@dharr please check this worksheet for atleat square cavity it should work 

error_in_cavity_work.mw

@dharr Thank you very much for the clarification. I now understand that pdsolve/numeric in Maple cannot directly handle a coupled PDE system.

For the square cavity, can I instead solve the energy equation (temperature PDE) separately using one of the available time-dependent methods such as Crank–Nicolson or FTCS, and then treat the H-shaped cavity as a completely separate problem (using another approach )?

My goal is to reproduce the isotherm and streamline plots (like Fig. 12 and 13 in the paper), at least starting with the square geometry.

Would that be a correct approach in Maple?

I mistakenly used method=fd assuming it meant a finite difference scheme. I now understand that Maple only supports specific named methods like CrankNicholson, Euler, or LaxWendroff for single PDEs.

@KIRAN SAJJAN 

No one ready to give reply here.

Simply deleted the question. And reply also. Without notice.

 I have checked similar work but no were i got this type plot command due to that only i have posted the question.

I am trying from last 10 days i have not got this plots. I have tried with python there i got the plots but compared to that maple is easy thats why i am trying here. 

I have not got any response here. 

You suggested the worksheet there thebplot is correct but they have not mention the plot command how to get that plot. Expected worksheet

Please any one help me to solve.

Thank you

Dont delete the question

I have not recived the reply due to that i have posted the question seperately.

@KIRAN SAJJAN   @dharr

How to get the plots for this govering equation. as suggested by kiran sajjan

Mn := .5; We := 1.5; Omega := 1.5; Grt := 1.5; Grc := 1.5; Grf := 1.5; Pr := 6; Nb := 1.5; Nt := 2; Ntc := .5; Nct := .8; beta := 1.5; d := .8; x := 0; varphi := (1/2)*Pi; b := .6; a := .5; t := 1; lambda := 1; Rd := 3; alpha := 0.5e-1; f := 3; yL := -.8; yR := 1.5; OdeSys := {diff(Gamma(y), y$2)+Nt*(diff(theta(y), y$2))/Nb = 0, diff(phi(y), y$2)+Nct*(diff(theta(y), y$2)) = 0, (Pr*Rd+1)*(diff(theta(y), y$2))+Nb*Pr*(diff(theta(y), y))*(diff(Gamma(y), y))+Nt*Pr*(diff(theta(y), y))^2+Ntc*Pr*(diff(phi(y), y$2))+beta = 0, diff(psi(y), y$4)-Mn^2*(diff(psi(y), y$2))/(Omega^2+1)+Grt*theta(y)+Grc*phi(y)-Grf*Gamma(y)-2*We^2*(Mn^2*(diff(psi(y), y$2))/(Omega^2+1)-Grt*theta(y)-Grc*phi(y)+Grf*Gamma(y))^3 = 0}; Cond := {(D(psi))(1+a*cos(2*Pi*(x-t)/lambda))-alpha*((D@@2)(psi))(1+a*cos(2*Pi*(x-t)/lambda)) = -1, (D(psi))(-d-b*cos(2*Pi*(x-t)/lambda+varphi))+alpha*((D@@2)(psi))(-d-b*cos(2*Pi*(x-t)/lambda+varphi)) = -1, Gamma(1+a*cos(2*Pi*(x-t)/lambda)) = 0, Gamma(-d-b*cos(2*Pi*(x-t)/lambda+varphi)) = 1, phi(1+a*cos(2*Pi*(x-t)/lambda)) = 0, phi(-d-b*cos(2*Pi*(x-t)/lambda+varphi)) = 1, psi(1+a*cos(2*Pi*(x-t)/lambda)) = (1/2)*f, psi(-d-b*cos(2*Pi*(x-t)/lambda+varphi)) = -(1/2)*f, theta(1+a*cos(2*Pi*(x-t)/lambda)) = 0, theta(-d-b*cos(2*Pi*(x-t)/lambda+varphi)) = 1};
sol := dsolve({Cond[], OdeSys[]}, numeric, output = listprocedure, range = yL .. yR);
i  want same plots given in this manner

please reply for this question. waiting for the reply.

i have tried from last 2 days but not got. due to that reason i am posting here. i am getting contour plots in circular motion but i want in pulsatile flow motion (wavy nature)

expected results

@acer 

Thank you for your reply sir, 

Dear sir here i have given a work  will all equations they have ploted streamlines like a flow pattern of fluid.

i also need to find similar plots which is given in plots 9, 10 or 11 given in pdf peristatic_flow_paper_demo.pdf

but i have similar equations but in my equations i am not able to get same streamline flow i am getting as circular path. 

it should be osulatary motion.

why it is circular motion in the above plots . in the base work wich is given as oscilatory. if iam using sine or cos function also it is giving the same circular motion only. 

if we mention plots in the circualr motion there will be wrong representation of stream function/ stram lines.

@sand15 paper2_new_efficiency_plots_2025.mw

for these plots

 i need the animation of that plots with the variation of  X=0..1 in first plot and tau=0..2 in second plot.

please give me solution for it

@Rouben Rostamian  

Download first_order_pde.mw

@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 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

please check my question and rectify my errors.

i have posted a new question that is automatically deleted

Download circular_cylider_entropy_plot.mw

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

Modify my work sheet for solution