# Heating water flowing through Copper tube

1. Dec 6, 2011

### seanist5890

Hey guys,

Im designing a system where water flows through a copper tube or coil where it is heated and sprayed out the other end. My question is, how does the length of the tube/coil play a role in this heat transfer problem?

What I would like to do is pass the water through the inlet at a given temperature (likely room temp) and heat it using the copper tubing inside of a handheld device, and spray it out the other end at a temperature around 37 °C. What would be a good equation or set of equations to use? Thanks.

2. Dec 6, 2011

### rktpro

Because H=i^2rt and r=rho L/A ; more the length, more the resistance and more is the heat generated.
But remember that H is also proportional to i^2
Therefore, you must also aim for amount of current to be more.

3. Dec 7, 2011

### Mech_Engineer

What you're asking for is more complex than you realize, but you basically need to utilize heat transfer to calculate the convective coefficient of the fluid flowing through the tube, and based on this you can find the temperature rise per unit length of the tube.

To a first approximation, if you assume that heat transfer between the fluid and the tube is high (high reynold's number e.g. turbulent, etc.) and the length of the tube is long compared to the thermal entry length, your basic calculation will depend on:
• The mass flow rate of the fluid (kg/s).
• Initial Temperature (*C or K)
• Final Temperature (*C or K)
• Fluid specific heat capacity (J/(kg*K))
Multiplying the mass flow rate by water's heat capacity and the temperature difference will net the first-order required power in watts.

$Power = c_{p}*m_{dot}*\Delta T$

I've attached a PDF with a sample calculation in it.

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4. Dec 7, 2011

### seanist5890

Thanks both of you for your contributions.