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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!

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!