×
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!
  • Students Click Here

*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

Jobs

Transient Finite Difference Boundary Conditions

Transient Finite Difference Boundary Conditions

Transient Finite Difference Boundary Conditions

(OP)
Hi everyone,

I am trying to find the temperature through an object of length L surrounded by air at one end and enclosed air at a different temperature on the other end. I am only considering one dimensional heat transfer through the object in the x direction. At x(0) I have the temperature increasing linearly to illustrate changing temperature throughout the year. At x(L) however I have a different case. I want to have T(L) initially at 273k (0 degrees Celsius), and calculate temperatures at each timestep based on convection into the surrounding enclosed air.

My one problem is that I don't know how to calculate the change in temperature of the enclosed air.

So far I have thought about somehow calculating a heat transfer rate "q" based on q=rho*V*A*dT/dt and q=hA(Tin-T(L)). However in order to use those equations I would need to know the change in temperature of the air for each timestep.

Does anyone have any advice on how to solve for that inside air temperature?

Also if anyone needs anything clarified I can probably draw up a diagram to show you.

RE: Transient Finite Difference Boundary Conditions

" I would need to know the change in temperature of the air for each timestep"

That comes from the removal(addition) of heat during the previous time step

TTFN
FAQ731-376: Eng-Tips.com Forum Policies

RE: Transient Finite Difference Boundary Conditions

To calculate the change in temperature of air you need a further equation on the heat balance of the volume of air. This may be difficult to define correctly, depending on your setup, as it could require assumptions on the convective behavior of air.
One point is unclear to me in your description: I understand that the sides of the object (a bar I assume) are adiabatic and that the only heat loss is from the front area at x=L, correct? If so, it is a very simple problem and finite differences are not necessary to solve.

prex
http://www.xcalcs.com : Online engineering calculations
http://www.megamag.it : Magnetic brakes and launchers for fun rides
http://www.levitans.com : Air bearing pads

RE: Transient Finite Difference Boundary Conditions

(OP)
Well let me try to clarify a bit more. The bar is initially at 0 degrees C and is heated by the air at x=0. At x=L the bar will heat the enclosed air which is also initially at 0 degrees. The sides are adiabatic.

My question is how can I calculate the temperature of that enclosed air based on the volume, surface area etc.

RE: Transient Finite Difference Boundary Conditions

Again: to calculate the temperature of air at x=L you need one more equation for that enclosed space. This might account for the heat capacity of air (rarely relevant, but...) and should account for how heat goes out. If you can describe the geometry of your setup, possibly with a sketch, this would help.
And, sorry, I was wrong in saying you don't need finite differences for this problem: only the final steady state solution can be calculated by formula.

prex
http://www.xcalcs.com : Online engineering calculations
http://www.megamag.it : Magnetic brakes and launchers for fun rides
http://www.levitans.com : Air bearing pads

RE: Transient Finite Difference Boundary Conditions

(OP)
Basically the top bar is used as insulation for the system. I can compute the temperature at the bottom boundary T(L) using finite diff. analysis. I need some equation that can compute the temperature Tin. The inside of the chamber has a constant volume V and We can use the assumption that the temperature in the chamber changes uniformly. Thanks again for the help.



RE: Transient Finite Difference Boundary Conditions

The condition of zero heat transfer across the walls is unrealistic: the walls have mass and heat capacity as well as the insulating material, whatever it is (the heat capacity of air being likely negligible). So you need to account for the heat transfer from the inner face of the lid to the enclosed air and from the air to the walls, that will absorb heat until a steady state is reached with possibly a nearly zero net heat loss (at steady state).
Not an easy problem: a realistic solution requires an assumption on the convective behavior of air in the enclosed space (may vary a lot depending on shape and dimensions).
IMHO only an important research programme would justify a detailed analysis as compared to a test: I recall of such calculations done to estimate the heat loss through the penetrations of the cover of a nuclear reactor.

prex
http://www.xcalcs.com : Online engineering calculations
http://www.megamag.it : Magnetic brakes and launchers for fun rides
http://www.levitans.com : Air bearing pads

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