MATLAB: Solving a 4th degree energy balance

Question

Hi!

For my graduation I am working on a energy balance. It looks like this:

Heat flow from radiation (sun) = heat flow from convection + heat flow from radiation(emission)

Using the formulas from thermodynamic's and a known heat flux from the sun, I get this:

α x A x Q = αc x A x (T1-T2) + ε x σ x A x T1^4

All values except T1 are known which leaves me with the next equation:

T1^4 + 1,8E8 T1 - 2,3E10 = 0

Can I calculate this with MATLAB? And if so, how do I approach this problem?

Thanks.

Answer 1

Requires Symbolic Toolbox:

syms T1
eq=T1.^4 + 1.8e8*T1 - 2.3e10 == 0
%4 solutions
sol=vpasolve(eq)
%real one
sol=sol(2)