Velocity and Temp. profiles for stagnation point (m=1)

[mejia198021]

Hi,

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 (f''' +1/2f*f''=0) and Energy Eqn. (2*theta''+Pr*f*theta'=0). 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. that are f'=0, f=0, theta=o and phi=0.

Can someone please suggest any info., that would be great.

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

 

[jvicens]

for any input.

Hello,

It seems like you are working on a very interesting problem. Stagnation point flow is a classic problem in fluid mechanics and it is great that you are using MATLAB to solve it. Incorporating the Blasius equation and energy equation into your code is definitely the right approach.

To incorporate the boundary conditions of f'=0, f=0, theta=0, and phi=0, you can add them as additional equations in your function file. For example, your function file could look like this:

function df = stagnation(t,f)

dfdt = [f(2); %this is f'
-f(1)*f(3); %this is f''
f(3); %this is theta'
-2*f(3)/Pr*f(1)]; %this is theta''

%add the boundary conditions
df(1) = f(2); %f' = 0
df(2) = f(1); %f = 0
df(3) = f(3); %theta = 0
df(4) = f(4); %phi = 0

You can also add the conditions directly in the ode45 function call, like this:

[t,y] = ode45(@stagnation,tintval,[0.0 0.0 0.33206 0.0]);

This will set the initial conditions for f', f, theta, and phi to the values you specified.

I hope this helps. Good luck with your project!

 

[tacman]

for your time.Hi,

I am not an expert in this particular field, but I can offer some general advice. It looks like you are on the right track with using ode45 and incorporating the Blasius and Energy equations. In order to incorporate the boundary conditions, you can use the "events" option in ode45 to specify when the boundary conditions should be satisfied. You can do this by defining a function that evaluates the boundary conditions at each time step and then use that function in the "events" option of ode45.

As for the different values of Pr, you can create a loop that runs ode45 for each value of Pr and stores the results in separate arrays. This will allow you to plot the velocity and temperature profiles for each value of Pr.

Additionally, it may be helpful to consult with a subject matter expert or do some research on similar problems to gain a better understanding of the equations and how to incorporate them into your code.

I hope this helps and good luck with your project!