How can i solve these equations in Matlab?

[koii123]

Equation 1:

Equation 2:

Equation 3:

Equation 4:

Equation 5:

I would like to solve

, (not the one with a star)
and i want to define values for p, η₀, η_r, θ₀, θ_r.
i have tried to solve them, but didn't work,
can someone please help and show me step by step?

 

[phyzguy]

What exactly are you trying to do? I count 10 unknowns (α, α*, p, η0, ηR, θ, θ0, S0, Z, β), and only 5 equations. So the system is underdetermined and there are an infinite number of possible solutions. You either need to fix some of the values or find more equations until the number of equations equals the number of unknowns. What exactly have you tried so far?

 

[koii123]

What exactly are you trying to do? I count 10 unknowns (α, α*, p, η0, ηR, θ, θ0, S0, Z, β), and only 5 equations. So the system is underdetermined and there are an infinite number of possible solutions. You either need to fix some of the values or find more equations until the number of equations equals the number of unknowns. What exactly have you tried so far?

Actually, i have values for p, η₀, η_r, θ₀, θ_r,
for example:
p=101325,
η₀=4.43,
η_r=0.181,
θ₀=313.15,
θ_r=373.15,
also, as you can see, it is possible to solve α , because these 5 equations can be combined into 1

 

[phyzguy]

OK, that makes more sense. So can you do the following?

(1) Solve equation 4 for the ratio β/S0.
(2) Divide equation 5 by S0 to get β/S0 on the LHS. Then plug the result from step 1 into this and solve this equation for Z.
(3) Take the result from step 2 and plug it into equation 3, then solve this equation for α.

Edit:

Actually, I see now that it is even simpler than that. You can combine equations 4 and 5 to give:

(1+5.1E-9*p)^Z = 1

Solve this for Z and plug it into equation 3 to give α.

 

[phyzguy]

Looking more at your equations. Equations 4 and 5 together imply that:

(1+5.1E-9*p)^Z = 1

Since p = 101325, (1+5.1E-9*p) = 1.0005, so this equation is only satisfied for Z = 0. Equation 3 then implies that α=0. Are you sure this is all correct, or am I missing something?