Insert symbolic equation in another symbolic equation

Hello i have the equation eq5 that has been solved and is now only a function of y. I want now to insert this function (r) inside eq6 and solve that, but it gives me an error. How can i solve this?

eq5 = hw2*(q-r)==y;
r = solve(eq5,r);
eq6 = @(y) sigma*eps*((r^4)-T_inf^4)-y;
y0=0;
sol = fsolve(eq6,y0);

[KSSV]

Show us the full code.

[Mirko Rizzi]

this is the full code, i had to solve a 6 equation system (i have substitute the q used before with s in the cose)

Pr_g = (Cp_g*mu_g)/k_g;

hg = 0.023 * (k_g/((D(len-i+1))^1.8)) * (((4*m_dot_g)/(pi*mu_g))^0.8) * (Pr_g^0.33);

hw1 = kw1/tw1;

hw2 = kw2/tw2;

syms x y z p s r

eq1 = hg*(Tc-x)==y;

x = solve(eq1,x);

eq2 = hw1*(x-z)==y;

z = solve(eq2,z);

eq3 = p*(z-Tl)==y;

p = solve(eq3,p);

eq4 = p*(Tl-s)==y;

s = solve(eq4,s);

eq5 = hw2*(s-r)==y;

r = solve(eq5,r);

eq6 = @(y) sigma*eps*((r^4)-T_inf^4)-y;

y0=0;

q = fsolve(eq6,y0);

[Dyuman Joshi]

Your code is still incomplete, you need to give the values for variables.

Pr_g = (Cp_g*mu_g)/k_g;

Unrecognized function or variable 'Cp_g'.

    hg = 0.023 * (k_g/((D(len-i+1))^1.8)) * (((4*m_dot_g)/(pi*mu_g))^0.8) *        (Pr_g^0.33);
    hw1 = kw1/tw1;
    hw2 = kw2/tw2;
    syms x y z p s r
    eq1 = hg*(Tc-x)==y;
    x = solve(eq1,x);
    eq2 = hw1*(x-z)==y;
    z = solve(eq2,z);
    eq3 = p*(z-Tl)==y;
    p = solve(eq3,p);
    eq4 = p*(Tl-s)==y;
    s = solve(eq4,s);
    eq5 = hw2*(s-r)==y;
    r = solve(eq5,r)
    eq6 = @(y) sigma*eps*((r^4)-T_inf^4)-y
    y0=0;
    q = fsolve(eq6,y0);

[Mirko Rizzi]

there are files inside, i should share all the folder, just try to understand what i am doing, numbers are not necessary

[Mirko Rizzi]

i have a function r, which depend on y

i have another function where i want to insert r, so that the equation depends only on y, and solve this last equation to find y

[Dyuman Joshi]

Why not define eq6 as a symbolic expression like you have done for other eq and use solve?

[Mirko Rizzi]

if i use this:

% eq6 = sigma*eps*((r^4)-T_inf^4)==y;

% sol = solve(eq6,y)

it gives me a vector of 4 same elements:

root(z^4 - (148549786974450477987*z^3)/27487790694400 + (66201117630463850684060566839278314716507*z^2)/6044629098073145873530880000 - (25694677813792110401306682574502596589303194435085805665710978025618652510443*z)/2420199345095688424498763567867944239211734959652864000000 + 3804255296569717375581777916032849021112749976946199317897911767146631227587687/1141798154164767904846628775559596109106197299200000000, z, 1)

root(z^4 - (148549786974450477987*z^3)/27487790694400 + (66201117630463850684060566839278314716507*z^2)/6044629098073145873530880000 - (25694677813792110401306682574502596589303194435085805665710978025618652510443*z)/2420199345095688424498763567867944239211734959652864000000 + 3804255296569717375581777916032849021112749976946199317897911767146631227587687/1141798154164767904846628775559596109106197299200000000, z, 2)

root(z^4 - (148549786974450477987*z^3)/27487790694400 + (66201117630463850684060566839278314716507*z^2)/6044629098073145873530880000 - (25694677813792110401306682574502596589303194435085805665710978025618652510443*z)/2420199345095688424498763567867944239211734959652864000000 + 3804255296569717375581777916032849021112749976946199317897911767146631227587687/1141798154164767904846628775559596109106197299200000000, z, 3)

root(z^4 - (148549786974450477987*z^3)/27487790694400 + (66201117630463850684060566839278314716507*z^2)/6044629098073145873530880000 - (25694677813792110401306682574502596589303194435085805665710978025618652510443*z)/2420199345095688424498763567867944239211734959652864000000 + 3804255296569717375581777916032849021112749976946199317897911767146631227587687/1141798154164767904846628775559596109106197299200000000, z, 4)

[Mirko Rizzi]

if i view the entire function r, copy what it is written and substitute it inside works fine, but as it is in the cycle i can't copy and paste manually at every passage

Answer 1

[Dyuman Joshi]

Use vpa to get numerical values. Convert them to double() if you need the values to be in numeric data type.

syms z
%first root, copied from above
sol1=vpa(root(z^4 - (148549786974450477987*z^3)/27487790694400 + (66201117630463850684060566839278314716507*z^2)/6044629098073145873530880000 - (25694677813792110401306682574502596589303194435085805665710978025618652510443*z)/2420199345095688424498763567867944239211734959652864000000 + 3804255296569717375581777916032849021112749976946199317897911767146631227587687/1141798154164767904846628775559596109106197299200000000, z, 1))

sol1 = 

549277.87721495737433337758873113

double(sol1)

ans = 5.4928e+05

[Mirko Rizzi]

thanks! but if i solve every solution that i have, i get different values, why? they are all the same

[Dyuman Joshi]

They look same because the syntax of the output above is same except for the number of root.

Since solve() was unable to find the explicit value, it returns the solution as -

root(equation,variable,1)
root(equation,variable,2)
root(equation,variable,3)
root(equation,variable,4)

You can see at the end of the each expression there's a number, denoting which root it refers to. The value of roots will, of course, depend upon the coefficients.s

[Mirko Rizzi]

thanks for explaining me!