how to solve the below transcendental equation for the given data?

Question

M.Rameswari Sudha 2024-4-8

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2104226-how-to-solve-the-below-transcendental-equation-for-the-given-data

回答： Manikanta Aditya 2024-4-9

采纳的回答： Manikanta Aditya

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format compact

syms T t0

lambda=600; b=3;

theta=0.02;

c=5;

k=250;

h=1.75;

p=50;

M=.12;

Id=0.003;

TC=(k/T)+(c*lambda)+((lambda*(c*theta+h)*(exp(theta*t0)-theta*t0-1))/(T*(theta)^2))+((lambda*b*(T-t0)^2)/(2*T))+((lambda*p*M^2*Id)/(2*T));

dTCdt0=diff(TC,t0);

dTCdT=diff(TC,T);

[T,t0]=solve(dTCdt0,dTCdT)

Warning: Unable to solve symbolically. Returning a numeric solution using vpasolve.

T =

0.8526169358775188513228900752894

t0 =

0.5263315087626859744339029312836

t0=subs(t0);

digits(3)

t0=vpa(t0)

t0 =

0.526

T=subs(T);

T=vpa(T)

T =

0.853

TC=subs(TC);

digits(3)

TC=vpa(TC);

TC=round(TC)

TC =

3587

%z=sqrt((2*k*(h+c*theta)*b)/(b+h+(c*theta)))*(sqrt(3800)-137.816)

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Manikanta Aditya 2024-4-9

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Hi @M.Rameswari Sudha,

The issue you're facing with the code not working consistently is likely due to the symbolic engine being reset or cleared between runs. This can happen if you're running the code in different sessions or if some other operation clears the symbolic engine's state.

To ensure consistent behavior, you could try encapsulating the entire code in a function and calling that function each time you want to execute it. This way, the symbolic engine's state is reset at the beginning of each function call.

Here's an example of how you could structure the code as a function:

function [T, t0, TC] = solve_transcendental_equation()
    syms T t0
    lambda = 600; b = 3;
    theta = 0.02;
    c = 5;
    k = 250;
    h = 1.75;
    p = 50;
    M = 0.12;
    Id = 0.003;
    TC = (k/T) + (c*lambda) + ((lambda*(c*theta+h)*(exp(theta*t0)-theta*t0-1))/(T*(theta)^2)) + ((lambda*b*(T-t0)^2)/(2*T)) + ((lambda*p*M^2*Id)/(2*T));
    dTCdt0 = diff(TC, t0);
    dTCdT = diff(TC, T);
    [T_sol, t0_sol] = vpasolve(dTCdt0, dTCdT, [T, t0]);
    T = double(T_sol);
    t0 = double(t0_sol);
    TC = subs(TC);
    digits(3);
    TC = vpa(TC);
    TC = round(TC);
end

You can then call this function as many times as you need, and it should provide consistent results:

[T, t0, TC] = solve_transcendental_equation()

I hope this helps, if this helps, let me know I will post as answer, you can accept it to make it more helpful.

M.Rameswari Sudha 2024-4-9

Hi@Manikanta Aditya,

Thank you. Now, I understand the mistake. I got the answer.

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Answer 1

Manikanta Aditya 2024-4-9

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2104226-how-to-solve-the-below-transcendental-equation-for-the-given-data#answer_1438641

在 MATLAB Online 中打开

Hi,

The issue you're facing with the code not working consistently is likely due to the symbolic engine being reset or cleared between runs. This can happen if you're running the code in different sessions or if some other operation clears the symbolic engine's state.

To ensure consistent behavior, you could try encapsulating the entire code in a function and calling that function each time you want to execute it. This way, the symbolic engine's state is reset at the beginning of each function call.

Here's an example of how you could structure the code as a function:

function [T, t0, TC] = solve_transcendental_equation()
syms T t0
lambda = 600; b = 3;
theta = 0.02;
c = 5;
k = 250;
h = 1.75;
p = 50;
M = 0.12;
Id = 0.003;
TC = (k/T) + (c*lambda) + ((lambda*(c*theta+h)*(exp(theta*t0)-theta*t0-1))/(T*(theta)^2)) + ((lambda*b*(T-t0)^2)/(2*T)) + ((lambda*p*M^2*Id)/(2*T));
dTCdt0 = diff(TC, t0);
dTCdT = diff(TC, T);
[T_sol, t0_sol] = vpasolve(dTCdt0, dTCdT, [T, t0]);
T = double(T_sol);
t0 = double(t0_sol);
TC = subs(TC);
digits(3);
TC = vpa(TC);
TC = round(TC);
end