Calculating nozzle shape for melting hot glue

[DustinSmith]

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!

 

[billy_joule]

Thermal Conductivity of glue: 0.25 Watt/m - °C

In which state? Liquid or solid?
What is the heat of fusion?

I think this would be a very difficult heat transfer problem. The change of state, the converging nozzle, the melting range (most thermopolymers don't have a melting point), and how the fluid properties (density, viscosity, conductivity etc) change over that range would all make it a very hard problem.
A textbook on injection molding/ plastic extrusion would probably be a good place to start.

The mass flow rate is ultimately determined by the power of the heater. Pretty much any nozzle will work given enough power.

 

[DustinSmith]

Thanks for the response -

For the purpose of this problems, let's simply set a target temperature of 70 C. After looking at this problem some more, I realize that I will need to know how much energy the material holds before I know how much the temperature will increase.

How do I calculate the thermal transfer of a truncated cone? Maybe I could start by looking at how much energy is transfer ed into the material and make some predictions about how long it will take for the center of the material to reach the target temperature.

Thanks again

 

[davenn]

All the hot glue guns I have owned or seen, the nozzle isn't heated . Its just a coned shaped outlet
the heating/melting is done further in, in a cylindrical tube that has a just slightly larger internal diameter than the glue stick

the nozzle just reduces that diameter down to a smaller size to ease in the use of application of the glue

Dave

 

[DustinSmith]

All the hot glue guns I have owned or seen, the nozzle isn't heated . Its just a coned shaped outlet
the heating/melting is done further in, in a cylindrical tube that has a just slightly larger internal diameter than the glue stick

the nozzle just reduces that diameter down to a smaller size to ease in the use of application of the glue

Dave

I must have a strange one because the glue stick is pushed into the nozzle which has a heat coil where the nozzle threads into the hot glue gun. I am sure it does not do the bulk of the heat transfer, but now I am just curious.

 

[davenn]

I must have a strange one because the glue stick is pushed into the nozzle which has a heat coil where the nozzle threads into the hot glue gun. I am sure it does not do the bulk of the heat transfer, but now I am just curious.

nothing like this huh ?? ...

there's varieties in shape and manufacture but they all work the same
cold glue stick in the back end, hot melt out the nozzle

http://www.bing.com/images/search?q=hot+glue+guns&FORM=HDRSC2if yours is different, maybe a pic of your one so we all know what you are referring tocheers
Dave

 

[DustinSmith]

nothing like this huh ?? ...

if yours is different, maybe a pic of your one so we all know what you are referring to

Dave

Latter I'll see if I can post a picture of it, but really I am just interested in the math at this point.

More than anything I am curious how to calculate the rate of heat soaking into a material based on it's shape. In the past I encountered a situations where I was unsure how fast heat would soak into another material, and just guessed until it worked. It would be nice for this project, and future projects to be a little more intentional.