Gabriel samaila

MaplePrimes Activity


These are replies submitted by Gabriel samaila

@tomleslie 

could it be that the version of the maple im using is not supporting the code?


 

restart;

ODEs:= {diff(phi(y), y, y)-Re*Sc*v(y)*(diff(phi(y), y))+Nt*(diff(theta(y), y, y)+(diff(theta(y), y))/y)/Nb = 0,
         diff(v(y), y, y)+(diff(v(y), y))/y-(Ha^2/(1-eta)^2+1/y^2)*v(y)-Re*v(y)*(diff(v(y), y)) = 0,
         diff(theta(y), y, y)+Ec*Pr*(diff(v(y), y)-v(y)/y)^2-Pr*Re*v(y)*(diff(theta(y), y))+Nb*(diff(theta(y), y))*(diff(phi(y), y))+Nt*(diff(theta(y), y))^2 = 0};

{diff(diff(phi(y), y), y)-Re*Sc*v(y)*(diff(phi(y), y))+Nt*(diff(diff(theta(y), y), y)+(diff(theta(y), y))/y)/Nb = 0, diff(diff(v(y), y), y)+(diff(v(y), y))/y-(Ha^2/(1-eta)^2+1/y^2)*v(y)-Re*v(y)*(diff(v(y), y)) = 0, diff(diff(theta(y), y), y)+Ec*Pr*(diff(v(y), y)-v(y)/y)^2-Pr*Re*v(y)*(diff(theta(y), y))+Nb*(diff(theta(y), y))*(diff(phi(y), y))+Nt*(diff(theta(y), y))^2 = 0}

(1)

BCs := {phi(1) = 0, phi(eta) = 1, theta(1) = 0, theta(eta) = 1, v(1) = 0, v(eta) = 1};

{phi(1) = 0, phi(eta) = 1, v(1) = 0, v(eta) = 1, theta(1) = 0, theta(eta) = 1}

(2)

HaVals:=[1, 2, 5, 10]:
colors:=[red, green, blue, black]:
for j from 1 by 1 to numelems(HaVals) do
    pVals := [eta = .5, Ha = HaVals[j], Sc = .8, Nt = .1, Nb = .1, Re = 2, Ec = 0.1e-1, Pr = 10];
    sol:=dsolve( `union`(eval(ODEs, pVals), eval(BCs, pVals)), numeric);
    ptheta[j]:= plots:-odeplot(sol, [y, theta(y)], y=0.5..1, color=colors[j]);
    pphi[j]:= plots:-odeplot(sol, [y, phi(y)], y=0.5..1, color=colors[j]);
    pv[j]:= plots:-odeplot(sol, [y, v(y)], y=0.5..1, color=colors[j]);
od:
displ_opt:= titlefont=[times, bold, 20],
            legend=[seq(typeset("Ha= ", HaVals[j]),j=1..4)],
            legendstyle=[font=[times, bold, 16]],
            size=[800,600]:
plots:-display( convert(ptheta, list),
                title="theta(y) vs y",
                displ_opt
              );
plots:-display( convert(pphi, list),
                title="phi(y) vs y",
                displ_opt
              );
plots:-display( convert(pv, list),
                title="v(y) vs y",
                displ_opt
              );

Error, (in plots:-display) display does not accept the legend option

 

Error, (in plots:-display) display does not accept the legend option

 

Error, (in plots:-display) display does not accept the legend option

 

NULL


 

Download odeProb3_(1).mw

@tomleslie 

i really appriciate your effort

@tomleslie 

pretty good thankyou.

but the command 

#Fig. 3 (changing values of Ha):
P:= Ha:
vals:= [1, 2, 5, 10]:
sols:= [seq(Solve(P= v), v= vals)]:
colors:= [red, green, blue]:
for F in [v,theta,phi](y) do
   print(plots:-display(
      [seq(
         plots:-odeplot(sols[k], [y,F], color= colors[k], legend= [P= vals[k]]),
         k= 1..nops(vals)
      )],
      labeldirections= [horizontal,vertical]
   ))
od:

was to help me generate V, theta and Phi for different values of Ha. 
 

@tomleslie

very interesting, thank you. but i actually want to do is plot for pr=0.044, and hold it and plot for pr=0.71, hold it and plot for pr=2 in same layout. i only know how to do it in MATLAB using hold on command

@tomleslie 

thank you for your previous post. my second question was that, i want to plot figure 1-8. it seems like it is two graphs in one layout.

thank you

@tomleslie 

hy tomleslie, could you please show me how to plot multiple graphs in one layout?. find attach soundalgekar2004-deka.pdf . i want to plot the way this author plot. see my code combine_variables.mw . secondly the attached table 1 and table 2 is not correct in some cases do you know how i can improve the accuracy of the values to be close to the attached author?  table.docx thank you

@tomleslie 

i really appriciate all your post, i have begening learn  lot of things about maple. 

 

@tomleslie 

just like the temperature profile, it is possible to plot f(eta) against eta and f’( eta) against eta in “R_0_fix.mw code”

@tomleslie 

i really appreciate your previous posts. You have solve my problem completely and I understood every bit of the code 

@tomleslie 

the two codes explains my broblem new_when_a_0.mw  and new_when_R_0.mw.

thank you so much for your help

@tomleslie

my question is in the code “when_R_0.mw” I kept R=0 and vary a.But this time around I want to make a=0 so that D(theta)(0)=0 in the boundary conditions  and vary  R in the same code “when_R_0.mw”. That is what the code “when_a_0.mw” is all about 

@tomleslie 

thank you for your prevoius post, please dont get tied of me. the attach codes when_R_0.mw 

solves the equation when R=0, which similar to final_axiz.mw  but i tried to make a=0 when_a_0.mw and varry R in the same code is giving 0 all through could it be true?

@tomleslie 

You have already done everything for me. In fact the used different values for infinity as 65,35,23 and 14 for pr=0.044,0.72,2.0; and 7.0 respectively. By setting the value of infinity, i got more closer results as on the paper.

thank you i really appriciate.

@vv 

the solution does not converge for infinity >14 and discover that the solution becomes closser as infinity be comes larger.

@vv 

yes noted thank you but not thesame as table1 in singh2000-thermometer.pdf

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