Heat Transfer: Calculating Time to Heat 1000L of Water

In summary, the conversation discusses a problem with determining the time it takes for a bag of 1000L of water to heat up to a specific temperature while inside a metal frame. The temperature outside the bag remains constant at a higher temperature, and the water inside is naturally convecting. The individual is seeking guidance on what equations to use and if the vertical and horizontal parts of the bag need to be treated differently. The solution is suggested to lie in Lumped Systems Analysis, which involves formulating an energy balance to solve for the required time.
  • #1
blitzn
2
0
Hi guys,

Hoping to see if I can get a bit of help with a heat transfer equation. Apologies if this is not in the correct forum as this is my first post.

I need to find out how long it will take a bag of 1000L of water (in a 1m3 cubic bag) to heat up to a specific temperature. The bag is placed in a metal frame.

The temperature outside the bag will stay at a constant temperature that is higher than in the bag. The reason that I'm having problems is that my heat transfer knowledge is limited to working out temperature differences for planar surfaces that only deal with conduction.

The water in the bag is not being agitated but will be moving due to natural convection.

Much appreciated if anyone can point me in the right direction i.e. as to what equations to use. Also is it true that I have to treat the vertical and horizantal parts of the bag differently?

Thanks,
 
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  • #2
Have you studied Lumped Systems Analysis?
 
  • #3
No I haven't. Would you say that is where the answer lies?
 
  • #4
Well, whenever I'm trying to find how long it would take some to heat up or cool down, I always think of Lumped Systems Analysis, as there is a time rate term in the equations.

Essentially, the energy balance breaks down into {Change in Internal Energy During Time Interval dt} = {rate of heat flow to or from ambient during time interval dt}.

As long as you know how to properly formulate the energy balance, you should be able to solve for your time as required.
 

1. How do you calculate the time it takes to heat 1000L of water?

To calculate the time it takes to heat 1000L of water, you will need to know the starting temperature, the desired final temperature, and the power of the heating source. You can use the formula Q = m * c * ΔT to calculate the amount of heat required, where Q is the heat energy, m is the mass of water, c is the specific heat capacity of water, and ΔT is the change in temperature. Then, you can use the formula t = Q/P to calculate the time, where t is the time, Q is the heat energy calculated in the previous step, and P is the power of the heating source.

2. What is the specific heat capacity of water?

The specific heat capacity of water is the amount of heat energy required to raise the temperature of 1 gram of water by 1 degree Celsius. It is approximately 4.186 joules per gram per degree Celsius (J/g°C). This means that it takes 4.186 joules of energy to raise the temperature of 1 gram of water by 1 degree Celsius.

3. How does the starting temperature affect the time it takes to heat 1000L of water?

The starting temperature does affect the time it takes to heat 1000L of water. The higher the starting temperature, the less time it will take to heat the water to the desired final temperature. This is because the initial temperature difference (ΔT) is greater, resulting in a higher amount of heat energy required.

4. Can you use the same formula to calculate the time to heat different amounts of water?

Yes, you can use the same formula to calculate the time to heat different amounts of water. The only difference would be in the value of m (mass of water) in the formula. You would need to adjust the value of m to match the amount of water you are trying to heat.

5. What factors can affect the time it takes to heat 1000L of water?

There are several factors that can affect the time it takes to heat 1000L of water. These include the starting temperature, desired final temperature, power of the heating source, and the efficiency of the heating system. Other factors that can affect the time include the type of heating source (e.g. gas, electric, solar), the insulation of the water container, and the surrounding temperature. These factors should be taken into consideration when calculating the time to heat 1000L of water.

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