Solve equation including parameters dependent on main variable

% Temperature
T_C=300;
T_E=linspace(0,300);
tau=T_C./T_E;

% Phase angle
alpha=deg2rad(90);

% Dead-volume ratio
X=0;

% Heat lifted
Q_max=0.085377;

Analysis

% Reduced dead volume
S=(2*X*tau)./(tau+1);

% Heat lifted and Work done
A=sqrt(tau.^2 + k^2 + 2*tau*k*cos(alpha));
B=tau + k + 2*S;
delta=A./B;
theta=(atan((k*sin(alpha))./(tau + k*cos(alpha))));

For range of values of tau, I want to have 'k'. But the problem is there are variables in Q_max equation such as delta and theta which are dependant on k by themselves. What should I do?

ratio=solve('Q_max==(pi*sqrt(1-delta).*delta.*sin(theta))./((1+k).*sqrt(1+delta).*(1+sqrt(1-delta.^2)))','k');

Answer 1

[Yongjian Feng]

1. k shall be a symbol, once you do this before it is used, then this will take care of the dependency of delta and theta.

syms k;

2. solve takes function and symbol(s), not char array

ratio=solve(Q_max==(pi*sqrt(1-delta).*delta.*sin(theta))./((1+k).*sqrt(1+delta).*(1+sqrt(1-delta.^2))), k);

3. There are some issues of your script, for example, T_E starts with 0, so tau = T_C/T_E is infinity. You might need to clean those up.