[Moderator: long pasted output deleted - OP has provided file in reply]

How can I plot stream lines between two concentric spheres?

u := c1*BesselK(0, alpha1*r) + c2*BesselI(0, alpha1*r) + c3*BesselK(0, alpha2*r) + c4*BesselI(0, alpha2*r) - A1*k^2*(k^2 - (-alpha^2*j*s + 4*c*s)/c)*BesselK(0, k*r)/((-alpha1^2 + k^2)*(-alpha2^2 + k^2)) - B1*k^2*(k^2 - (-alpha^2*j*s + 4*c*s)/c)*BesselI(0, k*r)/((-alpha1^2 + k^2)*(-alpha2^2 + k^2)) + ur*(-alpha^2*j*s + 4*c*s)/(c*(1 + c));

w := (-1 - c)/(2*s*(4.*c - alpha^2*j))*collect(diff(diff(r*diff(u, r), r)/r, r) + (alpha^2 - 4*c*s)*diff(u, r)/(1 + c) - A1*k^3*BesselK(1, k*r) + B1*k^3*BesselI(1, k*r), [c1, c2, c3, c4], factor);

om := (-1)/2*diff(u, r)/r;

fn1 := collect(simplify(subs(subs(r = 1, u))), [c1, c2, c3, c4], factor);
fn2 := collect(simplify(subs(subs(r = sigma, u))), [c1, c2, c3, c4], factor);
fn3 := collect(simplify(subs(r = 1, w)), [c1, c2, c3, c4], factor);
fn4 := collect(simplify(subs(r = sigma, w)), [c1, c2, c3, c4], factor);
soln := simplify(solve({fn1 = 0, fn2 = 0, fn3 = 0, fn4 = 0}, {c1, c2, c3, c4}));

int((4*h1*lambda*k*BesselK(0, k*Zeta)/Zeta^3)*Zeta*BesselK(1, alpha*Zeta), Zeta = 1 .. infinity)

Can any one help me to find the values of this integral?

How can i plot stream lines by using velocity components (tx+1, -ty-t^2)? or by stream function?