Use NDSolve with finite element method for a transient conduction problem?

[ksel13 (Kesihain Selvarajoo)]

Hi! I’m a final year Mechanical Engineering student trying to use Mathematica to solve a transient Conduction problem to plot history of temperature at a point. The question is attached below .

When using NDSolve , an error pops up saying that boundary and initial conditions are inconsistent. The Code is attached below

When using NDSolve with the finite element method an error pops up saying that
NDSolve::femcscd: The PDE is convection dominated and the result may not be stable. Adding artificial diffusion may help.
and
NDSolve::fembdnl: The dependent variable in (T^(1,0,0))[0,y,t]==0 in the boundary condition DirichletCondition[(T^(1,0,0))[0,y,t]==0,r==0.] needs to be linear.
The code is attached below

I’ve also attached the mathematica file. Will appreciate any help
[1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=4416projectq1.JPG&userId=1810612
[2]: https://community.wolfram.com//c/portal/getImageAttachment?filename=4416q1NDSolve.JPG&userId=1810612
[3]: https://community.wolfram.com//c/portal/getImageAttachment?filename=4416q1NDSolveFiniteElement.JPG&userId=1810612

Project Q1.nb (181 KB)

[trounev (Alexander Trounev)]

There is a cylinder, and you use plane geometry. Equation QE is therefore erroneous. You do not use FEM at all. To use FEM, call Needs["NDSolveFEM"], then read the tutorial on a page FEMDocumentation/guide/FiniteElementMethodGuide.