how to plot this velocity profile...i have solved equation by laplace transform.equqtion in terms of exponentian and complementary error function...have tried and defined functions but output was blank...pls help me out

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Dilip Jose am 8 Jan. 2020

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https://de.mathworks.com/matlabcentral/answers/499363-how-to-plot-this-velocity-profile-i-have-solved-equation-by-laplace-transform-equqtion-in-terms-of

Bearbeitet: KSSV am 16 Mai 2023

close all
syms z;
gr=2;
gc=2;
M=1;
w=0.5;
pr=7;
sc=2.01;
t=0.4;
m=(M+(2*1i*w));
s1=z;
s2=(2*sqrt(t));
x=((s1)./(s2));
a1=(x*t);
a2=(2*m*(sqrt(pi)));
a=((m)./(pr-1));
b=((m)./(sc-1));
x=((s1)./(s2));
u1=((x^2+(m*t))*t);
u2=4*m;
d1=(x*(sqrt(t)))*(1-4*m*t);
d2=(8*m^3/2);
v1=gr;
v2=(a*(1-pr));
k1=gc;
k2=(b*(1-sc));
h1=exp(a*t);
h2=2;
e1=(exp(2*x*(sqrt(m*t))));
e2=(erfc(x+(sqrt(m*t))));
e3=(exp(-2*x*(sqrt(m*t))));
e4=(erfc(x-(sqrt(m*t))));
b1=(exp(2*x*((sqrt((m+a)*t)))));
b2=(erfc(x+(sqrt((m+a)*t))));
b3=(exp(-2*x*(sqrt((m+a)*t))));
b4=(erfc(x-(sqrt((m+a)*t))));
e5=exp(-(x^2+(m*t)));
c1=(exp(2*x*(sqrt(pr*a*t))));
c2=(erfc(x*(sqrt(pr)+(sqrt(a*t)))));
c3=((exp(-2*x*(sqrt(pr*a*t)))));
c4=(erfc(x*(sqrt(pr)-(sqrt(a*t)))));
l1=(exp(2*x*(sqrt(sc*b*t))));
l2=(erfc(x*(sqrt(sc)+(sqrt(b*t)))));
l3=((exp(-2*x*(sqrt(sc*b*t)))));
l4=(erfc(x*(sqrt(sc)-(sqrt(b*t)))));
f1=(exp(b*t));
f2=2;
l=((a1)./(a2));
f=((f1)./(f2));
h=((h1)./(h2));
j1=((u1)./(u2));
j2=((d1)./(d2));
j3=((v1)./(v2));
j4=((k1)./(k2));
q1=(2*(j1*((e1*e2)+(e3*e4))+(j2*((e3*e4)-(e1*e2))-(l*e5))));
q2=((j3+j4)*(1/2)*((e1*e2)+(e3*e4)));
q3=((j3*(h*(b1*b2)+(b3*b4))));
q4=((j4*(f*(b1*b2)+(b3*b4))));
q5=(j3*(erfc(x*sqrt(pr))));
q6=(j4*erfc(x*sqrt(sc)));
q7=(j3*(h*((c1*c2)+(c3*c4))));
q8=(j4*(f*((l1*l2)+(l3*l4))));
q=(q1+q2-q3-q4-q5-q6+q7+q8);
fplot(z,q);
xlim([0 5])
ylim([0 1])
title('Axial velocity profiles for different values of gr & gc');