I am building a nozzle for my hot glue gun, and it has made me realize that my math skills have become quite rusty. My goal is to figure out how fast I can extrude a hot glue stick through nozzle of different lengths. My assumption is that the longer the nozzle is (assuming I keep it at temperature), the more surface area there will be to heat the glue stick. While I could just start experimenting, curiosity has taken hold of me and I would like to know how to find the answer mathematically. After browsing the internet for a while I believe Fourier’s law is what I need to use, but I am having trouble applying the equation. From what I understand, I need to calculate heat conduction through truncated cone (melted end of hot glue against nozzle), where heat is applied to the curved surface. This will tell me what volume glue I can melt at a given nozzle temperature / length. Knowns: Hot glue stick diameter (base of cone): 13 mm Nozzle diameter (truncated end of cone): 3 mm Temperature of Nozzle: 190 C Melting temperature of glue: 70 C Thermal Conductivity of glue: 0.25 Watt/m - °C Thanks!