imparter

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These are questions asked by imparter

hai, 
greetings,

I require help to plot graphs by changing differernt parameters. i am enclosing my codes and sample codes,

 my_codes.mw

nanofluid_sample.mw

Thanks in advance.

Hai any one help me to plot the curves and remove the errors  i am attaching the codes and  sample graph. thanks in advanced.
 

 

test.mw

 

 

I am unable to the get the output  in ans2 , error is comming

 

restart:
with(DETools):
with(PDEtools):
u[o](r,z):=(-1/4)*diff(p[o](z),z)*(1-r^2):
ode:=gamma1*diff(u[o](r,z),z)+(1/r)*diff(v[1](r)*r,r)=0:
#dsolve( (ode), { v[1](r) } ):
IC1 := {v[1](0) = 0}:
ans2 := combine(dsolve(`union`(ode, IC1),{v[1](r)}));
 

I am unable to integrate this equation

restart:
with(DETools):
with(IntegrationTools):
u[1](r,z):=(C[o]^2*exp(2*lambda*z)-D[o]^2*exp(-2*lambda*z))+(lambda/2)*(C[o]*exp(lambda*z)-D[o]*exp(-lambda*z))*(1-r^4)+A[1](z)*r^2:
M1:=int(u[1](r,z), z):
 

 How to display the result in the desired form in partial differential equation and also collect the same terms

i am attaching sample codes

restart:
with(DETools):
P[o](z):=C[o]*exp(lambda*z)+D[o]*exp(-lambda*z):
u[o](r,z):=(1-r^2)*diff(P[o](z),z):
v[o](r,z):=(2*r-r^3)*diff(P[o](z),z,z):
A1:=P[o](z)*u[o](r,z):
# we want the result out put  like this
A1 := lambda*(C[o]^2*exp(2*lambda*z)-D[o]^2*exp(-2*lambda*z))*(1-r^2):
A2:=P[o](z)*(1+r^2)+v[o](r,z)+A1:
#we want the  resultant output like this
A2:=lambda^2*(C[o]*exp(lambda*z)+D[o]*exp(-lambda*z))*(1+r^2+2*r-r^3)+A1:
 

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