Question: how to PLOT PDE IBCS for different Sc , Pr, Gr, Gm at fixed t? Also for Nusselt (theta prime) ,skin friction (f double prime)


 

restart

with(PDEtools)

with(plots)

P__r := .71; lambda := 1.0; K__r := 1.0; S__r := .5; m := .5; M := sqrt(10.0); `ϰ` := .5; Omega := sqrt(5.0); Gr := 6.0; Gm := 5.0; S__c := .22

PDE := {diff(phi(x, t), t) = (diff(phi(x, t), x, x))/S__c-K__r*phi(x, t)+S__r*(diff(theta(x, t), x, x)), diff(theta(x, t), t) = lambda*(diff(theta(x, t), x, x))/P__r, diff(u(x, t), t) = diff(u(x, t), x, x)-M^2*(u(x, t)-m*w(x, t))/(m^2+1)-u(x, t)/`ϰ`-2*Omega^2*w(x, t)+Gr*theta(x, t)+Gm*phi(x, t), diff(w(x, t), t) = diff(w(x, t), x, x)+M^2*(m*u(x, t)-w(x, t))/(m^2+1)-w(x, t)/`ϰ`+2*Omega^2*u(x, t)}

{diff(phi(x, t), t) = 4.545454545*(diff(diff(phi(x, t), x), x))-1.0*phi(x, t)+.5*(diff(diff(theta(x, t), x), x)), diff(theta(x, t), t) = 1.408450704*(diff(diff(theta(x, t), x), x)), diff(u(x, t), t) = diff(diff(u(x, t), x), x)-9.999999999*u(x, t)-5.999999996*w(x, t)+6.0*theta(x, t)+5.0*phi(x, t), diff(w(x, t), t) = diff(diff(w(x, t), x), x)+14.00000000*u(x, t)-9.999999999*w(x, t)}

(1)

``

IBC := {phi(0, t) = 1, phi(9, t) = 0, phi(x, 0) = 0, theta(0, t) = 1, theta(9, t) = 0, theta(x, 0) = 0, u(0, t) = t, u(9, t) = 0, u(x, 0) = 0, w(0, t) = 0, w(9, t) = 0, w(x, 0) = 0}

sol := pdsolve(PDE, IBC, numeric, spacestep = 0.1e-1)

_m2167514531200

(2)

p1 := sol:-plot(t = .3, color = red); p2 := sol:-plot(t = .5, color = gold); p3 := sol:-plot(t = .7, color = purple); p4 := sol:-plot(t = 1., color = green); plots[display]({p1, p2, p3, p4})

 

q1, q2, q3, q4 := seq(eval(u(x, t), sol:-value(t = t0, output = listprocedure)), t0 = [.3, .5, .7, 1]); plot([q1, q2, q3, q4], 0 .. 10, color = [red, gold, purple, green])

 

p1 := sol:-plot(t = 1, S__c = .1, color = red); p2 := sol:-plot(t = 1, S__c = .2, color = gold); p3 := sol:-plot(t = 1, S__c = .3, color = purple); p4 := sol:-plot(t = 1, S__c = .4, color = green); plots[display]({p1, p2, p3, p4})

Error, (in plot/options2d) unexpected option: .22 = .1

 

Error, (in plot/options2d) unexpected option: .22 = .2

 

Error, (in plot/options2d) unexpected option: .22 = .3

 

Error, (in plot/options2d) unexpected option: .22 = .4

 

 

q1, q2, q3, q4 := seq(eval(diff(u(0, t), t), sol:-value(t = t0, output = listprocedure)), t0 = [.3, .5, .7, 1]); plot([q1, q2, q3, q4], 0 .. 10, color = [red, gold, purple, green])

Error, (in plot) procedure expected, as range contains no plotting variable

 

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how to PLOT PDE IBCS for different  Sc , Pr, Gr, Gm at fixed t? Also for Nusselt (theta prime)  ,skin friction (f double prime)?

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