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 Author Comment/Response 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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