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

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M.Rameswari Sudha on 8 Apr 2024
Answered: Manikanta Aditya on 9 Apr 2024
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)
##### 3 CommentsShow 1 older commentHide 1 older comment
Manikanta Aditya on 9 Apr 2024
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 on 9 Apr 2024
Thank you. Now, I understand the mistake. I got the answer.

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### Accepted Answer

Manikanta Aditya on 9 Apr 2024
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
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.
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