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Question: how to solve a system of equation and get array of answers

Question:how to solve a system of equation and get array of answers

m_magooda 20 Maple
solve syntax
April 18 2018
0

Hello,

I've a big amount of equations, i tried to solve them and get the answer as an array but for some reason it's not working, is solve the right one for this or what?

thank you

the 2 files aren't related, but both contain a system of equation i tried to solve but without avail

Advheat-ex53.mw

Advheat-ex54.mw
 

> 

restart
> 

k := 1.4:
> 

eqs := {T[4]+T[4]+T[8]+T[8]-4*T[5] = 0, (1/2)*hi*`Δx`*(Ti-T[1])+(1/2)*k*`Δy`*(T[2]-T[1])/`Δx`+(1/2)*k*`Δx`*(T[3]-T[1])/`Δy` = 0, (1/2)*k*`Δy`*(T[1]-T[2])/`Δx`+(1/2)*hi*`Δx`*(Ti-T[2])+k*`Δx`*(T[4]-T[2])/`Δy` = 0, (1/2)*k*`Δy`*(T[8]-T[9])/`Δx`+(1/2)*ho*`Δx`*(To-T[9])+(1/2)*epsilon*sigma*`Δx`*(Ts^4-T[9]^4) = 0, T[4]+T[1]+T[4]+T[6]-4*T[3] = 0, (1/2)*k*`Δx`*(T[3]-T[6])/`Δy`+(1/2)*k*`Δy`*(T[7]-T[6])/`Δx`+(1/2)*ho*`Δx`*(To-T[6])+(1/2)*epsilon*sigma*`Δx`*(Ts^4-T[6]^4) = 0, k*`Δx`*(T[5]-T[8])/`Δy`+(1/2)*k*`Δy`*(T[9]-T[8])/`Δx`+ho*`Δx`*(To-T[8])+epsilon*sigma*`Δx`*(Ts^4-T[8]^4) = 0, T[3]+T[2]+T[5]+T[7]-4*T[4] = 0, (1/2)*k*`Δy`*(T[6]-T[7])/`Δx`+k*`Δx`*(T[4]-T[7])/`Δy`+(1/2)*k*`Δy`*(T[8]-T[7])/`Δx`+ho*`Δx`*(To-T[7])+epsilon*sigma*`Δx`*(Ts^4-T[7]^4) = 0}

{2*T[4]+2*T[8]-4*T[5] = 0, 35*`Δx`*(573.15-T[1])+.7000000000*`Δy`*(T[2]-T[1])/`Δx`+.7000000000*`Δx`*(T[3]-T[1])/`Δy` = 0, .7000000000*`Δy`*(T[1]-T[2])/`Δx`+35*`Δx`*(573.15-T[2])+1.4*`Δx`*(T[4]-T[2])/`Δy` = 0, .7000000000*`Δy`*(T[8]-T[9])/`Δx`+146.5750000*`Δx`*(20-T[9])+.4500000000*sigma*`Δx`*(-T[9]^4+4569760000) = 0, 2*T[4]+T[1]+T[6]-4*T[3] = 0, .7000000000*`Δx`*(T[3]-T[6])/`Δy`+.7000000000*`Δy`*(T[7]-T[6])/`Δx`+146.5750000*`Δx`*(20-T[6])+.4500000000*sigma*`Δx`*(-T[6]^4+4569760000) = 0, 1.4*`Δx`*(T[5]-T[8])/`Δy`+.7000000000*`Δy`*(T[9]-T[8])/`Δx`+293.15*`Δx`*(20-T[8])+.9*sigma*`Δx`*(-T[8]^4+4569760000) = 0, T[3]+T[2]+T[5]+T[7]-4*T[4] = 0, .7000000000*`Δy`*(T[6]-T[7])/`Δx`+1.4*`Δx`*(T[4]-T[7])/`Δy`+.7000000000*`Δy`*(T[8]-T[7])/`Δx`+293.15*`Δx`*(20-T[7])+.9*sigma*`Δx`*(-T[7]^4+4569760000) = 0}

 (1)
> 

T := Array(1 .. 9, `~`[rhs](convert(solve([eqs]), list)))

Error, invalid input: solve expects its 1st argument, eqs, to be of type {`and`, `not`, `or`, algebraic, relation(algebraic), ({list, set})({`and`, `not`, `or`, algebraic, relation(algebraic)})}, but received [{2*T[4]+2*T[8]-4*T[5] = 0, 35*`Δx`*(573.15-T[1])+.7000000000*`Δy`*(T[2]-T[1])/`Δx`+.7000000000*`Δx`*(T[3]-T[1])/`Δy` = 0, .7000000000*`Δy`*(T[1]-T[2])/`Δx`+35*`Δx`*(573.15-T[2])+1.4*`Δx`*(T[4]-T[2])/`Δy` = 0, .7000000000*`Δy`*(T[8]-T[9])/`Δx`+146.5750000*`Δx`*(20-T[9])+.4500000000*sigma*`Δx`*(-T[9]^4+4569760000) = 0, 2*T[4]+T[1]+T[6]-4*T[3] = 0, .700000...

  
> 

``


 

Download Advheat-ex54.mw
 

> 

restart:
> 

for i from 10 to 15 do T[i] := 90 end do:
> 

`Δx` := 1.2*(1/100):
> 

Qr := 5000:
> 

eqs := eqs, (1/2)*h*`Δx`*(Tinf-T[1])+k*`Δy`*(T[2]-T[1])/(2*`Δx`)+k*`Δx`*(T[4]-T[1])/(2*`Δy`)+(1/4)*g*`Δx`*`Δy` = 0; h*`Δx`*(Tinf-T[2])+(1/2)*k*`Δy`*(T[3]-T[2])/`Δx`+k*`Δx`*(T[5]-T[2])/`Δy`+(1/2)*k*`Δy`*(T[1]-T[2])/`Δx`+(1/2)*g*`Δx`*`Δy` = 0; h*((1/2)*`Δx`+(1/2)*`Δy`)*(Tinf-T[3])+k*`Δx`*(T[6]-T[3])/(2*`Δy`)+k*`Δy`*(T[2]-T[3])/(2*`Δx`)+(1/4)*g*`Δx`*`Δy` = 0; 2*T[5]+T[1]+T[10]-4*T[4]+g*`Δx`*`Δy`/k = 0; T[2]+T[4]-4*T[5]+T[6]+T[11]+g*`Δx`*`Δy`/k = 0; h*((1/2)*`Δx`+(1/2)*`Δy`)*(Tinf-T[6])+(1/2)*k*`Δy`*(T[7]-T[6])/`Δx`+k*`Δx`*(T[12]-T[6])/`Δy`+k*`Δy`*(T[5]-T[6])/`Δx`+(1/2)*k*`Δx`*(T[3]-T[6])/`Δy`+3*g*`Δx`*`Δy`*(1/4) = 0; h*`Δx`*(Tinf-T[7])+(1/2)*k*`Δy`*(T[8]-T[7])/`Δx`+k*`Δx`*(T[13]-T[7])/`Δy`+(1/2)*k*`Δy`*(T[6]-T[7])/`Δx`+(1/2)*g*`Δx`*`Δy` = 0; h*`Δx`*(Tinf-T[8])+(1/2)*k*`Δy`*(T[9]-T[8])/`Δx`+k*`Δx`*(T[14]-T[8])/`Δy`+(1/2)*k*`Δy`*(T[7]-T[8])/`Δx`+(1/2)*g*`Δx`*`Δy` = 0; h*`Δx`*(Tinf-T[9])+(1/2)*Qr*`Δy`+(1/2)*k*`Δx`*(T[15]-T[9])/`Δy`+k*`Δy`*(T[8]-T[9])/(2*`Δx`)+(1/2)*g*`Δx`*`Δy` = 0


 

Download Advheat-ex53.mw

 

 
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