Heat transfer from half cylinder adhesive bead

[jbenson5]

I am interested in the heat transfer from an adhesive bead. The bead is applied hot, and cools due to conduction into the substrate and convection into the ambient. The adhesive bead shape is a half cylinder (see attached figure). I am interested in understanding how the thermal conductivity of the substrate and bead diameter effect the rate of cooling.

I have taken graduate level heat transfer courses but it has been a long time. I know the general solution in cylindrical coordinates are Bessel functions, but I do not have radial symmetry due to the boundary condition at the substrate.

If a general solution is too difficult, I am interested in simplifications that will give an approximate solution. Some dimensionless parameters that will allow me to estimate the conduction and convection would be a good starting point.

Thanks!

 

[IRstuff]

What materials are involved? Is it a typical hot glue stick? What's the substrate?

TTFN (ta ta for now)
I can do absolutely anything. I'm an expert!

https://www.youtube.com/watch?v=BKorP55Aqvg

faq731-376 forum1529 Entire Forum list

http://www.eng-tips.com/forumlist.cfm

 

[jbenson5]

I’m interested in the general case which a generic material (the adhesive) with thermal conductivity k, on substrates with different thermal conductivities. I’m interested in formulating some equations to show how the rate of cooling is effected by bead size abs substrate conductivity.

 

[Compositepro]

The rate of heat flow out of your adhesive material depends on the thermal diffusivity, which is the ratio of thermal conductivity to heat capacity. Polymers have low thermal conductivity and high heat capacity, so the thermal diffusivity is exceptionally low. I cannot help you with geometry issues, but if your process involves making pastilles you will get a great increase in cooling rate if you blow cold air on the beads or dropping the beads into chilled water when they are cool enough to scrape off the surface.

 

[goutam_freelance]

The long formulations are passe' now-a-days. This can be easily solved with FEA in a few hours.