How do I obtain graphs of parameters like Reduced Sherwood no. vs Brownian motion parameter(Nb) from a bvp4c code that I have written
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Following are non-dimensional the set of equations that I have:
f"=g(g^2+gamma^2)/(g^2+lambda*gamma^2) ------ (1)
g'= (1/3)*f'^2-(2/3)*(f*f")+ Mn*f' ------------------------(2)
t"+Rd*t"+ 2*Pr*f*t'/3+ Nb*t'*p'+Nt*(t')^2= 0------(3)
p"+(2*Lew*f*p')/3+ Nt*t"/Nb= 0 ------------------------(4)
'f', 'g', 't', 'p' are the dependent variable and 'η' is the independent variable
gamma, lambda, Mn, Le, Rd, Nb, Nt, Pr are the parameters
converting these higher order equations to first order equations, I have let
f = y1, df/dη = y2, g = y3, t = y4, dt/dη = y5, p = y6, dp/dη = y7
Now, converting the above equations into 1st order ode
y1' = y2,
y2' = {y3*(y3^2+ gamma^2)}/(y3^2+ lambda*gamma^2) ,
y3' = y2^2/3 − (2/3)*y1*{y3*(y3^2+ gamma^2)/(y3^2+ lambda*gamma^2)} + Mny2,
y4' = y5,
y5' = −(1/(1+Rd))*{(2*Pr*y1*y5)/3 + Nb*y5*y7 + Nt*y5^2} ,
y6' = y7,
y7' = −(2*Le*y1*y7)/3 + {Nt/Nb*(1+Rd)}{(2*Pr*y1*y5)/3 + Nb*y5*y7 + Nt*y5^2}
I have solved the above equations numerically using bvp4c solver
However, I am not able to figure how do I plot graphs of
Reduced Sherwood number i.e p'(0) vs Nb or Nt, the Brownian motion and thermophoresis parameter respectively.
I have attached a picture of a graph from an already published research paper for reference.
The bvp4c code that I have used is:
function sol= proj
clc;clf;clear;
global lambda gama Pr Rd Lew Nb Nt Mn m
gama=1;
Lew=1;
Nt=1;
Rd=1;
Pr=5;
Mn=1;
pp=[0.5 1 1.5];
qq=[0.2 0.5 0.9];
%figure(1)
%plot(2,1);hold on
options=bvpset('stats','on','RelTol',1e-9);
m=linspace(0,10);
solinit= bvpinit(m,[1,0,0,0,0,0,0]);
for i=1:numel(pp)
lambda=pp(i);
for i=1:numel(qq);
Nb=qq(i)
sol= bvp4c(@projfun,@projbc,solinit,options);
y1=deval(sol,0)
solinit= sol;
plot(sol.x,sol.y(6,:));hold on
end
end
end
function f= projfun(x,y)
global lambda gama Pr Rd Lew Nb Nt Mn
f= [y(2)
y(3)*(y(3)^2+gama^2)/(y(3)^2+lambda*gama^2)
y(2)^2/3-(2*y(1)*y(3)*(y(3)^2+gama^2))/(3*(y(3)^2+lambda*gama^2))+Mn*y(2)
y(5)
-(2*Pr*y(1)*y(5))/(3*(1+Rd)) - (Nb*y(5)*y(7))/(1+Rd) - (Nt*y(5)^2)/(1+Rd)
y(7)
-(2*Lew*y(1)*y(7))/3+ Nt*((2*Pr*y(1)*y(5))/(3*(1+Rd)) + (Nb*y(5)*y(7))/(1+Rd) + (Nt*y(5)^2)/(1+Rd))/Nb];
end
function res= projbc(ya,yb)
res= [ya(1); ya(2)-1; ya(4)-1.0; ya(6)-1.0; yb(2); yb(4); yb(6)];
end
Could anyone please show me how do I implement the above-written code. to obtain the graphs of Reduced Sherwood no. i.e p'(0) vs Nb or Nt.
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/172077/image.jpeg)
1 个评论
Anil Gautam
2018-11-25
I also want to know how to plot such type of graphs usin bvp4c. naygarp . If you got something which is related to this . Plz share
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