Discussion Forum

Hello,

I'm trying to model the behavior of a hollow cylinder made of a certain material, with an inner radius r1 fixed at 0.5m and an outer radius r2 that I need to determine. The behavior I'm trying to model is that in response to combustion inside the cylinder for a certain period with a certain heat flux.

My problem depends only on the variable r (the radius). Therefore, I can reduce it to a 2D problem where instead of a cylinder, we have a hollow disk.

To model the combustion described above, I impose a heat flux at r1 = 0.5m. On the cylinder, the amount of heat provided is constant at Q=33333 [W] for 2 hours and then drops to 0. It is uniformly distributed. The total surface on which this flux applies is the inner surface of the hollow cylinder with a radius of r1 = 0.5m and a height of z=2 m (S = 2π×0.5×2 = 2π) and thus q = 5305.11 [W/m²].

Here's my question: Since I'm reducing the problem to 2D, can I still say that the inward heat flux is equal to 5301.11 [W/m²]? I feel like I need to adjust it, but I don't see how. I'm having trouble visualizing how we can talk about a surface quantity when the condition on the 2D disk applies to a contour and not a surface.

Thank you for your futur response !