Hi there, I would like to understand if my math notation is correct for the problem I am tring to solve: I have a steady heat source q (W/2 π) at the origin and a circular no-flow boundary at distance R from the origin. The material in the domain has a thermal conductivity K (W/mK) and a volumetri…

from dolfin import * dt = 5 # seconds D = 0.0000008 # diffusivity wm2/J Q =1/6.28 #w/m/2pi mesh = IntervalMesh(100,0,1) V = FunctionSpace(mesh, "Lagrange", 3) u = TrialFunction(V) v = TestFunction(V) r = Expression("x[0]", degree=1) u_0 = Constant(0) u_old = interpolate(u_0, V) a = dt*D*(inner(g…

Hi All, Me again. I’m trying to replicate a needle probe used to determine material conductivities. Conductivity is linearly proportional to slope of the change in temperature plotted against the natural log of time. Something is not right here. I am getting extremely high temperatures at the core…

Thank you Dokken, I believe my formulation is following that shown in the previous post. So I need something new. I am also using the weak formualtion for polar representation in the post linked to the previous post. I notice that as I increase the mesh intervals, The value of U at r=0 increases. …

To use discontinuous material parameters, have a look at either How to define different materials / importet 3D geometry (gmsh) or How to define boundary conditions on an irregular geometry? ,

Thanks Dokken, Can you explain why when I add the pointsource at Point(1), the spike in temperature is seen at r = 0? I tried placing the pointsource- at point(0) but then the heat seemed to flowing from the the opposite end.

To me, it seems strange that all your terms are scaled with r, i think there is a mistake in your derivation. Please do integration by parts in polar coordinates carefully.

I think my formulation is ok. I’m trying to represent the flow over a unit sector over a circle. r is multiplying d_theta which is one in this case. I’v divided the flow in at r =0, by two pi to get the amount of heat flow into the unit sector of the circle. I’m simplifying a 2d problem into a 1D p…

Polar - axisymetric poisson formulation with PointSource at origin

variational formulation

dokken May 4, 2020, 11:40pm 5

I would recommend having a look at this 1 D axisymmetric heat conduction with neumann boundaries and the link within thus post

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Polar - axisymetric poisson formulation with PointSource at origin

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