1 / 4

With

A transient problem. With. Derivation. Heat balance on arbitrary FIXED area in domain. Net rate of heat in = rate of increase in area. r density c specific heat. divergence. Fixed area. =. With scaling. And noting arbitrary nature of area.

emmy
Download Presentation

With

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. A transient problem With Derivation Heat balance on arbitrary FIXED area in domain Net rate of heat in = rate of increase in area r density c specific heat divergence Fixed area = With scaling And noting arbitrary nature of area

  2. Control Volume Solution—Start from the balance on area A Associate A with a control volume USE scalings A Mid point Rule (Area A = D2) Node i Approximate with finite difference 3 possibilities are Backward in time (explicit) Forward in time (implicit) Central difference in time Crank Nicolson Where “new” indicates evaluation at time t = current + dt

  3. Consider implicit scheme Data structure + physics (same as steady state problem) Or rearranging in a form suitable for an iterative solution Old time OR So with previous steady state code on modifying the ai coeff and source bi We can arrive at a solution fro the value of the nodal T’s at time t+dt based on the known T’s at time t MATLAB CODE data coefficient—modified fro tran terms and new boundary conditions (Set dt And nodal T’s=0) for jtim=1:100 solve (For Tnew initial setting Tnew=T) (store Thist(itim) at 61) (set T=Tnew) end plot Thist HOMEWORK BY NEXT CLASS Do this I just need the plot handed in

  4. Now Consider the Explicit Case Or rearranging in a form suitable for an iterative solution NO EQUATION TO SOLVE--EXPLICIT But must choose Such that Solution strategy **Calculate the coefficients using the steady state code ** choose time step and calculate **Set T = 0 for i = 1:500 for i = 1:n %nodes % solve Eq(1)—essentially similar code to one it of solve code T=Tnew store Thist end end Code this also And compare Temp hist at Mid point With imp sol

More Related