of constant heat application is important for understanding how a system responds to continuous heat input, as well as for ensuring the stability and efficiency of the system. It also allows for the prediction of long-term temperature changes and the identification of any potential issues or limitations.

4. What factors affect the steady state of constant heat application?

The steady state of constant heat application can be influenced by various factors, such as the thermal properties of the system, the rate of heat transfer, and the environmental conditions. Other factors may include the type of heat source, the size and shape of the system, and the presence of any insulating materials.

5. How can the steady state of constant heat application be calculated or measured?

The steady state of constant heat application can be calculated by using mathematical equations that take into account the heat input, heat output, and other relevant variables. It can also be measured through the use of specialized instruments, such as thermometers, thermocouples, and heat flux sensors, which can provide real-time data on the temperature changes within a system.

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