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m_magooda

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4 years, 186 days

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These are replies submitted by m_magooda

@mmcdara 

yes, it's a heat equation using finite difference method

I wanted to show the role of many parameters, but it's not pedagogical so i guess fsolve would do just fine

now I realize how mistaken i was regarding the order of equations, it would take like forever and no added value would be achieved

 

thank you again for your assistance, much appreciated

@mmcdara 

Thank you for the assistance, that was helpful

the 53 file worked just fine, i had problem with defining eqs as you mentioned

 

regarding the 54 file, I tried plugging values to anything that isn't T[1..9] so now I have a system of 9 equations with 9 T values

yet maple freezes? is it that hard with only couple of power 4 terms?

Fsolve works good, but I'm having a problem that may sound stupid ... how do i know which T is which in the array, does it use the numbering i used initially in defining the equations?

 

thank you
 

restart

k := 1.4:

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

{2*T[4]+2*T[8]-4*T[5] = 0, 2006.025000-4.900000000*T[1]+.7000000000*T[2]+.7000000000*T[3] = 0, .7000000000*T[1]-5.600000000*T[2]+2006.025000+1.400000000*T[4] = 0, 2*T[4]+T[1]+T[6]-4*T[3] = 0, .7000000000*T[8]-15.35750000*T[9]+304.8097426-0.2551500000e-8*T[9]^4 = 0, T[3]+T[2]+T[5]+T[7]-4*T[4] = 0, .7000000000*T[3]-16.05750000*T[6]+.7000000000*T[7]+304.8097426-0.2551500000e-8*T[6]^4 = 0, .7000000000*T[6]-32.11500000*T[7]+1.400000000*T[4]+.7000000000*T[8]+609.6194853-0.5103000000e-8*T[7]^4 = 0, .7000000000*T[7]-32.11500000*T[8]+1.400000000*T[5]+.7000000000*T[9]+609.6194853-0.5103000000e-8*T[8]^4 = 0}

(1)

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

T := Matrix(1, 9, {(1, 1) = 512.5292887, (1, 2) = 476.8840235, (1, 3) = 245.0709971, (1, 4) = 218.3964498, (1, 5) = 121.8993340, (1, 6) = 30.96180022, (1, 7) = 29.73144451, (1, 8) = 25.40221815, (1, 9) = 21.00542397})

(2)

T

Matrix(1, 9, {(1, 1) = 512.5292887, (1, 2) = 476.8840235, (1, 3) = 245.0709971, (1, 4) = 218.3964498, (1, 5) = 121.8993340, (1, 6) = 30.96180022, (1, 7) = 29.73144451, (1, 8) = 25.40221815, (1, 9) = 21.00542397})

(3)

``


 

Download Advheat-ex54.mw

 

Advheat-ex54.mw

@tomleslie Thank you, that did the trick

 

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