Solving a 4th degree energy balance

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Paneermeeuw
Paneermeeuw 2018-1-5
编辑： ayman alkezza 2019-7-13
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.

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采纳的回答

Birdman
Birdman 2018-1-5
编辑：Birdman 2018-1-5
Requires Symbolic Toolbox:
syms T1
eq=T1.^4 + 1.8e8*T1 - 2.3e10 == 0
%4 solutions
sol=vpasolve(eq)
%real one
sol=sol(2)

更多回答（2 个）

Torsten
Torsten 2018-1-5
help roots
Best wishes
Torsten.
ayman alkezza
ayman alkezza 2019-7-13
编辑：ayman alkezza 2019-7-13
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

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