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Suryakanth

Mr. Surya S

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again error...

Suryakanth 5
November 12 2023
0 0

@Rouben Rostamian  

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restart
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with(PDEtools); with(plots)
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inf := 10
> 

NULL
> 

deltaB := .5; Ma := .5; Lam := 2; Pr := .71; Nm := .5; Nr := .5; Nt := .5; Nb := .5; Ec := .5; Sc := .6; Kr := .5; betat := .5; Rd := .5
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NULL
> 

OdeSys := {diff(f(xi, eta), eta)-q1(xi, eta) = 0, diff(q1(xi, eta), eta)-q2(xi, eta) = 0, diff(q3(xi, eta), eta)-q4(xi, eta) = 0, diff(q5(xi, eta), eta)-q6(xi, eta) = 0, f(xi, eta)*q6(xi, eta)+(diff(q6(xi, eta), eta)+Nt*(diff(q4(xi, eta), eta))/Nb)/Sc-Kr*q5(xi, eta)-xi*(q1(xi, eta)*(diff(q5(xi, eta), xi))-q6(xi, eta)*(diff(f(xi, eta), xi))) = 0, q2(xi, eta)*f(xi, eta)-xi*(q1(xi, eta)*(diff(q1(xi, eta), xi))-q2(xi, eta)*(diff(f(xi, eta), xi)))-q1(xi, eta)^2+sin(xi)*cos(xi)/xi+(diff(q2(xi, eta), eta))*(1+deltaA)-(deltaA*deltaB*xi*xi)*q2(xi, eta)^2*(diff(q2(xi, eta), eta))-Ma*(q1(xi, eta)-sin(xi)/xi)+Lam*sin(xi)*(q3(xi, eta)+Nm*q3(xi, eta)*q3(xi, eta)-Nr*q5(xi, eta))/xi = 0, (1+4*Rd*(1/3))*(diff(q4(xi, eta), eta))/Pr+Nb*q4(xi, eta)*q6(xi, eta)+f(xi, eta)*q4(xi, eta)+(Ma*Ec*xi*xi)*(q1(xi, eta)-sin(xi)/xi)^2+Nt*q4(xi, eta)^2+((1+deltaA)*Ec*xi*xi)*q2(xi, eta)^2-(1/3)*Ec*deltaA*deltaB*xi^4*q2(xi, eta)^4-xi*(q1(xi, eta)*(diff(q3(xi, eta), xi))-q4(xi, eta)*(diff(f(xi, eta), xi))) = 0}; Cond := {f(0, eta) = 0, f(xi, 0) = 0, q1(0, eta) = 0, q1(xi, 0) = 0, q1(xi, inf) = sin(xi)/xi, q3(0, eta) = 0, q3(xi, inf) = 0, q4(xi, 0) = (q3(xi, 0)-1)*betat, q5(0, eta) = 0, q5(xi, 0) = 1, q5(xi, inf) = 0}
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NULL
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colour := [red, green, blue, black]
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deltaAVals := [.2, .4, .6, .8]
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NULL
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for j to numelems(deltaAVals) do Ans[j] := pdsolve((eval({Cond, OdeSys}, deltaA = deltaAVals[j]))[], numeric) end do

Error, (in pdsolve/numeric/match_PDEs_BCs) cannot handle systems with multiple PDE describing the time dependence of the same dependent variable, or having no time dependence

  
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NULL

Download first_order_pde.mw

@Carl Love Thank you But what are the ...

Suryakanth 5
November 09 2023
0 0

@Carl Love

Thank you

But what are the changes need to do in this plot sir.

I m not that much familier in this. 

By refering the link...

Suryakanth 5
November 08 2023
0 0

by using this post Pde i have given my equation please check the mistakes and reply

I m waiting for the reply.

Daily i m checking the same post. Please do help for this.

Thank you

entropy plots...

Suryakanth 5
November 08 2023
0 0

 

please check my question and rectify my errors.

i have posted a new question that is automatically deleted

> 

restart
> 

with(PDEtools); with(plots)
> 

inf := 10
> 

NULL
> 

deltaB := .5; Lam := .5; Pr := .71; Nm := .4; Nr := .4; Nt := .3; Nb := .4; Ec := .3; Sc := .6; Kr := .3; betat := .8; Rd := 2; deltaA := .8
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alphac := .1; `αt` := .1; Lt := .1; Br := .1
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``

``

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``
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``
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OdeSys := {f(xi, eta)*(diff(Phi(xi, eta), eta))+(diff(Phi(xi, eta), eta, eta)+Nt*(diff(Theta(xi, eta), eta, eta))/Nb)/Sc-Kr*Phi(xi, eta)-xi*((diff(f(xi, eta), eta))*(diff(Phi(xi, eta), xi))-(diff(Phi(xi, eta), eta))*(diff(f(xi, eta), xi))), (diff(f(xi, eta), eta, eta))*f(xi, eta)-xi*((diff(f(xi, eta), eta))*(diff(diff(f(xi, eta), eta), xi))-(diff(f(xi, eta), eta, eta))*(diff(f(xi, eta), xi)))-(diff(f(xi, eta), eta))^2+sin(xi)*cos(xi)/xi+(diff(f(xi, eta), eta, eta, eta))*(1+deltaA)-(deltaA*deltaB*xi*xi)*(diff(f(xi, eta), eta, eta))^2*(diff(f(xi, eta), eta, eta, eta))-Ma*(diff(f(xi, eta), eta)-sin(xi)/xi)+Lam*sin(xi)*(Theta(xi, eta)+Nm*Theta(xi, eta)*Theta(xi, eta)-Nr*Phi(xi, eta))/xi, (1+4*Rd*(1/3))*(diff(Theta(xi, eta), eta, eta))/Pr+Nb*(diff(Theta(xi, eta), eta))*(diff(Phi(xi, eta), eta))+f(xi, eta)*(diff(Theta(xi, eta), eta))+(Ma*Ec*xi*xi)*(diff(f(xi, eta), eta)-sin(xi)/xi)^2+Nt*(diff(Theta(xi, eta), eta))^2+((1+deltaA)*Ec*xi*xi)*(diff(f(xi, eta), eta, eta))^2-(1/3)*Ec*deltaA*deltaB*xi^4*(diff(f(xi, eta), eta, eta))^4-xi*((diff(f(xi, eta), eta))*(diff(Theta(xi, eta), xi))-(diff(Theta(xi, eta), eta))*(diff(f(xi, eta), xi)))}; Cond := {Phi(0, eta) = 0, Phi(xi, 0) = 1, Phi(xi, inf) = 0, Theta(0, eta) = 0, Theta(xi, inf) = 0, f(0, eta) = 0, f(xi, 0) = 0, (D[2](Theta))(xi, 0) = (Theta(xi, 0)-1)*betat, (D[2](f))(xi, 0) = 0, (D[2](f))(xi, inf) = sin(xi)/xi}
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colour := [red, green, blue, gold]
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NULL
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MaVals := [1, 2, 3, 5]
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NULL
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for j to numelems(MaVals) do Ans[j] := pdsolve((eval([OdeSys, Cond], Ma = MaVals[j]))[], numeric, timestep = 0.1e-1); Ng[j] := eval(alphat*(1+4*Rd*(1/3))*(eval(diff(Theta(xi, eta), eta), Ans[j]))^2+Lt*alphac*(eval(diff(Phi(xi, eta), eta), Ans[j]))^2/alphat+Lt*(eval(diff(Phi(xi, eta), eta), Ans[j]))*(eval(diff(Theta(xi, eta), eta), Ans[j]))+Ma*Br*(xi*(eval(diff(f(xi, eta), eta), Ans[j]))-sin(xi))^2+(Br*(1+deltaA)*xi*xi)*(eval(diff(f(xi, eta), eta, eta), Ans[j]))^2-(1/3)*Br*deltaA*deltaB*xi^4*(eval(diff(f(xi, eta), eta, eta), Ans[j]))^4, Ma = MaVals[j]); Bj[j] := (eval(alphat*(1+4*Rd*(1/3))*(eval(diff(Theta(xi, eta), eta), Ans[j]))^2+Lt*alphac*(eval(diff(Phi(xi, eta), eta), Ans[j]))^2/alphat+Lt*(eval(diff(Phi(xi, eta), eta), Ans[j]))*(eval(diff(Theta(xi, eta), eta), Ans[j])), Ma = MaVals[j]))/(eval(alphat*(1+4*Rd*(1/3))*(eval(diff(Theta(xi, eta), eta), Ans[j]))^2+Lt*alphac*(eval(diff(Phi(xi, eta), eta), Ans[j]))^2/alphat+Lt*(eval(diff(Phi(xi, eta), eta), Ans[j]))*(eval(diff(Theta(xi, eta), eta), Ans[j]))+Ma*Br*(xi*(eval(diff(f(xi, eta), eta), Ans[j]))-sin(xi))^2+(Br*(1+deltaA)*xi*xi)*(eval(diff(f(xi, eta), eta, eta), Ans[j]))^2-(1/3)*Br*deltaA*deltaB*xi^4*(eval(diff(f(xi, eta), eta, eta), Ans[j]))^4, Ma = MaVals[j])) end do

Error, invalid input: eval received _m1956857817248, which is not valid for its 2nd argument, eqns

  
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NULL
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with(plots); cols := [red, blue, black, green]; plotZ := display*([seq*(pdeplot*(Ans[k], [eta, Ng[k](xi, eta)], eta = 0 .. 5, xi = 1, color = cols[k]), k = 1 .. numelems(MaVals))], 'axes' = 'boxed', labels = [eta, 'Ng'], size = [600, 600]); plotP := display*([seq*(pdeplot*(Ans[k], [eta, Bej[k](eta, xi)], eta = 0 .. 5, xi = 1, color = cols[k]), k = 1 .. numelems(MaVals))], 'axes' = 'boxed', labels = [eta, 'Bj'], size = [600, 600])
> 

 

Download circular_cylider_entropy_plot.mw

Related post...

Suryakanth 5
November 06 2023
0 0

Similar problem asked few years back there answer is not there question is incomplete check here Related pot.

Modify my work sheet for solution

 

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