×
INTELLIGENT WORK FORUMS
FOR ENGINEERING PROFESSIONALS

# Contact US

Log In

#### Come Join Us!

Are you an
Engineering professional?
Join Eng-Tips Forums!
• Talk With Other Members
• Be Notified Of Responses
To Your Posts
• Keyword Search
• One-Click Access To Your
Favorite Forums
• Automated Signatures
On Your Posts
• Best Of All, It's Free!

*Eng-Tips's functionality depends on members receiving e-mail. By joining you are opting in to receive e-mail.

#### Posting Guidelines

Promoting, selling, recruiting, coursework and thesis posting is forbidden.

Students Click Here

# Nonlinear heat transfer FEA

 Forum Search FAQs Links MVPs

## 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).

### RE: Nonlinear heat transfer FEA

The best source of information about the theory behind Abaqus analysis procedure is the documentation of this software. There’s a whole Theory Guide in which equations and algorithms used by Abaqus for various simulation types are described. However, books about general FEA for thermomechanical applications should also be useful, especially that derivations in Abaqus documentation are reduced to minimum.

### RE: Nonlinear heat transfer FEA

Steady-state should be straightforward enough: use the standard methodology to derive the weak form (e.g., using Galerkin method of weighted residuals), determine the expression for k(T) (analogous to e.g., determining a displacement-dependent Young´s modulus for a solid mechanics rod problem), develop the discretized system "K(T)u=q" and apply an element interpolant (e.g., linear in a 1D bar), and then create the system of equations and solve it using e.g., direct iteration (more straightforward method) or Newton-Raphson.

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.

#### Red Flag This Post

Please let us know here why this post is inappropriate. Reasons such as off-topic, duplicates, flames, illegal, vulgar, or students posting their homework.

#### Red Flag Submitted

Thank you for helping keep Eng-Tips Forums free from inappropriate posts.
The Eng-Tips staff will check this out and take appropriate action.

### Reply To This Thread

#### Posting in the Eng-Tips forums is a member-only feature.

Click Here to join Eng-Tips and talk with other members! Already a Member? Login

Close Box

# Join Eng-Tips® Today!

Join your peers on the Internet's largest technical engineering professional community.
It's easy to join and it's free.

Here's Why Members Love Eng-Tips Forums:

• Talk To Other Members
• Notification Of Responses To Questions
• Favorite Forums One Click Access
• Keyword Search Of All Posts, And More...

Register now while it's still free!

Already a member? Close this window and log in.