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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:

    ti=0.0;
    tf=15.0;
    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
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