Advanced Search

KIRAN SAJJAN

40 Reputation

7 Badges

2 years, 173 days
Contact KIRAN SAJJAN

MaplePrimes Activity


These are replies submitted by KIRAN SAJJAN

@tomleslie By Referring below work ...

KIRAN SAJJAN 40
February 23 2023
0 0

@tomleslie By Referring below work seat how can i plot similar graphs for  my equation i want to plot U'(Y) versus Y  and Theta (Y) versus Y with differnt values of M = 0.5,1, 1.5

And table values  of Cf and Nu with Different values of M=0.5,1,1.5

@tomleslie  can we get similar tabl...

KIRAN SAJJAN 40
February 23 2023
0 0

@tomleslie  can we get similar table values and graphs in HPM method above given file need to match the answer for both the method 

but i have observed in the hpm code table values and Q as well as Theta_b values also not matching single degit for different values of parameter like M=3, Pr=7.2 and N=0.1

for any value not matching with numerical solution

thank you

in Q and Theta _b...

KIRAN SAJJAN 40
February 23 2023
0 0

@tomleslie  why you used in Q integration of U(Y) limit is 0 to 1 but u have given U(Y)(Y) what it means sir similarly in theta B also

By Referring below work seat...

KIRAN SAJJAN 40
February 22 2023
0 0

@tomleslie By Referring below work seat how can i plot similar graphs for  my equation i want to plot U'(Y) versus Y  and Theta (Y) versus Y with differnt values of M = 0.5,1, 1.5

And table values  of Cf and Nu with Different values of M=0.5,1,1.5

nanofluid_BVP_Sheikholeslami.mw

@tomleslie  can we plot the stream ...

KIRAN SAJJAN 40
February 22 2023
0 0

@tomleslie  can we plot the stream lines for Nussel number and skinfriction with given parameter values sir

@tomleslie i have given mine govern...

KIRAN SAJJAN 40
February 21 2023
0 0

@tomleslie i have given mine governing equation sir.. Below i m given same equation from the base paper

@tomleslie Which answer needed sir. Ac...

KIRAN SAJJAN 40
February 21 2023
0 0

@tomleslie

Which answer needed sir.

According to that i will follow the things

@tomleslie any demo code already pl...

KIRAN SAJJAN 40
February 21 2023
0 0

@tomleslie any demo code already ploted is there share me according to that i will try to do the same

  >......

KIRAN SAJJAN 40
February 21 2023
0 0

NULL

> 

eqat := {M.(D(theta))(0)+2.*Pr.f(0) = 0, diff(phi(eta), eta, eta)+2.*Sc.f(eta).(diff(phi(eta), eta))-(1/2)*S.Sc.eta.(diff(phi(eta), eta))+N[t]/N[b].(diff(theta(eta), eta, eta)) = 0, diff(g(eta), eta, eta)-2.*(diff(f(eta), eta)).g(eta)+2.*f(eta).(diff(g(eta), eta))-S.(g(eta)+(1/2)*eta.(diff(g(eta), eta)))-1/(sigma.Re[r]).((1+LinearAlgebra:-HermitianTranspose(d).exp(-eta))/(1+d.exp(-eta))).g(eta)-LinearAlgebra:-HermitianTranspose(beta).((1+LinearAlgebra:-HermitianTranspose(d).exp(-eta))^2/sqrt(1+d.exp(-eta))).g(eta).sqrt((diff(f(eta), eta))^2+g(eta)^2) = 0, diff(theta(eta), eta, eta)+2.*Pr.f(eta).(diff(theta(eta), eta))-(1/2)*S.Pr.eta.(diff(theta(eta), eta))+N[b].Pr.((diff(theta(eta), eta)).(diff(phi(eta), eta)))+N[t].Pr.((diff(theta(eta), eta))^2)+4/3.N.(diff((C[T]+theta(eta))^3.(diff(theta(eta), eta)), eta)) = 0, diff(f(eta), eta, eta, eta)-(diff(f(eta), eta))^2+2.*f(eta).(diff(f(eta), eta))+g(eta)^2-S.(diff(f(eta), eta)+(1/2)*eta.(diff(f(eta), eta, eta)))-1/(sigma.Re[r]).((1+LinearAlgebra:-HermitianTranspose(d).exp(-eta))/(1+d.exp(-eta))).(diff(f(eta), eta))-LinearAlgebra:-HermitianTranspose(beta).((1+LinearAlgebra:-HermitianTranspose(d).exp(-eta))^2/sqrt(1+d.exp(-eta))).(diff(f(eta), eta)).sqrt((diff(f(eta), eta))^2+g(eta)^2) = 0, g(0) = 1, g(6) = 0, phi(0) = 1, phi(6) = 0, theta(0) = 1, theta(6) = 0, (D(f))(0) = 1, (D(f))(6) = 0}
> 

sys1 := eval(eqat, {M = 0, N = 2, Pr = .8, S = -2.5, Sc = .5, d = 2, sigma = .2, C[T] = .5, N[b] = .4, N[t] = .4, Re[r] = 1.1, LinearAlgebra:-HermitianTranspose(beta) = .2, LinearAlgebra:-HermitianTranspose(d) = 1.5})
> 

sys2 := eval(eqat, {M = 0, N = 2, Pr = .8, S = -2.5, Sc = .5, d = 2, sigma = .2, C[T] = .5, N[b] = .4, N[t] = .4, Re[r] = 1.1, LinearAlgebra:-HermitianTranspose(beta) = .4, LinearAlgebra:-HermitianTranspose(d) = 1.5})
> 

sys3 := eval(eqat, {M = 0, N = 2, Pr = .8, S = -2.5, Sc = .5, d = 2, sigma = .2, C[T] = .5, N[b] = .4, N[t] = .4, Re[r] = 1.1, LinearAlgebra:-HermitianTranspose(beta) = .6, LinearAlgebra:-HermitianTranspose(d) = 1.5})
> 

sys4 := eval(eqat, {M = 0, N = 2, Pr = .8, S = -2.5, Sc = .5, d = 2, sigma = .2, C[T] = .5, N[b] = .4, N[t] = .4, Re[r] = 1.1, LinearAlgebra:-HermitianTranspose(beta) = .8, LinearAlgebra:-HermitianTranspose(d) = 1.5})
> 

sys5 := eval(eqat, {M = .5, N = 2, Pr = .8, S = -2.5, Sc = .5, d = 2, sigma = .2, C[T] = .5, N[b] = .4, N[t] = .4, Re[r] = 1.1, LinearAlgebra:-HermitianTranspose(beta) = .2, LinearAlgebra:-HermitianTranspose(d) = 1.5})
> 

sys6 := eval(eqat, {M = .5, N = 2, Pr = .8, S = -2.5, Sc = .5, d = 2, sigma = .2, C[T] = .5, N[b] = .4, N[t] = .4, Re[r] = 1.1, LinearAlgebra:-HermitianTranspose(beta) = .4, LinearAlgebra:-HermitianTranspose(d) = 1.5})
> 

sys7 := eval(eqat, {M = .5, N = 2, Pr = .8, S = -2.5, Sc = .5, d = 2, sigma = .2, C[T] = .5, N[b] = .4, N[t] = .4, Re[r] = 1.1, LinearAlgebra:-HermitianTranspose(beta) = .6, LinearAlgebra:-HermitianTranspose(d) = 1.5})
> 

sys8 := eval(eqat, {M = .5, N = 2, Pr = .8, S = -2.5, Sc = .5, d = 2, sigma = .2, C[T] = .5, N[b] = .4, N[t] = .4, Re[r] = 1.1, LinearAlgebra:-HermitianTranspose(beta) = .8, LinearAlgebra:-HermitianTranspose(d) = 1.5})
> 

sys9 := eval(eqat, {M = 1, N = 2, Pr = .8, S = -2.5, Sc = .5, d = 2, sigma = .2, C[T] = .5, N[b] = .4, N[t] = .4, Re[r] = 1.1, LinearAlgebra:-HermitianTranspose(beta) = .2, LinearAlgebra:-HermitianTranspose(d) = 1.5})
> 

sys10 := eval(eqat, {M = 1, N = 2, Pr = .8, S = -2.5, Sc = .5, d = 2, sigma = .2, C[T] = .5, N[b] = .4, N[t] = .4, Re[r] = 1.1, LinearAlgebra:-HermitianTranspose(beta) = .4, LinearAlgebra:-HermitianTranspose(d) = 1.5})
> 

sys11 := eval(eqat, {M = 1, N = 2, Pr = .8, S = -2.5, Sc = .5, d = 2, sigma = .2, C[T] = .5, N[b] = .4, N[t] = .4, Re[r] = 1.1, LinearAlgebra:-HermitianTranspose(beta) = .6, LinearAlgebra:-HermitianTranspose(d) = 1.5})
> 

sys12 := eval(eqat, {M = 1, N = 2, Pr = .8, S = -2.5, Sc = .5, d = 2, sigma = .2, C[T] = .5, N[b] = .4, N[t] = .4, Re[r] = 1.1, LinearAlgebra:-HermitianTranspose(beta) = .8, LinearAlgebra:-HermitianTranspose(d) = 1.5})
> 

sys13 := eval(eqat, {M = 1.5, N = 2, Pr = .8, S = -2.5, Sc = .5, d = 2, sigma = .2, C[T] = .5, N[b] = .4, N[t] = .4, Re[r] = 1.1, LinearAlgebra:-HermitianTranspose(beta) = .2, LinearAlgebra:-HermitianTranspose(d) = 1.5})
> 

sys14 := eval(eqat, {M = 1.5, N = 2, Pr = .8, S = -2.5, Sc = .5, d = 2, sigma = .2, C[T] = .5, N[b] = .4, N[t] = .4, Re[r] = 1.1, LinearAlgebra:-HermitianTranspose(beta) = .4, LinearAlgebra:-HermitianTranspose(d) = 1.5})
> 

sys15 := eval(eqat, {M = 1.5, N = 2, Pr = .8, S = -2.5, Sc = .5, d = 2, sigma = .2, C[T] = .5, N[b] = .4, N[t] = .4, Re[r] = 1.1, LinearAlgebra:-HermitianTranspose(beta) = .6, LinearAlgebra:-HermitianTranspose(d) = 1.5})
> 

sys16 := eval(eqat, {M = 1.5, N = 2, Pr = .8, S = -2.5, Sc = .5, d = 2, sigma = .2, C[T] = .5, N[b] = .4, N[t] = .4, Re[r] = 1.1, LinearAlgebra:-HermitianTranspose(beta) = .8, LinearAlgebra:-HermitianTranspose(d) = 1.5})

Download Nur(_Beta_star_Vs.M).mw

@tomleslie

These are the equation and Bc for the plot with different parameters here i kept demo figures from other research paper i want plot the similar

@tomleslie Those plots are demo plots f...

KIRAN SAJJAN 40
February 21 2023
0 0

@tomleslie

Those plots are demo plots from different paper i need to plot similar for the given parameter values in the equation with different values of M(M=1, M=2,M=3) and other parameters kept constant mentioned in the above equation 

@nm restart; N := 0; g := 1; A := 1...

KIRAN SAJJAN 40
February 16 2023
0 0

@nm 

restart; N := 0; g := 1; A := 1; B := 0; M := 1; lambda := 1; Ec := 1; OdeSys := diff(U(Y), Y, Y)+Theta(Y)+N*(Theta(Y)*Theta(Y))-(M*M)*U(Y), diff(Theta(Y), Y, Y)+Ec*(diff(U(Y), Y))^2; Cond := U(0) = lambda*(D(U))(0), Theta(0) = A+g*(D(Theta))(0), U(1) = 0, Theta(1) = B; Ans := dsolve([OdeSys, Cond], numeric, output = listprocedure);
NULL;
NUMERIC := [(eval(diff(U(Y), Y), Ans))(.5), (eval(U(Y), Ans))(.5)];

I m getting the numericala ans but i want analytical solution expression with same boundary condition is it possible?

@Carl Love  reference fig i kept si...

KIRAN SAJJAN 40
February 12 2023
0 0

@Carl Love  reference fig i kept sir.

 I have given the all parameter ranges in my code

Error clarification for the given code...

KIRAN SAJJAN 40
February 12 2023
0 0

surface_EX1.mw  @tomleslie

I m not able to find my error. I want to draw the Two-D plots what are the mistake check it sir.

I want draw like below mentioned plots

Thank you

Required values of the code...

KIRAN SAJJAN 40
February 02 2023
0 0

@KIRAN SAJJAN

These vales i needed i m getting wrong values 

Getting wrong values of hpm methof...

KIRAN SAJJAN 40
February 02 2023
0 0

Here I m getting wrong answer for f(x), Theta(x), and phi(x)
 

``

> 

restart:
> 

PDEtools[declare](f(x), prime = x)

` f`(x)*`will now be displayed as`*f

  

`derivatives with respect to`*x*`of functions of one variable will now be displayed with '`

 (1)
> 

PDEtools[declare](Theta(x), prime = x)

` Theta`(x)*`will now be displayed as`*Theta

  

`derivatives with respect to`*x*`of functions of one variable will now be displayed with '`

 (2)
> 

PDEtools[declare](Phi(x), prime = x)

` Phi`(x)*`will now be displayed as`*Phi

  

`derivatives with respect to`*x*`of functions of one variable will now be displayed with '`

 (3)
> 

N := 3; M := .1; Kp := .1; Gr := 0.1e-1; Gc := 0.1e-1; Pr := 1; S := 0.1e-1; Sc := .78; Kc := 0.1e-1; La := 1

3

  

.1

  

.1

  

0.1e-1

  

0.1e-1

  

1

  

0.1e-1

  

.78

  

0.1e-1

  

1

 (4)
> 

``
> 

f (x):=  sum((p^(i))*f [i] (x), i = 0 .. N) ;

f[0](x)+p*f[1](x)+p^2*f[2](x)+p^3*f[3](x)

 (5)
> 

Theta(x):=  sum((p^(i))*Theta[i] (x), i = 0 .. N) ;

Theta[0](x)+p*Theta[1](x)+p^2*Theta[2](x)+p^3*Theta[3](x)

 (6)
> 

Phi(x):= sum((p^(i))*Phi [i] (x), i = 0 .. N);

Phi[0](x)+p*Phi[1](x)+p^2*Phi[2](x)+p^3*Phi[3](x)

 (7)
> 

HPMEq1 := (1-p)*(diff(f(x), x, x, x))+p*(diff(f(x), x, x, x)+(1/2)*(diff(f(x), x, x))*f(x)-(M^2+Kp)*(diff(f(x), x)-La)+Gr*Theta(x)+Gc*Phi(x))

(1-p)*(diff(diff(diff(f[0](x), x), x), x)+p*(diff(diff(diff(f[1](x), x), x), x))+p^2*(diff(diff(diff(f[2](x), x), x), x))+p^3*(diff(diff(diff(f[3](x), x), x), x)))+p*(diff(diff(diff(f[0](x), x), x), x)+p*(diff(diff(diff(f[1](x), x), x), x))+p^2*(diff(diff(diff(f[2](x), x), x), x))+p^3*(diff(diff(diff(f[3](x), x), x), x))+(1/2)*(diff(diff(f[0](x), x), x)+p*(diff(diff(f[1](x), x), x))+p^2*(diff(diff(f[2](x), x), x))+p^3*(diff(diff(f[3](x), x), x)))*(f[0](x)+p*f[1](x)+p^2*f[2](x)+p^3*f[3](x))-.11*(diff(f[0](x), x))-.11*p*(diff(f[1](x), x))-.11*p^2*(diff(f[2](x), x))-.11*p^3*(diff(f[3](x), x))+.11+0.1e-1*Theta[0](x)+0.1e-1*p*Theta[1](x)+0.1e-1*p^2*Theta[2](x)+0.1e-1*p^3*Theta[3](x)+0.1e-1*Phi[0](x)+0.1e-1*p*Phi[1](x)+0.1e-1*p^2*Phi[2](x)+0.1e-1*p^3*Phi[3](x))

 (8)
> 

HPMEq2 := (1-p)*(diff(Theta(x), x, x))/Pr+p*((diff(Theta(x), x, x))/Pr+(1/2)*(diff(Theta(x), x))*f(x)+S*Theta(x))

(1-p)*(diff(diff(Theta[0](x), x), x)+p*(diff(diff(Theta[1](x), x), x))+p^2*(diff(diff(Theta[2](x), x), x))+p^3*(diff(diff(Theta[3](x), x), x)))+p*(diff(diff(Theta[0](x), x), x)+p*(diff(diff(Theta[1](x), x), x))+p^2*(diff(diff(Theta[2](x), x), x))+p^3*(diff(diff(Theta[3](x), x), x))+(1/2)*(diff(Theta[0](x), x)+p*(diff(Theta[1](x), x))+p^2*(diff(Theta[2](x), x))+p^3*(diff(Theta[3](x), x)))*(f[0](x)+p*f[1](x)+p^2*f[2](x)+p^3*f[3](x))+0.1e-1*Theta[0](x)+0.1e-1*p*Theta[1](x)+0.1e-1*p^2*Theta[2](x)+0.1e-1*p^3*Theta[3](x))

 (9)
> 

HPMEq3 := (1-p)*(diff(Phi(x), x, x))/Sc+p*((diff(Phi(x), x, x))/Sc+(1/2)*(diff(Phi(x), x))*f(x)+Kc*Phi(x))

1.282051282*(1-p)*(diff(diff(Phi[0](x), x), x)+p*(diff(diff(Phi[1](x), x), x))+p^2*(diff(diff(Phi[2](x), x), x))+p^3*(diff(diff(Phi[3](x), x), x)))+p*(1.282051282*(diff(diff(Phi[0](x), x), x))+1.282051282*p*(diff(diff(Phi[1](x), x), x))+1.282051282*p^2*(diff(diff(Phi[2](x), x), x))+1.282051282*p^3*(diff(diff(Phi[3](x), x), x))+(1/2)*(diff(Phi[0](x), x)+p*(diff(Phi[1](x), x))+p^2*(diff(Phi[2](x), x))+p^3*(diff(Phi[3](x), x)))*(f[0](x)+p*f[1](x)+p^2*f[2](x)+p^3*f[3](x))+0.1e-1*Phi[0](x)+0.1e-1*p*Phi[1](x)+0.1e-1*p^2*Phi[2](x)+0.1e-1*p^3*Phi[3](x))

 (10)
> 

for i from 0 to N do equ[1][i] := coeff(HPMEq1, p, i) = 0 end do

diff(diff(diff(f[0](x), x), x), x) = 0

  

diff(diff(diff(f[1](x), x), x), x)+(1/2)*(diff(diff(f[0](x), x), x))*f[0](x)-.11*(diff(f[0](x), x))+.11+0.1e-1*Theta[0](x)+0.1e-1*Phi[0](x) = 0

  

diff(diff(diff(f[2](x), x), x), x)+(1/2)*(diff(diff(f[0](x), x), x))*f[1](x)+(1/2)*(diff(diff(f[1](x), x), x))*f[0](x)-.11*(diff(f[1](x), x))+0.1e-1*Theta[1](x)+0.1e-1*Phi[1](x) = 0

  

diff(diff(diff(f[3](x), x), x), x)+(1/2)*(diff(diff(f[0](x), x), x))*f[2](x)+(1/2)*(diff(diff(f[1](x), x), x))*f[1](x)+(1/2)*(diff(diff(f[2](x), x), x))*f[0](x)-.11*(diff(f[2](x), x))+0.1e-1*Theta[2](x)+0.1e-1*Phi[2](x) = 0

 (11)
> 

for i from 0 to N do equ[2][i] := coeff(HPMEq2, p, i) = 0 end do

diff(diff(Theta[0](x), x), x) = 0

  

diff(diff(Theta[1](x), x), x)+(1/2)*(diff(Theta[0](x), x))*f[0](x)+0.1e-1*Theta[0](x) = 0

  

diff(diff(Theta[2](x), x), x)+(1/2)*(diff(Theta[0](x), x))*f[1](x)+(1/2)*(diff(Theta[1](x), x))*f[0](x)+0.1e-1*Theta[1](x) = 0

  

diff(diff(Theta[3](x), x), x)+(1/2)*(diff(Theta[0](x), x))*f[2](x)+(1/2)*(diff(Theta[1](x), x))*f[1](x)+(1/2)*(diff(Theta[2](x), x))*f[0](x)+0.1e-1*Theta[2](x) = 0

 (12)
> 

for i from 0 to N do equ[3][i] := coeff(HPMEq3, p, i) = 0 end do

1.282051282*(diff(diff(Phi[0](x), x), x)) = 0

  

1.282051282*(diff(diff(Phi[1](x), x), x))+(1/2)*(diff(Phi[0](x), x))*f[0](x)+0.1e-1*Phi[0](x) = 0

  

1.282051282*(diff(diff(Phi[2](x), x), x))+(1/2)*(diff(Phi[0](x), x))*f[1](x)+(1/2)*(diff(Phi[1](x), x))*f[0](x)+0.1e-1*Phi[1](x) = 0

  

1.282051282*(diff(diff(Phi[3](x), x), x))+(1/2)*(diff(Phi[0](x), x))*f[2](x)+(1/2)*(diff(Phi[1](x), x))*f[1](x)+(1/2)*(diff(Phi[2](x), x))*f[0](x)+0.1e-1*Phi[2](x) = 0

 (13)

cond[1][0] := f[0](0) = 0, (D(f[0]))(0) = 0, Theta[0](0) = 1, Phi[0](0) = 1, Theta[0](5) = 0, Phi[0](5) = 0, (D(f[0]))(5) = 1; for j to N do cond[1][j] := f[j](0) = 0, (D(f[j]))(0) = 0, Theta[j](0) = 0, Phi[j](0) = 0, Theta[j](5) = 0, Phi[j](5) = 0, (D(f[j]))(5) = 0 end do

> 

ans := dsolve({cond[1][0], equ[1][0], equ[2][0], equ[3][0]})

{Phi[0](x) = -(1/5)*x+1, Theta[0](x) = -(1/5)*x+1, f[0](x) = (1/10)*x^2}

 (14)

for k to 3 do ans := `union`(ans, dsolve({cond[1][k], (eval({equ[1][k], equ[2][k], equ[3][k]}, ans))[]})) end do; for j from 0 to 3 do f[j](x) = eval(f[j](x), `~`[evalf](ans)) end do; for j from 0 to 3 do Theta[j](x) = eval(Theta[j](x), `~`[evalf](ans)) end do; for j from 0 to 3 do Phi[j](x) = eval(Phi[j](x), `~`[evalf](ans)) end do

Phi[3](x) = 0.1061288360e-7*x^10-0.2402855688e-7*x^9+0.7248453644e-6*x^8-0.9648079535e-5*x^7+0.4540935411e-6*x^6-0.4470852750e-5*x^5+0.5843971476e-3*x^4+0.1037090128e-3*x^3+0.8513437276e-2*x

 (15)

"Theta(x):= evalf(eval(Theta(x), ans)); convert(Theta(x),'rational'); subs(x=1,Theta(x));"

0.1561249804e-1

 (16)

"f(x):= evalf(eval(f(x), ans)); convert(f(x),'rational'); subs(x=1,f(x))"

-0.1358056204e-1

 (17)

"Phi(x):= evalf(eval(Phi(x), ans)); convert(Phi(x),'rational'); subs(x=1, Phi(x));"

0.9188590027e-2

 (18)

``


 

Download ham_final-1.mw

1 2 3 4 5 6 Page 5 of 6