1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Using ode45 to solve Vel. and Temp. profiles

  1. Apr 10, 2007 #1
    1. The problem statement, all variables and given/known data
    Find the velocity and temperature profiles for stagnation point flow (m=1) for various values of Pr (Pr=0.6,1,1.5,5,10)

    Show that δ/δT ~Pr^0.4 by calculating δ and δT with 99% recovery of free stream velocity and temperature profiles, respectively.

    Plot θ'(0) vs. Pr and compare against θ'(0)=0.5704Pr^0.4.

    Also determine Cf(x) and Nux in terms of Rex and Pr.

    Extend these results for the mass transfer for Shx. Where the Reynold number based on x is defined as Rex=U(x)x/v.

    2. Relevant equations
    Blasius Equation: f''' =1/2*f*f''=0
    Energy Equation: 2θ''+Pr*f*θ'=0

    Boundary Conditions:
    At the surface (η=0):
    f ' =0, f=0
    θ=0 and Φ=0

    Outside Boundary Layer:
    (y->infin., η->infin.):
    f ' -> 1,
    θ->1 and Φ->1.

    3. The attempt at a solution

    Can anyone assist me in the findings of the velocity and temp. profiles for stagnation point flow (m=1) for Varoius values of Pr (.6,1,1.5,5,10). At this moment I am using Matlab's ode45 to solve this problem along with applying the Blasius Eqn and Energy Eqn. I have been reading on the use of ode45 and I think I know what I need to do, but I am not sure how to incorporate the above equations along with the B.C.. For this problem I might need to apply one only B.C., which would be the conditions at the surface.

    Can someone please suggest any info., that would be great. Below is what I have started to solve the first part of the problem.

    so far this is what I have in my M-file - this is the main part of the code:

    tintval=[ti tf];
    bcinit=[0.0 0.0 0.33206];

    [t,y]= ode45(@stagnation,tintval,bcinit);

    %t=the scalar time
    %y=the column vector
    %ode45 is the solver
    %@rigid is the function handle calling function
    %[0.0 15.0] is the time to be evaluated from ti to tf
    %[0.0....etc] is the initial conditions

    this next part is the function that is being called by ode45:

    function df=stagnation(t,f)

    dfdt = [

    Of course it is not much, but that is why I need some help. Thank you
  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted