INTELLIGENT WORK FORUMS
FOR ENGINEERING PROFESSIONALS

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.

Jobs

looking for help w/ heat equation + surface convection

looking for help w/ heat equation + surface convection

(OP)
Hi,

I have an application in which I have a semi-infinite solid subjected to surface convection at the x=0 boundary and a time varying fluid temperature. I am familiar with the heat equation (d2Tdx2 = 1/alpha dTdt) and I've been able to solve my problem by discretizing the spatial domain and time marching with an rk4 solver, but I am trying a method which does not require tracking as many state variables as I potentially need to solve for many different semi-infinite bodies at once.

I came across an approximate integral method (ref. Ozisik, Heat Conduction) in which an approximate spatial distribution is enforced over a thermal boundary distance (delta) and the heat equation is reduced to solving a differential equation describing delta.

My problem is actually integrating the equation. At time zero the surface temperature rate of change is infinite (also the thermal boundary layer has zero thickness), which I've confirmed by looking at available exact solutions for my problem which have a constant fluid temperature. This equates to a thermal boundary rate initially at infinity. At any time after t=0 there will be a positive boundary layer thickness and the equations won't blow up.

How do I handle time zero and getting the whole thing started? The text just leave it at "Equation (9-36) can be integrated numerically".

Thanks for any insight anyone can offer.

RE: looking for help w/ heat equation + surface convection

Start at time t=0.1, with a reasonable approximation for the first condition.

Heat transfer requires approximations and assumptions for everything else.

RE: looking for help w/ heat equation + surface convection

(OP)
Thanks, I'm thinking I'd try approximating the time derivative at t=0 assuming a very small thermal bounday depth, 1 micrometer or so. Then compare solution against constant fluid temp exact solution to be sure it's reasonable.

RE: looking for help w/ heat equation + surface convection

Real world, the IR images of the film thickness are are in the textbooks are not "scaled" but appear much thickner than that: Try 1/2 to 1 millimeter (20 - 40 thousandth inch) as an approximation.

Your time interval for heat transfer in a real-world large application (unless it is an explosion or internal combustion engine fuel combustion) is on the order of minutes and tens of minutes not milliseconds. So I'd try to stay away from the very, very tiny increments that will distort your starting conditions.

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!


Resources


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:

Register now while it's still free!

Already a member? Close this window and log in.

Join Us             Close