Can it be possible to draw Fig. 4 with Pr (0 to 2) on X-axis and for different values of M=0,1,2 OR plot(Nt,-T0(5)) with M=0,1,2

function main
 Pr=6.2; fw=0.5; Nb=.5;L=-1; K=.100;Nt=.5;Le=1;R=1; Kc=0.2;
%M=1; 
 M=input('M=');
xa=0;xb=6;
solinit=bvpinit(linspace(xa,xb,100),[0 1 0 1 0 1 0]);
sol=bvp4c(@ode,@bc,solinit);
xint=linspace(xa,xb,100);
sxint=deval(sol,xint);
function res=bc(ya,yb)
res=[ya(1)-fw; ya(2)-L; ya(4)-1; Nb*ya(7)+Nt*ya(5);yb(2); yb(4); yb(6)];      
end 
function dydx=ode(x,y)    
dydx=[y(2);  y(3);  y(2)^2+(M+K)*y(2)-y(3)*y(1); 
      y(5);         -(Pr*y(1)*y(5)+Nb*y(5)*y(7)+Nt*y(5)^2)/(1+R);
      y(7);         (Nt/Nb)*(Pr*y(1)*y(5)+Nb*y(5)*y(7)+Nt*y(5)^2)/(1+R)-Le*y(7)*y(1)+Kc*Le*y(6)];             
end
% T0 = deval(sol,0)
% plot(Nt,-T0(5))
plot(xint,sxint([4],:),'--','Linewidth',1);   %for f'
title('Fig.4 Variation of Temperature Profile f`(\eta)with M ')
xlabel('\eta'); 
ylabel('f`(\eta)');
hold on
end

[MINATI]

Can it be posiible to find analytical solution(symbolic notation) of the given code. Pl. help

Answer 1

[madhan ravi]

Parameterizing function

function main
L=-1;
fw=0.5;
Nb=.5;
Nt=.5;
Pr=6.2; 
K=.100;
Le=1;
R=1;
Kc=0.2;

for M=0:2
xa=0;xb=6;
solinit=bvpinit(linspace(xa,xb,100),[0 1 0 1 0 1 0]);
sol=bvp4c(@(x,y)ode(x,y,M,Pr,Nb,K,Nt,Le,R,Kc),@(ya,yb)bc(ya,yb,L,fw,Nb,Nt),solinit);
xint=linspace(xa,xb,100);
sxint=deval(sol,xint);
figure
plot(xint,sxint(4,:),'--','Linewidth',1);   %for f'
title(['Fig.4 Variation of Temperature Profile f`(\eta)with M = ' ,num2str(M)])
xlabel('\eta'); 
ylabel('f`(\eta)');
end
end
function res=bc(ya,yb,L,fw,Nb,Nt)
                 % ^^^^^^^^^^^^^---- parameterization
res=[ya(1)-fw; ya(2)-L; ya(4)-1; Nb*ya(7)+Nt*ya(5);yb(2); yb(4); yb(6)];      
end 
function dydx=ode(x,y,M,Pr,Nb,K,Nt,Le,R,Kc)  
                  %   ^^^^^^^^^^^^^^^^^^^^---- parameterization
dydx=[y(2);  y(3);  y(2)^2+(M+K)*y(2)-y(3)*y(1); 
      y(5);         -(Pr*y(1)*y(5)+Nb*y(5)*y(7)+Nt*y(5)^2)/(1+R);
      y(7);         (Nt/Nb)*(Pr*y(1)*y(5)+Nb*y(5)*y(7)+Nt*y(5)^2)/(1+R)-Le*y(7)*y(1)+Kc*Le*y(6)];             
end

[MINATI]

Thanks

Madhan Ravi

Thanks a lot but in X-axis i need variation of Pr=[0 to 2] with variation of given M

All curves in one figure

[madhan ravi]

Anytime :) , do the same way I showed you for M , remove figure and add hold on as it's in your question.

it's not likely to keep adding question one by one in each comment ... (please read how to parameterize a function)

function main
L=-1;
fw=0.5;
Nb=.5;
Nt=.5;
K=.100;
Le=1;
R=1;
Kc=0.2;
M=0:2;
Pr=0:2;
for i=1:numel(Pr) % if number of Pr and M vary use nested loops
xa=0;xb=6;
solinit=bvpinit(linspace(xa,xb,100),[0 1 0 1 0 1 0]);
sol=bvp4c(@(x,y)ode(x,y,M(i),Pr(i),Nb,K,Nt,Le,R,Kc),@(ya,yb)bc(ya,yb,L,fw,Nb,Nt),solinit);
xint=linspace(xa,xb,100);
sxint=deval(sol,xint);
plot(xint,sxint(4,:),'--','Linewidth',1);   %for f'
hold on
title(['Fig.4 Variation of Temperature Profile f`(\eta)with M = ' ,num2str(M),' Pr = ',num2str(Pr)])
xlabel('\eta'); 
ylabel('f`(\eta)');
end
end
function res=bc(ya,yb,L,fw,Nb,Nt)
                 % ^^^^^^^^^^^^^---- parameterization
res=[ya(1)-fw; ya(2)-L; ya(4)-1; Nb*ya(7)+Nt*ya(5);yb(2); yb(4); yb(6)];      
end 
function dydx=ode(x,y,M,Pr,Nb,K,Nt,Le,R,Kc)  
                  %   ^^^^^^^^^^^^^^^^^^^^---- parameterization
dydx=[y(2);  y(3);  y(2)^2+(M+K)*y(2)-y(3)*y(1); 
      y(5);         -(Pr*y(1)*y(5)+Nb*y(5)*y(7)+Nt*y(5)^2)/(1+R);
      y(7);         (Nt/Nb)*(Pr*y(1)*y(5)+Nb*y(5)*y(7)+Nt*y(5)^2)/(1+R)-Le*y(7)*y(1)+Kc*Le*y(6)];             
end

[MINATI]

Actually M and Pr variation happens simultaneously with given data.

Thank you again

************

it's not likely to keep adding question one by one in each comment ... (please read how to parameterize a function

It is not as that you thought but still unsolved

[MINATI]

Dear

madhan ravi

In X-axis variation should come as Pr=0 to 2 and parallaly variation for M=0, 1, 2 to draw fig. 4

I am still unable to draw