@sand15 

There are two different regions are there sir first two equations are region one from -1 to 0 and other is 0 to 1 

I want two seperate plots 

In the paper they given combinly in one plot but i need seperately. 

From these conditions i have solved malualy i have not got the solution. Due to that i have checked here. 

Long back also i have posted similar question regarding two region but they have ploted those graphs in matlab and that equations also pde. 

But in this case it is different. 

I need two different cases 

One is from -1 to 0 and 

Another from 0 to 1 

Seperate plots for solving the ode.

But i am not getting how to take boundaries separately 

For both cases. 

@sand15 Sir, how to solve independently in that some boundary will be missed i have not understood the plot command. for any one graph show me sir from the base paper. similar papers i have checked but in that they have solved using two regions means they have solved first for -1 to 0 and solved for 0 to 1 and merged both graphs in single plot 

last time also I posted a question. regarding two different boundary conditions ( means two region plots in one graph)

but i have not recived any reply and similar posts or question is there means please tag it i will check according to that i will solve  

@dharr 

Dear sir, 

According to the suggestions I have checked the values of parameters given in the base pdf. Nusselt number value and shearhood number and not exactly getting same when we exicute the worksheet. 

What is the error in the calculation,?

Why Different reading is getting for the given parameter values. There is lage difference in the values. 

Thank you.

@dharr 

Thank you for your suggestions. Now the worksheet is executing, but for the given parameters, the graphs are not the same as given in the base paper.sachin_base_paper.mw

refence_of_sachin_base_paper.pdf why this error is getting for the given parameter values in plots as well as table values?  

@dharr 

Dear sir 

I have attached the pdf also according to the suggestions I have checked then also am getting the error. Sir

In the worksheet the nusselt number and shearhood number is not matching with base paper given in the pdf 

I have checked the similar papers in that also similar solution implemented as given in the pdf.

@dharr 

is this  correct ? sachin_base_paper.mw  but here I'm getting wrong values for the table which is given in base paper Table_values_of_sachin_base.mw  refence_of_sachin_base_paper.pdf

What is the mistake in the code ?

Why the graph is not converging? For the given value of parameters.

Please Help me to solve the problem.

@Rouben Rostamian  please check this worksheet sir getting some error in boundary  pde_error_two_boundary.mw

@Rouben Rostamian  

restart:

with(PDEtools):

declare(u(r,z), v(r,z), w(r,z), Theta(r,z), p(r,z)):

PDE1 := diff(r*u(r,z), r)/r + diff(w(r,z), z) = 0:

PDE2 := u(r,z)*diff(u(r,z),r) + w(r,z)*diff(u(r,z),z) - v(r,z)^2/r - 2*v(r,z)

         = -diff(p(r,z),r) + (1/lambda^2)*(epsilon^2*(diff(u(r,z),r$2) + diff(u(r,z),r)/r - u(r,z)/r^2) + diff(u(r,z),z$2)):

PDE3 := u(r,z)*diff(v(r,z),r) + w(r,z)*diff(v(r,z),z) + (u(r,z)*v(r,z))/r + 2*u(r,z)

         = (1/lambda^2)*(epsilon^2*(diff(v(r,z),r$2) + diff(v(r,z),r)/r - v(r,z)/r^2) + diff(v(r,z),z$2)):

PDE4 := u(r,z)*diff(w(r,z),r) + w(r,z)*diff(w(r,z),z)

         = -1/(epsilon^2)*diff(p(r,z),z) + (1/lambda^2)*(epsilon^2*(diff(w(r,z),r$2) + diff(w(r,z),r)/r) + diff(w(r,z),z$2)):

PDE5 := u(r,z)*(-Theta(r,z)/r + diff(Theta(r,z),r)) + w(r,z)*diff(Theta(r,z),z)

         = 1/Pr/lambda^2*(epsilon^2*(diff(Theta(r,z),r$2) + diff(Theta(r,z),r)/r - Theta(r,z)/r^2) + diff(Theta(r,z),z$2)):

BCs := {u(r,1) = L*diff(u(r,1),z), u(r,1) = -L*diff(u(r,1),z), 

        v(r,1) = 0, w(r,1) = 0, Theta(r,1) = 1}:

sol := pdsolve({PDE1, PDE2, PDE3, PDE4, PDE5}, {u(r,z), v(r,z), w(r,z), Theta(r,z), p(r,z)},  BCs):

@Rouben Rostamian  

In maple only give me the suggestions how to implement the conditions for pde equation. I don't want to convert pde into ode. I need the solution of pde equation only .

I seen some post of pde solution also those are also nonlinear equation. 

How to get this pde solution without transferring into ode 

@Rouben Rostamian  

They used siries solution in terms of  v0 and v1  but it difficult to use series solution for the complex terms because in my extension I have used multiple parameters .

 I need the solution by pde only because similar articles not used series solution they given directly pde equation. 

Is it chance to simply by pde only ? 

Suggest me any post related to pde equation with two different boundary .

In that they have given -1 to 0 and again 0 to 1 given. 

In matlab also I have tied but for only 0to 1 I'm getting or -1 to 0 only getting. Combining both boundary in single plot not getting. 

@Rouben Rostamian  

Dear sir the parameter values are given in the image above the graph. And the related pdf is given below once check it sir. What are the points you are asking may included in pdf I think. pde_paper_.pdf

Please give the maple code how to implement it .

It is mentioned as homework.

 I am ready to type the code . How to implement for pde I m not getting. Due to that I have posted image file. 

Please update the maple code to solve .

 It will be helpful for me to generate the solution. 

After long back I have posted the question. I have familiar with ode equation. But pde little bit different. 

Please help me to solve these Questions. 

Thank you 

@acer all cf columns together and nu columns together sir

[|Gr=0.1, eta= 0.001,0.002..220, cf, nu |,|Gr=0.5, eta= 0.001,0.002..220, cf, nu |,|Gr=1, eta= 0.001,0.002..220, cf, nu |] in this manner.

Fistly for one value of Gr like Gr=0.1 , all corresponding values of cf and nu for eta= (0..20,0.01)

In next columns for the value of Gr=0.5 all corresponding values. In the similar way remaing values.