faisal

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6 years, 197 days

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These are questions asked by faisal

help me on thispde_solutionalpha.mw
 

restart

M := 1; S := .78; K := .5; Sh := .2; alpha := .7; R := .3; N := .6; k := .5

pde1 := diff(u(y, t), t)+S.(diff(u(y, t), y))-2*k^2*u(y, t) = diff(u(y, t), y, y)+theta(y, t)+N.C(y, t)+M.u(y, t)+u(y, t)/K

                pde2 := theta(y, t)+t*(diff(theta(y, t), t))+S*(diff(theta(y, t), y)) = (diff(theta(y, t), y, y))/Pr-alpha.theta(y, t)

pde3 := C(y, t)+t*(diff(C(y, t), t))+S*(diff(C(y, t), y)) = (diff(C(y, t), y, y))/Sh-R.C(y, t)

PDE := unapply({pde || (1 .. 3)}, Pr)

proc (Pr) options operator, arrow; {C(y, t)+t*(diff(C(y, t), t))+.78*(diff(C(y, t), y)) = 5.000000000*(diff(diff(C(y, t), y), y))-.3*C(y, t), diff(u(y, t), t)+.78*(diff(u(y, t), y))-.50*u(y, t) = diff(diff(u(y, t), y), y)+theta(y, t)+.6*C(y, t)+3.000000000*u(y, t), theta(y, t)+t*(diff(theta(y, t), t))+.78*(diff(theta(y, t), y)) = (diff(diff(theta(y, t), y), y))/Pr-.7*theta(y, t)} end proc

(1)

IBC := {C(0, t) = 1, C(1, t) = 0, C(y, 0) = 0, theta(0, t) = 1, theta(1, t) = 0, theta(y, 0) = 0, u(0, t) = 0, u(1, t) = 0, u(y, 0) = 0}

``

PrList := [.71, 7, 10, 100]; Colours := table(`~`[`=`](PrList, ["blue", "red", "green", "cyan"])); for Pr in PrList do pds := pdsolve(PDE(Pr), IBC, numeric); Plots[Pr] := pds:-plot[display](u(y, t), t = .5, linestyle = "solid", colour = Colours[Pr], legend = sprintf("Pr=%2.2f", Pr), title = "Velocity Profile", labels = ["y", "theta"]) end do; plots:-display([seq(Plots[Pr], `in`(Pr, PrList))])

 

NULL


 

Download pde_solutionalpha.mw

 

how may i encounter this problem,

Please help me on this ode solve (dsolve) wit
 

restart

with(plots):

ps := 8933:

Eq1 := 8*(11-10*d)*(eta*(diff(f(eta), `$`(eta, 3)))+diff(f(eta), `$`(eta, 2)))/((1-phi)^2.5*(1-phi+phi*ps/pf))+4*f(eta)*(diff(f(eta), `$`(eta, 2)))+m*(1-4*(diff(f(eta), eta))*(diff(f(eta), eta))) = 0;

8*(11-10*d)*(eta*(diff(diff(diff(f(eta), eta), eta), eta))+diff(diff(f(eta), eta), eta))/((1-phi)^2.5*(1+7.958981045*phi))+4*f(eta)*(diff(diff(f(eta), eta), eta)) = 0

(1)

Eq2 := 2*knf*(eta*(diff(theta(eta), `$`(eta, 2)))+diff(theta(eta), eta))/(Pr*kf*(1-phi(eta)+phi*ps*cps/(pf*cpf)))+f(eta)*(diff(theta(eta), eta))-n*(diff(f(eta), eta))*theta(eta) = 0;

186.4367280*(eta*(diff(diff(theta(eta), eta), eta))+diff(theta(eta), eta))/(1-phi(eta)+.8253667629*phi)+f(eta)*(diff(theta(eta), eta)) = 0

(2)

Va := [.1, .1, .1]:

`Vφ` := [0.5e-1, 0.5e-1, 0.5e-1]:

etainf := 8:

bcs := f(a) = 0, (D(f))(a) = 0, theta(a) = 1, (D(f))(etainf) = 1/2, theta(etainf) = 0;

f(a) = 0, (D(f))(a) = 0, theta(a) = 1, (D(f))(8) = 1/2, theta(8) = 0

(3)

dsys := {Eq1, Eq2, bcs}:

for i to 3 do for h to 3 do phi := `Vφ`[i]; a := Va[h]; dsol[h][i] := dsolve(dsys, numeric, continuation = d); print(a); print(phi); print(dsol[h][i](0)) end do end do

Error, (in fproc) unable to store 'YP[3]' when datatype=float[8]

 

``


 

Download Grosan.mw

h bcs


Please help me on this :

restart; with(PDETools), with(plots)

n := .3:

Eq1 := (1-n)*(diff(f(x, y), `$`(y, 3)))+(1+x*cot(x))*f(x, y)*(diff(f(x, y), `$`(y, 2)))-(diff(f(x, y), y))/Da+(diff(f(x, y), y))^2+n*We*(diff(f(x, y), `$`(y, 2)))*(diff(f(x, y), `$`(y, 3)))+sin(x)*(theta(x, y)+phi(x, y))/x = x*((diff(f(x, y), y))*(diff(f(x, y), y, x))+(diff(f(x, y), `$`(y, 2)))*(diff(f(x, y), x))):

Eq2 := (diff(theta(x, y), `$`(y, 2)))/Pr+Nt*(diff(theta(x, y), y))^2/Pr+Nb*(diff(phi(x, y), y))*(diff(theta(x, y), y))/Pr+(1+x*cot(x))*f(x, y)*(diff(theta(x, y), y)) = x*((diff(f(x, y), y))*(diff(theta(x, y), x))+(diff(theta(x, y), y))*(diff(f(x, y), x))):

Eq3 := Nb*(diff(phi(x, y), `$`(y, 2)))/(tau*Pr)+Nt*(diff(theta(x, y), `$`(y, 2)))/(tau*Pr)+(1+x*cot(x))*f(x, y)*(diff(phi(x, y), y)) = x*((diff(f(x, y), y))*(diff(phi(x, y), x))+(diff(phi(x, y), y))*(diff(f(x, y), x))):

ValWe := [0, 5, 10]:

bcs := {Nb*(D[2](phi))(x, 0)+Nt*(D[2](theta))(x, 0) = 0, f(0, y) = ((1/12)*y)^2*(6-8*((1/12)*y)+3*((1/12)*y)^2), f(x, 0) = 0, phi(0, y) = -.5*y, phi(x, 12) = 0, theta(0, y) = (1-(1/12)*y)^2, theta(x, 0) = 1, theta(x, 12) = 0, (D[2](f))(x, 0) = Da^(1/2)*(D[2, 2](f))(x, 0)+Da*(D[2, 2, 2](f))(x, 0), (D[2](f))(x, 12) = 0}:

pdsys := {Eq1, Eq2, Eq3}:

p1 := ans[1]:-plot(theta(x, y), x = 1, color = blue):

plots[display]({p1, p2, p3})

 

``


 

Download untitle_2_(1).mw


Hello Dr/Prof?sir?madam

i have problem on running the ode bcs

there is cos n sine in ther ode

any idea to solve this ?

i have attched it

thnks
Maple Worksheet - Error

Failed to load the worksheet /maplenet/convert/Sc.mw .

Download Sc.mw

DEAR SIR,

PLEASE HELP ME WITH THAT QUESTION

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