Solving a 4th degree energy balance

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

[Birdman]

Requires Symbolic Toolbox:

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

[Paneermeeuw]

Thanks! It returns 126 °C, which seems about right.

Answer 2

[Torsten]

help roots

Best wishes

Torsten.

[Paneermeeuw]

This one returns 129 °C which also seems right, thanks!

Answer 3

[ayman alkezza]

any one help me :

when running the code give me infinity results

-------------------------

for t=0:1800:36000

dt=1800 ;

QCBW=135.*(Ab).*(Tb-tw);

QLOSS=14.*(Ab).*(Tb-Ta);

Qcwg= hcwg.*Aw.*(tw-Tg);

Qrwg=hrwg.*Aw.*(tw-Tg);

Qe=hevwg.*Aw.*(tw-Tg);

Qcga= hcgo.*Ag.*(Tg-Ta);

Qrga= hrgoa.*Ag.*(Tg-Ta);

(s=dT/dt)---------------------------

s1=(((I.*Ab.*ab)-(QCBW-QLOSS))./(mb.*cpb));

s2=(((I.*Aw.*aw)+(QCBW-Qrwg-Qcwg-Qe))./(mw.*cpw));

s3=(((I.*Ag.*ag)+(Qcwg+Qrwg+Qe-Qcga-Qrga))./(mg.*cpg));

Tb=s1.*t;

tw=s2.*t;

Tg=s3.*t

end