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I want to build a geyser attached to a pump with copper tubing running into an oil tank. This is done because the oil solidifies at a temperature below 15 degrees Celsius. I have done a few calculations to determine the amount of time it would take to heat the oil, but i am not sure if they are correct.

Pumping velocity = $3m/s$

Water temperature = $60C$

oil temp =$ 5C$

Desired Temp $20C$

15000 liter oil tank

20mm diameter copper tubing was used

6m of tubing is submerged into the oil

Calculating the heat transfer coefficient: $$Re=(C.d)/Vf$$ $$ =(3x0.02)/0.475x10^{-6}$$ $$=126 315$$ thus the flow would be turbulant

$$Nu=0.023Re^{0.8}xPr^{0.33} (0.33 for cooling)$$ $$Nu=397.98$$

$$Nu=(α.d)/λ$$ $$α=(Nu.λ)/d$$ $$=(397.98x654.3x10^{-6})/0.02$$ $$α=13.02kW/m^2.K$$

I then used the following equation for the heat transfer inside the tank: $$Q^*=αA(deltaT)$$ $$Q^*=13020xπx0.02x6(60-40)$$ $$= 31.248kW$$

Energy required to heat the oil: $$Q=mcpT$$ $$Q=15000x1800x(20-5)$$ $$Q=405000J$$

Heating time: $$t=405000/31.248$$

$$t=3.6 Hours$$

Can someone please tell me how you would do the calculations. Also please assume any information not provided.

Thank you.

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