I have to calculate the dimensions of a pipe heat exchanger (a continuous pipe doing u turns) , it needs to be considered submerged in a hot substance (fixed wall temperature) and needs to heat the fluid inside the pipe up to a certain temperature without surpassing it, and absorbing a fixed amount of heat. Basically I have a fixed mass Flux, I need to choose the right internal pipe diameter, which will determine a certain pipe length.
I have a range of possible diameters, the thing is that if I choose the smaller diameter, the pipes are shorter in length but i have a greater average velocity of the flow (higher Reynolds) .
If instead I choose the bigger diameter, pipes will be longer and heavier, but the average velocity of the flow is lower (lower Reynolds).
I'm prone to choose the smallest pipe diameter possible since the heat exchanger will be lighter, but is there a way to calculate an optimal solution? For example a way to minimize pressure drops due to fluid friction?. Remember that I have a whole range, not just two diameters.
Thank you for any suggestion
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