Struggling with Inline Heater Design

[Veen]

I'm designing an inline heater for a coffee brewing project. My plan is to use an aluminum tube with Nichrome heater wire wrapped around it to heat the water flow. For brewing I need to dispense somewhere around 16 fl-oz per minute at a temperature of 205 F.

I would like to determine feasibility and optimize the design for pipe length (heat transfer surface area) but am struggling with the thermodynamics/heat transfer aspect of this problem (my worst subjects when I was in school...)

I'm using the formula for heat conduction as in on this site http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/heatcond.html but am having trouble relating it to my system. I'm not sure this is the right approach to solve the system and could use some help in steering towards the correct solution.

I'm pretty rusty when it comes to heat transfer and any steering in the right direction will be greatly appreciated. I took a photo of my logic on paper for a more clear idea of what I'm talking about. Thanks!

 

[Integral]

It is difficult to compute temperature form energy input. May be best to do some trials to find how much length you need to get the required temp. This should be quick and easy with very reliable results.

I would recommend considering using copper tube rather then AL. Copper is a natural biocide and will help control any possible bacteria build up.

 

[AlephZero]

Start with what is easy to calculate. From the mass flow, the temperature change, and the specific heat of water you can find the power required for the heater.

If you supply that amount of power, in steady state conditions the heater wire and the tube will rise to whatever temperature it takes to transfer the power into the water. So the basic question from a design point of view is whether you are going to melt the tube or the heater wire.

The numbers I got for the power required was quite small compared with something like an electric kettle, which suggests that overheating the tube and wire isn't going to be a problem.

I don't know how soluble either copper or aluminum is in hot coffee, so I think I have two options - either find out or make a design so the question is irrelevant, for example by coating the pipe with something inert like PTFE.

 

[Veen]

Integral: I was already starting to think that I'd be better off just building and observing that trying to calculate the solution and I still think that is partially what I'll end up doing. I had initially picked aluminum because it was a better alternative heat transfer wise than stainless. Copper may be better yet, but I have not yet found a source of copper that is NSF certified and an withstand high temperature.

AlephZero: Using the formula, \dot{Q}=c\dot{m}\DeltaT I see that I need to supply 2.8kW to reach 205 F. What I'm having trouble doing is relating this to time. 2.8kW for how long? Maybe the transient solution is what I should be seeking? I only think the solubility of aluminum or copper in water is relevant as the hot water will not reach the coffee grounds until after it has left the heating pipe. I had considered some type of liner inside the pipe but am worried about it adversely effecting heat transfer. I think with sme searching I should be able to find a copper tube that is food safe.