initial guessing - for mixed boundary condition

Question

N Nithya 2022-9-5

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1795190-initial-guessing-for-mixed-boundary-condition

回答： Sarthak 2023-9-13

f'''+(1/2)*f*f''+lamda*theta

theta''+pr*(1/2*f*theta'+f'*theta

with B.C f(eta) = 0,f'(eta) = delta*f''(eta) , theata(eta)=1+beta*theta'(eta) at eta = zero

f'(eta) = 1 ,theta(eta) = 0 as eta = infinity

close all

solinit = bvpinit(linspace(0,2),@exlinit );

options = bvpset('RelTol',1e-6);

sol = bvp4c(@convec,@bvp,solinit,options);

figure(1)

plot(sol.x,sol.y(4,:),'linewidth',1.5);

%plot(sol.x,sol.y(5,:),'--','linewidth',1.5);

hold on

function dy = convec(t,y)

lamda = 1;

Pr = 6.2;

dy(1) = y(2);

dy(2) = y(3);

dy(3) = -(1/2)*y(1)*y(3)+lamda*y(4);

dy(4) = y(5);

dy(5) = -(Pr)*(1/2*y(1)*y(5)+y(2)*y(4));

dy =[dy(1);dy(2);dy(3);dy(4);dy(5)];

end

function res = bvp(ya,yb)

delta = 0.5;

beta = 1;

res = [ya(1)-0

ya(2)-delta*ya(3)

yb(2)-1;

ya(4)-1-beta*ya(5);

yb(4)-0];

end

function v = exlinit(t)

v = [0

1

1-exp(-t)

1

exp(-t)];

end

the program is running but not getting correct one for example temperature profile ie y(4)

kindly give a suggestion for guessing a initial condition for the problem

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Torsten 2022-9-5

在 MATLAB Online 中打开

From your equations, it should be

dy(3) = -(1/2)*y(1)*y(3)-lamda*y(4);

instead of

dy(3) = -(1/2)*y(1)*y(3)+lamda*y(4);

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Answer 1

Sarthak 2023-9-13

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1795190-initial-guessing-for-mixed-boundary-condition#answer_1308786

在 MATLAB Online 中打开

Hi N Nithya,

I understand you are looking for a way of initial guessing, but I found something else in the code which might help.

The equation for dy(3) should be:

dy(3) = -(1/2)*y(1)*y(3) - lamda*y(4)

The original equation, dy(3) = -(1/2)y(1)y(3) + lamday(4), is incorrect because the term lamday(4) should be negative.

The negative sign in front of the term lamda*y(4) is important because it ensures that the derivative of dy(3) is always negative. This is necessary because dy(3) represents the rate of change of y(3), and the rate of change of y(3) should always be negative when y(3) is increasing.

Hope this solves your query.