How would I go about comparing the efficiency of different heater block shapes for the outlined system?
So, in the attached diagram there is a cylindrical heater cartridge (A) that is used to transfer heat to the cylindrical polymer (B) through the heater block(C).
(A): Heater Cartridge
(B): Polymer liquid flow, carrying heat out
(C): Heater block, aluminium
(D): Temperature Sensor
This setup is for the heater block of a 3D printer. The aim being to provide constant heat to the polymer (B) that flows through the system. The aluminium block acts as a thermal storage to reduce temperature fluctuation in the polymer filament as the flow rate changes. The temperature sensor (D) reacts to changes and controls the heater cartridge in order to try and maintain constant temperature.
I wish to redesign this heater block to find the most efficient shape for this function.
So, my question is how would I calculate the efficiency of different shapes for this purpose? Losses to the surrounding air will have to be taken into account as the surface area will change with different shapes. Different shapes having different surface area to volume ratios.
I must admit I don't know where to start with this problem, it has been quite some time since I've had any formal thermodynamics education. Any answers, pointers or links to resources are greatly appreciated. Thank you!