How can I solve an equation with more than one variable?

Hi,

I have constants which are

G=44*10^3;

b=2.95e-10;

tao=0.02;

k=1.38e-23;

delta_fo=0.5;

epsilon_ref=10^6;

q=1.8;

p=0.3;

And also I have these variables

epsilon_p=[0.001,0.01,0.1,1,10]

T=[773,873,973,1073,1173]

My equation is

sigma_t=tao*G*(1-(((k*T)/(delta_fo*G*b^3*log(epsilon_ref/epsilon_p)))^(1/q))^(1/p))

I want to solve this equation for example epsilon_p=0.001 when T=773.

But can't do anything.Hope anyone can help me.

Answer 1

[Stephan]

You can solve for all cases in one calculation and save teh result as a matrix by using a function handle:

G=44*10^3;
b=2.95e-10;
tao=0.02;
k=1.38e-23;
delta_fo=0.5;
epsilon_ref=10^6;
q=1.8;
p=0.3;
epsilon_p=[0.001,0.01,0.1,1,10]
T=[773,873,973,1073,1173]
sigma_t= @(epsilon_p,T) tao*G*(1-(((k*T')./(delta_fo*G*b^3*log(epsilon_ref./epsilon_p))).^(1/q)).^(1/p))

sol = sigma_t(epsilon_p,T)

result:

sol =

   1.0e+09 *

   -0.2663   -0.3313   -0.4242   -0.5643   -0.7910
   -0.3336   -0.4150   -0.5314   -0.7069   -0.9908
   -0.4078   -0.5072   -0.6495   -0.8641   -1.2112
   -0.4888   -0.6080   -0.7786   -1.0358   -1.4518
   -0.5765   -0.7171   -0.9182   -1.2216   -1.7122

This works because of vectorization - on of the things that make Matlab great. Every row is one value of T and all the values of epsilon. Every column stands for changing T and the correspondig entry in epsilon:

>> Line3 = sigma_t(epsilon_p,T(3))

Line3 =

   1.0e+09 *

   -0.4078   -0.5072   -0.6495   -0.8641   -1.2112

[Aybike Elverdi]

Thanks a lot!