I have a question regarding how long it takes to heat a storage tank using a coil heater
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The stainless steel steam pipe forms a circular coil inside the storage tank, and then extends outside the tank where it is discharged to the outside through a drain valve. It is known that the saturation steam table pressure is 0.6 Mpa and the temperature is 165℃ ； The inner diameter of the steam pipe is 45 mm, with a length of 50 meters; thus, the heat exchange area is 7㎡ ； There is a total of 2000 kg of water in the heated tank, with its temperature rising from 50°C to 100°C ； From the table, the specific heat capacity of water is CP=4.2 kj/(kg·℃), and the heat transfer coefficient of the coil is U=1100 w/m2·℃. The storage tank is insulated as a whole, with no consideration for heat loss. How long does it take for water to heat from 50°C to 100°C? If we consider the range of 50–100°C, then the coil area will be required for the calculation ； But if you calculate the time in reverse, it doesn’t work; I’ve looked up a lot of information but still can’t figure it out. Q, please help solve this: handshake
To calculate the time required to heat from 50°C to 100°C, we need to consider the energy required to heat the water and the rate at which heat is supplied by the steam pipes. First, calculate the total energy required to heat the water (Q): Q = m * Cp * ΔT. Where: – m is the mass of water (2000 kg), – Cp is the specific heat capacity of water (4.2 kJ/kg·℃), – ΔT is the temperature increase (100 – 50 = 50℃). Thus, Q = 2000 kg * 4.2 kJ/kg·℃ * 50℃ = 420,000 kJ. Next, calculate the heat power transferred through the steam pipe (P): P = U * A * ΔT’. Where: – U is the heat transfer coefficient of the coil (1100 W/m²·℃; note that it needs to be converted to kJ/s·m²·℃ since the unit of total energy is kJ), – A is the heat exchange area of the coil (70; this value isn’t entirely clear, so I assume it’s 7 m²), – ΔT’ is the temperature difference between the steam and the water temperature (165 – (50 + 100)/2 = 90℃). Here, it is assumed that the water temperature increases linearly, so an average value is used for estimation. P = 1100 W/m²·°C * 7 m² * 90°C = 1100 J/s·m²·°C * 7 m² * 90°C / 1000 = 1100 kJ/s·m²·°C * 7 m² * 90°C / 1000 = 0.77 kJ/s * 90 = 69.3 kJ/s. Next, calculate the required time (t): t = Q / P = 420000 kJ / 69.3 kJ/s ≈ 6059 seconds. Therefore, theoretically, it takes about 6059 seconds, or roughly 1 hour and 41 minutes (6059 s ≈ 101 minutes), to heat these 2000 kg of water from 50°C to 100°C. Please note that this calculation is based on theory; in practical applications, various variables may affect the final result. .
This post was last edited by Sihai Youxian Tian on 2023-11-24 at 17:03; see attachment
1. Calculate the heat required to raise the temperature of water from 50°C to 100°C, without considering heat losses. 2. Calculate the heating power of the steam. 3. Heat ÷ Power = Time.
The heat transfer coefficient of the coiled tube can’t necessarily reach such a high value, right?
How did you calculate the area of this coil?
I’m sorry for the delayed reply; it’s extremely detailed, and thank you so much! {:1_90:}
Sorry for the late reply, thanks! !
Just calculate the area normally and then compare it with 7 square units
It’s just a guess, it’s not me who calculated it!