gabbbooooo

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These are questions asked by gabbbooooo

Good day all,

please I am new Maple user, i used the same code to solve boundary layer flow. Itried to use the same code in solving nanofluid but the solution is not coverging at some point. But the author i want to compared my results with had solution at those points.

Is there any way i can get solution of this model at this with these values?. Please i need your help. Thank you in advance

secod_code.mw

NULL

restart

with*plots; ode1 := (1+1/bet)*(diff(f(eta), eta, eta, eta))-(diff(f(eta), eta))^2+f(eta)*(diff(f(eta), eta, eta))+Gr*(theta(eta)+lambda1*theta(eta)^2)+Gc*(phi(eta)+lambda2*phi(eta)^2)-M*(diff(f(eta), eta)) = 0

(1+1/bet)*(diff(diff(diff(f(eta), eta), eta), eta))-(diff(f(eta), eta))^2+f(eta)*(diff(diff(f(eta), eta), eta))+Gr*(theta(eta)+lambda1*theta(eta)^2)+Gc*(phi(eta)+lambda2*phi(eta)^2)-M*(diff(f(eta), eta)) = 0

(1)

ode2 := (diff(theta(eta), eta, eta))*(1+(4*R*(1/3))*(theta(eta)+CT)^3)/Pr+4*R*(theta(eta)+CT)^2*(diff(theta(eta), eta))^2+f(eta)*(diff(theta(eta), eta))+Nb*(diff(phi(eta), eta))*(diff(theta(eta), eta))+Nt*(diff(theta(eta), eta))^2-de*(f(eta)*(diff(f(eta), eta))*(diff(theta(eta), eta))+f(eta)^2*(diff(theta(eta), eta, eta))) = 0

(diff(diff(theta(eta), eta), eta))*(1+(4/3)*R*(theta(eta)+CT)^3)/Pr+4*R*(theta(eta)+CT)^2*(diff(theta(eta), eta))^2+f(eta)*(diff(theta(eta), eta))+Nb*(diff(phi(eta), eta))*(diff(theta(eta), eta))+Nt*(diff(theta(eta), eta))^2-de*(f(eta)*(diff(f(eta), eta))*(diff(theta(eta), eta))+f(eta)^2*(diff(diff(theta(eta), eta), eta))) = 0

(2)

ode3 := diff(phi(eta), eta, eta)+Pr*Le*(diff(phi(eta), eta))*f(eta)+Nt*(diff(theta(eta), eta, eta))/Nb-Pr*Le*dc*(f(eta)*(diff(f(eta), eta))*(diff(phi(eta), eta))+f(eta)^2*(diff(phi(eta), eta, eta))) = 0

diff(diff(phi(eta), eta), eta)+Pr*Le*(diff(phi(eta), eta))*f(eta)+Nt*(diff(diff(theta(eta), eta), eta))/Nb-Pr*Le*dc*(f(eta)*(diff(f(eta), eta))*(diff(phi(eta), eta))+f(eta)^2*(diff(diff(phi(eta), eta), eta))) = 0

(3)

bcs1 := f(0) = 0, (D(f))(0) = 1+xi*((D^2)(f))(0), (D(f))(6) = 0, theta(6) = 0, phi(0) = 1+`ς`*(D(phi))(0), theta(0) = 1+Zeta*(D(theta))(0), phi(6) = 0

f(0) = 0, (D(f))(0) = 1+xi*(D(f))(0)^2, (D(f))(6) = 0, theta(6) = 0, phi(0) = 1+varsigma*(D(phi))(0), theta(0) = 1+Zeta*(D(theta))(0), phi(6) = 0

(4)

NULL

 

L := [0., .1, .4, 1]

[0., .1, .4, 1]

(5)

 
  

NULL


  for k to 10 do
      sol_All := dsolve
                 ( eval
                   ( {bcs1, ode1, ode2,ode3},
                     [xi= L[k],R=1, CT=0.2, Gr=0.5, Gc=0.5, lambda1=0.2, lambda2=0.2, Pr=0.72, Nb=0.5,  Le=1, dc=0.2, de=0.2, Nt=0.5, Zeta=0.5, varsigma=0.5, M=1.5, bet=1.5]
                   ),
                   [f(eta), theta(eta),phi(eta)],
                   numeric,
                   output = listprocedure
                 );
      Y_sol || k := rhs(sol_All[5]);
      YP_sol || k := -rhs(sol_All[6]);

feta || k := rhs(sol_All[4]);
      fpeta || k := rhs(sol_All[3]);

phieta || k := rhs(sol_All[8]);
      phipeta || k := rhs(sol_All[7])
  end do:

Error, (in dsolve/numeric/bvp) initial Newton iteration is not converging

 

for k to 10 do L[k], [(Y_sol || k)(0), (YP_sol || k)(0)] end do

0., [Y_sol1(0), YP_sol1(0)]

 

.1, [Y_sol2(0), YP_sol2(0)]

 

.4, [Y_sol3(0), YP_sol3(0)]

 

1, [Y_sol4(0), YP_sol4(0)]

 

Error, invalid subscript selector

 

for k to 10 do L[k], [(feta || k)(0)] end do

0., [feta1(0)]

 

.1, [feta2(0)]

 

.4, [feta3(0)]

 

1, [feta4(0)]

 

Error, invalid subscript selector

 

NULL

Error, mismatched or missing bracket/operator

"for k  from 1 to  10 do L[k], ([phieta ||k(0),phipeta||k(0)]); od; "

 

NULL

  plot( [ seq((Y_sol||j)(eta), j = 1..6)],
         eta = 0 .. 6,
         labels = [eta, theta(eta)],
         axes = boxed
      );
plot( [ seq((YP_sol||j)(eta), j = 1..6)],
         eta = 0 .. 8,
         labels = [eta, thetaprime(eta)],
         axes = boxed
      );

 plot( [ seq((feta||j)(eta), j = 1..6)],
         eta = 0 .. 8,
         labels = [eta, f(eta)],
         axes = boxed
      );
  plot( [ seq((fpeta||j)(eta), j = 1..6)],
         eta = 0 .. 5,
         labels = [eta, fprime(eta)],
         axes = boxed
      );
plot( [ seq((phipeta||j)(eta), j = 1..6)],
         eta = 0 .. 5,
         labels = [eta, phiprime(eta)],
         axes = boxed
      );

plot( [ seq((phieta||j)(eta), j = 1..6)],
         eta = 0 .. 5,
         labels = [eta, phi(eta)],
         axes = boxed
      );

Warning, expecting only range variable eta in expression Y_sol1(eta) to be plotted but found name Y_sol1

 

 

Warning, expecting only range variable eta in expression YP_sol1(eta) to be plotted but found name YP_sol1

 

 

Warning, expecting only range variable eta in expression feta1(eta) to be plotted but found name feta1

 

 

Warning, expecting only range variable eta in expression fpeta1(eta) to be plotted but found name fpeta1

 

 

Warning, expecting only range variable eta in expression phipeta1(eta) to be plotted but found name phipeta1

 

 

Warning, expecting only range variable eta in expression phieta1(eta) to be plotted but found name phieta1

 

 
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