Hi, I want to solve a equation for a variable. I am not able to figure out which command should I use to solve it and how.

The problem is as follows

 tauc*alp_g*G*As + Skyemi*eps_g*sig*As*Tsky.^4 - eps_g*sig*As*Tg.^4 - ha*As*(Tg - Tamb) + (T2 - Tg)/((delxr)/(1/(hi*As)+(kroof*As)))

I want to solve for the variable Tg.

Answer 1

[Walter Roberson]

If you have the symbolic toolbox then you can

syms Tg

and then define the equation and use solve()

Otherwise you can do some minor algebra to expand the equation into a polynomial, and write out the terms from largest to smallest, and use roots() to get numeric solutions.

Note: there will be four solutions but we do not have enough information to know if they will all be real-valued

[Dhruv Sangal]

Yeah solve function does gives me solution, but it gives me values in form of real and imaginary both, I want in real only since Tg is temperature. Moreover it needs to run for 24 iteration with lot of other parameters involved in the mentioned equation uses the value of Tg at previous time step. So I am not sure how to do that.

[Dhruv Sangal]

For 1st iteration I have the value for Tg

[Walter Roberson]

Use

   syms Tg nonnegative

Using the previous value would be useful if you were doing a numeric solution using fsolve() or fzero(), but you do not need to use those.

Direct numeric approach:

all_Tg = roots( [As^2*delxr*eps_g*hi*sig, 0, 0, 1+hi*(delxr*ha+kroof)*As^2, -hi*((Skyemi*Tsky^4*eps_g*sig+G*alp_g*tauc+Tamb*ha)*delxr+kroof*T2)*As^2-T2] );
Tg = all_Tg( imag(all_Tg) == 0 & real(all_Tg) >= 0 );