Nonlinear heat transfer FEA
Nonlinear heat transfer FEA
(OP)
Hello everyone.
I'm trying to describe Abaqus solver for my masters thesis, more exactly, for problem of heat conduction in solid, with temperature dependent thermal conductivity (k=k(T)).
I would like to derive the formulas from the ground up (see bottom picture), with example of a simple truss (1D). For start, I would work with steady-state problem and later upgrade to transient. I realize, that this is a non-linear problem, and am aware how Abaqus solves plastic deformation (Newton-Raphson alghoritm).
I have basically turned around google and google scholar, but all i find are books that are too general (FE), have to do with plasticity or articles that are too specific.
I am almost desperate at this point, so I'm asking this community to please give me some hint or maybe some literature for solving heat conduction with k = k(T).
I'm trying to describe Abaqus solver for my masters thesis, more exactly, for problem of heat conduction in solid, with temperature dependent thermal conductivity (k=k(T)).
I would like to derive the formulas from the ground up (see bottom picture), with example of a simple truss (1D). For start, I would work with steady-state problem and later upgrade to transient. I realize, that this is a non-linear problem, and am aware how Abaqus solves plastic deformation (Newton-Raphson alghoritm).
I have basically turned around google and google scholar, but all i find are books that are too general (FE), have to do with plasticity or articles that are too specific.
I am almost desperate at this point, so I'm asking this community to please give me some hint or maybe some literature for solving heat conduction with k = k(T).

RE: Nonlinear heat transfer FEA
RE: Nonlinear heat transfer FEA
You will find this type of problem in many books dealing with normal FE and nonlinear FE. Start with your course notes, and then move to linear FE (to get acquainted with the process of formulating the problem when k is not temperature dependent), and then find a book detailing the nonlinear FE for 1D elements - preferably for the problem at hand, but do note that the nonlinear elastic rod problem is essentially analogous to what you are solving.
The transient problem is much more complicated. It will require discretization also for the time domain and a numerical time integration procedure.
I would recommend "The Finite Element Method" by Thomas J.R. Hughes; nonlinear FE by Reddy; FE for solids by Zienkiewicz & Taylor; 1D FE by A. Öchsner & M. Merkel for a start.