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Rashid Raja

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Here is the code which i am using for co...

Rashid Raja 10
October 23 2013

@Carl Love stream_lines.mws

> 

restart;
> 

eq1 := diff(f(eta),eta,eta,eta)+(1+lambda)*(f(eta)*diff(f(eta),eta,eta)-(diff(f(eta),eta))^2+(B)^2)+k*(((diff(f(eta),eta,eta))^2-f(eta)*diff(f(eta),eta,eta,eta,eta)));

diff(diff(diff(f(eta), eta), eta), eta)+(1+lambda)*(f(eta)*(diff(diff(f(eta), eta), eta))-(diff(f(eta), eta))^2+B^2)+k*((diff(diff(f(eta), eta), eta))^2-f(eta)*(diff(diff(diff(diff(f(eta), eta), eta), eta), eta)))

 (1)
> 

eq2 := diff(h(eta),eta,eta)+(1+lambda)*(f(eta)*diff(h(eta),eta)-diff(f(eta),eta)*h(eta)-A)+k*((diff(f(eta),eta,eta)*diff(h(eta),eta)-diff(f(eta),eta)*diff(h(eta),eta,eta)+diff(f(eta),eta,eta,eta)*h(eta)-f(eta)*diff(h(eta),eta,eta,eta)));

diff(diff(h(eta), eta), eta)+(1+lambda)*(f(eta)*(diff(h(eta), eta))-(diff(f(eta), eta))*h(eta)-A)+k*((diff(diff(f(eta), eta), eta))*(diff(h(eta), eta))-(diff(f(eta), eta))*(diff(diff(h(eta), eta), eta))+(diff(diff(diff(f(eta), eta), eta), eta))*h(eta)-f(eta)*(diff(diff(diff(h(eta), eta), eta), eta)))

 (2)
> 

eq3 := diff(theta(eta),eta,eta)+Pr*(f(eta)*diff(theta(eta),eta)+`N[b]`*diff(phi(eta),eta)*diff(theta(eta),eta)+`N[t]`*(diff(theta(eta),eta))^2);

diff(diff(theta(eta), eta), eta)+Pr*(f(eta)*(diff(theta(eta), eta))+`N[b]`*(diff(phi(eta), eta))*(diff(theta(eta), eta))+`N[t]`*(diff(theta(eta), eta))^2)

 (3)
> 

eq4 := diff(phi(eta),eta,eta)+S[c]*f(eta)*diff(phi(eta),eta)+`N[t]`/`N[b]`*(diff(theta(eta),eta,eta));

diff(diff(phi(eta), eta), eta)+S[c]*f(eta)*(diff(phi(eta), eta))+`N[t]`*(diff(diff(theta(eta), eta), eta))/`N[b]`

 (4)
> 

bc:=f(0)=0,D(f)(0)=1,D(f)(N)=B,D(D(f))(N)=0,h(0)=0,D(h)(N)=1,D(D(h))(N)=0,theta(0)=1,theta(N)=0,phi(0)=1,phi(N)=0;

f(0) = 0, (D(f))(0) = 1, (D(f))(N) = B, ((D@@2)(f))(N) = 0, h(0) = 0, (D(h))(N) = 1, ((D@@2)(h))(N) = 0, theta(0) = 1, theta(N) = 0, phi(0) = 1, phi(N) = 0

 (5)
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interface(displayprecision = 7)

7

 (6)
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b := 11; bb := b-1

11

10

 (7)
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N:=10;lambda:=0.1;A:=0.84;B:=0.1;k:=0.1;`N[b]`:=0.1;`N[t]`:=0.1;Pr:=10;S[c]:=1;

10

.1

.84

.1

.1

.1

.1

10

1

 (8)
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A1 := dsolve({bc, eq1, eq2, eq3, eq4}, numeric, output = array([seq(0+0.5e-2*i, i = 0 .. 200*bb)]), method = bvp[midrich])
> 

with(plots)
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interface(displayprecision = 7)

7

 (9)
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b := 11; bb := b-1

11

10

 (10)
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g(eta):=Int(h(eta),eta);

Int(h(eta), eta)

 (11)
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c1 := [x*f(eta)+g(eta), eta]

[x*f(eta), eta]

 (12)
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contourplot(c1, x = -10 .. 10, eta = 0 .. 10, contours = [-2, -1, 0, 1, 2], 0 .. N)

Error, (in plot/iplot2d) invalid 1st argument (the function) [x*f(eta), eta]

  
> 

%?
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%?
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Example for understanding

`?`

 (13)
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c1 := [cos(x)-2*cos(.4*y), sin(x)-2*sin(.4*y), y]

[cos(x)-2*cos(.4*y), sin(x)-2*sin(.4*y), y]

 (14)
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c2 := [cos(x)+2*cos(.4*y), sin(x)+2*sin(.4*y), y]

[cos(x)+2*cos(.4*y), sin(x)+2*sin(.4*y), y]

 (15)
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contourplot({c1, c2}, x = 0 .. 2*Pi, y = 0 .. 10, grid = [25, 15])

 
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`?`

 (16)
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%?



Download stream_lines.mws

 

how to draw constant stream lines with m...

Rashid Raja 10
October 20 2013
0 0

Dear Dr rlopez
i am solving a system of four coupled differential equations using bvp[midrich]approach.. here is the command which i am using:

A1:=dsolve({eq1,eq2,eq3,eq4,bc},numeric,output = array([seq(0+0.5e-2*i, i = 0 .. 200*bb)]),method=bvp[midrich]);
c1 := [x*f(y)+g(y), y];
> r1:=contourplot(c1,[x=-10..10 ,y=-10..10,contours=[-2,-1,0,1,2], color=red,style=line,thickness=2,0..N)];
display(r1, axis = boxed)

I have two questions

1) i need to plot stream lines for the function psi:= x*f(y)+g(y) for some constant values of psi like psi:= -2,-1,0,1,2 etc where we have
g(y):=gamma*int(h(y))
f(y) and h(y) are the two unknowns from eq 1 and eq 2.

2)using this command A1: although i can obtain numerical data in matrix form but how can i select a particular dependent variable from this num data and export it to graphical software like Tecplot.
Regards
Rashid
Email: rashidraja15@yahoo.com

how to draw constant stream lines with m...

Rashid Raja 10
October 20 2013

Dear Dr rlopez
i am solving a system of four coupled differential equations using bvp[midrich]approach.. here is the command which i am using:

A1:=dsolve({eq1,eq2,eq3,eq4,bc},numeric,output = array([seq(0+0.5e-2*i, i = 0 .. 200*bb)]),method=bvp[midrich]);
c1 := [x*f(y)+g(y), y];
> r1:=contourplot(c1,[x=-10..10 ,y=-10..10,contours=[-2,-1,0,1,2], color=red,style=line,thickness=2,0..N)];
display(r1, axis = boxed)

I have two questions

1) i need to plot stream lines for the function psi:= x*f(y)+g(y) for some constant values of psi like psi:= -2,-1,0,1,2 etc where we have
g(y):=gamma*int(h(y))
f(y) and h(y) are the two unknowns from eq 1 and eq 2.

2)using this command A1: although i can obtain numerical data in matrix form but how can i select a particular dependent variable from this num data and export it to graphical software like Tecplot.
Regards
Rashid
Email: rashidraja15@yahoo.com

need help in a maple code...

Rashid Raja 10
September 30 2013
0 0

Dear sir rlopez         

        there is a system of four coupled equations which i am solving with bvpmidrich] approach..there is a physical constant "A" in my second equation.. can i calculate  numerical values of "A"  by fixing all the other parameters like lambda, K etc at eta=0..by using bvpmidrich approach. if so how is it possible.

i m writting my system of equations maple code  as under:   >

eq1 := diff(f(eta),eta,eta,eta)+(1+lambda)*(f(eta)*diff(f(eta),eta,eta)-(diff(f(eta),eta))^2+(B)^2)+k*(((diff(f(eta),eta,eta))^2-f(eta)*diff(f(eta),eta,eta,eta,eta)));       >

eq2 := diff(h(eta),eta,eta)+(1+lambda)*(f(eta)*diff(h(eta),eta)-diff(f(eta),eta)*h(eta)-A)+k*((diff(f(eta),eta,eta)*diff(h(eta),eta)-diff(f(eta),eta)*diff(h(eta),eta,eta)+diff(f(eta),eta,eta,eta)*h(eta)-f(eta)*diff(h(eta),eta,eta,eta)));       >

eq3 := diff(theta(eta),eta,eta)+Pr*(f(eta)*diff(theta(eta),eta)+`N[b]`*diff(phi(eta),eta)*diff(theta(eta),eta)+`N[t]`*(diff(theta(eta),eta))^2);       >

eq4 := diff(phi(eta),eta,eta)+S[c]*f(eta)*diff(phi(eta),eta)+`N[t]`/`N[b]`*(diff(theta(eta),eta,eta));       >

bc:=f(0)=0,D(f)(0)=1,D(f)(N)=B,D(D(f))(N)=0,h(0)=0,D(h)(N)=1,D(D(h))(N)=0,theta(0)=1,theta(N)=0,phi(0)=1,phi(N)=0;   (2)  bc := f(0) = 0, D(f)(0) = 1, D(f)(10) = 0.1, (D )(f)(10) = 0,   (2)  h(0) = 0, D(h)(10) = 1, (D )(h)(10) = 0, theta(0) = 1,   theta(10) = 0, phi(0) = 1, phi(10) = 0   >

N:=10;lambda:=0.1;A:=0.84;B:=0.1;k:=0.1;`N[b]`:=0.1;`N[t]`:=0.1;Pr:=10;S[c]:=1;   N := 10  

lambda := 0.1  

A := 0.84  

B := 0.1  

k := 0.1  

N[b] := 0.1  

N[t] := 0.1  

Pr := 10  

S[c] := 1   > lambda := .1;   lambda := 0.1   > k := .1;   k := 0.1   > A := .84;   A := 0.84   >

A1:=dsolve({eq1,eq2,eq3,eq4,bc},numeric,method=bvp[midrich]);  

A1 := proc(x_bvp) ... end proc  

>

with(plots): > p1:=odeplot(A1, [[eta,diff(f(eta),eta), color=red,style=line,thickness=2]],0..N):

> display({p1}, axes=boxed, title=`Velocity f'`);   > q1:=odeplot(A1, [[eta,diff(h(eta),eta), color=blue,style=line,thickness=2]],0..N): > display({q1}, axes=boxed, title=`Velocity h'`);  

> r1:=odeplot(A1, [[eta,theta(eta), color=green,style=line,thickness=2]],0..N): > display({r1}, axes=boxed, title=`temp`);   > s1:=odeplot(A1, [[eta,phi(eta), color=orange,style=line,thickness=2]],0..N): > display({s1}, axes=boxed, title=`concentration`);

need help in a maple code...

Rashid Raja 10
September 30 2013

Dear sir rlopez         

        there is a system of four coupled equations which i am solving with bvpmidrich] approach..there is a physical constant "A" in my second equation.. can i calculate  numerical values of "A"  by fixing all the other parameters like lambda, K etc at eta=0..by using bvpmidrich approach. if so how is it possible.

i m writting my system of equations maple code  as under:   >

eq1 := diff(f(eta),eta,eta,eta)+(1+lambda)*(f(eta)*diff(f(eta),eta,eta)-(diff(f(eta),eta))^2+(B)^2)+k*(((diff(f(eta),eta,eta))^2-f(eta)*diff(f(eta),eta,eta,eta,eta)));       >

eq2 := diff(h(eta),eta,eta)+(1+lambda)*(f(eta)*diff(h(eta),eta)-diff(f(eta),eta)*h(eta)-A)+k*((diff(f(eta),eta,eta)*diff(h(eta),eta)-diff(f(eta),eta)*diff(h(eta),eta,eta)+diff(f(eta),eta,eta,eta)*h(eta)-f(eta)*diff(h(eta),eta,eta,eta)));       >

eq3 := diff(theta(eta),eta,eta)+Pr*(f(eta)*diff(theta(eta),eta)+`N[b]`*diff(phi(eta),eta)*diff(theta(eta),eta)+`N[t]`*(diff(theta(eta),eta))^2);       >

eq4 := diff(phi(eta),eta,eta)+S[c]*f(eta)*diff(phi(eta),eta)+`N[t]`/`N[b]`*(diff(theta(eta),eta,eta));       >

bc:=f(0)=0,D(f)(0)=1,D(f)(N)=B,D(D(f))(N)=0,h(0)=0,D(h)(N)=1,D(D(h))(N)=0,theta(0)=1,theta(N)=0,phi(0)=1,phi(N)=0;   (2)  bc := f(0) = 0, D(f)(0) = 1, D(f)(10) = 0.1, (D )(f)(10) = 0,   (2)  h(0) = 0, D(h)(10) = 1, (D )(h)(10) = 0, theta(0) = 1,   theta(10) = 0, phi(0) = 1, phi(10) = 0   >

N:=10;lambda:=0.1;A:=0.84;B:=0.1;k:=0.1;`N[b]`:=0.1;`N[t]`:=0.1;Pr:=10;S[c]:=1;   N := 10  

lambda := 0.1  

A := 0.84  

B := 0.1  

k := 0.1  

N[b] := 0.1  

N[t] := 0.1  

Pr := 10  

S[c] := 1   > lambda := .1;   lambda := 0.1   > k := .1;   k := 0.1   > A := .84;   A := 0.84   >

A1:=dsolve({eq1,eq2,eq3,eq4,bc},numeric,method=bvp[midrich]);  

A1 := proc(x_bvp) ... end proc  

>

with(plots): > p1:=odeplot(A1, [[eta,diff(f(eta),eta), color=red,style=line,thickness=2]],0..N):

> display({p1}, axes=boxed, title=`Velocity f'`);   > q1:=odeplot(A1, [[eta,diff(h(eta),eta), color=blue,style=line,thickness=2]],0..N): > display({q1}, axes=boxed, title=`Velocity h'`);  

> r1:=odeplot(A1, [[eta,theta(eta), color=green,style=line,thickness=2]],0..N): > display({r1}, axes=boxed, title=`temp`);   > s1:=odeplot(A1, [[eta,phi(eta), color=orange,style=line,thickness=2]],0..N): > display({s1}, axes=boxed, title=`concentration`);

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