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Student Support Forum: 'couple ode NDSolve (compressible boundary layer)' topicStudent Support Forum > General > "couple ode NDSolve (compressible boundary layer)"

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Ayden
03/30/12 04:26am

Hi, just wondering if someone can help me solve this problem. i am trying to solve for the compressible boundary layer. I've tried using NDSolve as well as the shooting method but have been unsuccessful. Below is my code

h = 301350; P = 1; v = 1.4; M = 2.9; S = 120; R = 287; T = 300; c = \
1004.5; sol =
First[NDSolve[{f'''[x] ==
1/g[x]^(1/2)*((h + c*S)/(g[x]*h +
c*S)) (-(g'[
x]*((T/S) +
1)*(1 - (T/S)*g[x])/(2*
g[x]^(1/2)*(g[x]*(T/S) + 1)^2)) f''[x] - f[x]*f''[x]),
g''[x] ==
1/g[x]^(1/2)*((h + c*S)/(g[x]*h + c*S)) - P*f[x]*g'[x] -
P (g[x]^(1/2)*((h + c*S)/(g[x]*h + c*S)) (v - 1) M^2 f''[
x]^2 - (g'[
x]*((T/S) +
1)*(1 - (T/S)*g[x])/(2*
g[x]^(1/2)*(g[x]*(T/S) + 1)^2)) g'[x]), f[0] == 0,
f'[0] == 0, g'[0] == 0, f'[1000] == 1, g[1000] == 1}, f[x], g[x],
Method -> {"Shooting",
"StartingInitialConditions" -> {f[0] == f'[0] == g'[0] == 0,
f''[0] == 0.5, g[0] == 0.5}}]]

This gives me the error "The independent variable g appears in the head of the expression \
g[x]. The independent variables should always be arguments"

My other approach is below;
h = 301350; P = 1; v = 1.4; M = 0.5; S = 120; R = 287; T = 300; c = \
1004.5; sol =
NDSolve[{
f'''[x] ==
1/g[x]^(1/2)*((h + c*S)/(g[x]*h +
c*S)) (-(g'[
x]*((T/S) +
1)*(1 - (T/S)*g[x])/(2*g[x]^(1/2)*(g[x]*(T/S) + 1)^2)) f''[
x] - f[x] f''[x]),
g''[x] ==
1/g[x]^(1/2)*((h + c*S)/(g[x]*h + c*S)) - P*f[x]*g'[x] -
P (g[x]^(1/2)*((h + c*S)/(g[x]*h + c*S)) (v - 1) M^2 f''[
x]^2 - (g'[
x]*((T/S) +
1)*(1 - (T/S)*g[x])/(2*
g[x]^(1/2)*(g[x]*(T/S) + 1)^2)) g'[x]), f[0] == 0,
f'[0] == 0, f'[10] == 1, g[10] == 1, g'[0] == 0}, {f, g}, {x, 0,
10}]

This one gives me several errors regarding infinity and indeterminate expressions.

My notebook file is attached for your reference. I was able to solve for the incompressible blasius solution, byt this coupled set of odes is proving to be challenging.

Hope someone can help. Thank you in advance





Attachment: boundary_layer.nb, URL: ,
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