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Question: plot f'', theta prime? at eta 0 only,, varies Pr with f'' or theta prime

Question:plot f'', theta prime? at eta 0 only,, varies Pr with f'' or theta prime

faisal 15
plotting
December 14 2017
0

My Question

how may i know which is the theta prime or f double prime or theta only or f prime and theta double prime?

 i have attach double prime

tq maple
 

> 

restart
> 

with(student)
> 

with(plots)
> 

inf := 3
> 

equ1 := (diff(f(eta), `$`(eta, 3)))/((1-`ϕ`)^2.5*(1-`ϕ`+`ϕ`*rho[s]/rho[f]))+(diff(f(eta), eta, eta))*f(eta)-(diff(f(eta), eta))^2+1+M*(1-(diff(f(eta), eta))) = 0
> 

equ2 := (1+4/(3*N*k))*(diff(theta(eta), eta, eta))+Pr*(1-`ϕ`+`ϕ`*rho[s]*Cp[s]/(rho[f]*Cp[f]))*(diff(theta(eta), eta))*f(eta)/k+Br*(diff(f(eta), eta, eta))^2/(k*(1-`ϕ`)^2.5) = 0
> 

Bcs := f(0) = 0, (D(f))(0) = `ε`, (D(f))(inf) = 1, theta(inf) = 0, theta(0) = 1
> 

Pr := 6.2; Cp[s] := 385; Cp[f] := 4179; `ϕ` := .1; rho[f] := 997.1; rho[s] := 8933; k[s] := 400; k[f] := .613; k := (k[s]+2*k[f]-2*`ϕ`*(k[f]-k[s]))/(k[s]+2*k[f]+`ϕ`*(k[f]-k[s])); Br := .1; M := 1; N := 1
> 

func := proc (v) options operator, arrow; rhs((dsolve({equ1, equ2, subs(`ε` = v, [Bcs])[]}, numeric))(0)[3])/(1-`ϕ`)^2.5 end proc; plot(func, -1 .. 1, title = typeset((diff(f(eta), eta, eta))*versus*`ε`/(1-'`ϕ`')^2.5), titlefont = [times, italic, 18])

 
> 

func2 := proc (v) options operator, arrow; rhs((dsolve({equ1, equ2, subs(`ε` = v, [Bcs])[]}, numeric))(0)[5]) end proc; plot(func2, -1 .. 1, title = typeset((diff(theta(eta), eta))*versus*`ε`), titlefont = [times, italic, 18])

 
> 

``


 

Download plot.mw
 

> 

restart
> 

with(student)
> 

with(plots)
> 

inf := 3
> 

equ1 := (diff(f(eta), `$`(eta, 3)))/((1-`ϕ`)^2.5*(1-`ϕ`+`ϕ`*rho[s]/rho[f]))+(diff(f(eta), eta, eta))*f(eta)-(diff(f(eta), eta))^2+1+M*(1-(diff(f(eta), eta))) = 0
> 

equ2 := (1+4/(3*N*k))*(diff(theta(eta), eta, eta))+Pr*(1-`ϕ`+`ϕ`*rho[s]*Cp[s]/(rho[f]*Cp[f]))*(diff(theta(eta), eta))*f(eta)/k+Br*(diff(f(eta), eta, eta))^2/(k*(1-`ϕ`)^2.5) = 0
> 

Bcs := f(0) = 0, (D(f))(0) = `ε`, (D(f))(inf) = 1, theta(inf) = 0, theta(0) = 1
> 

Pr := 6.2; Cp[s] := 385; Cp[f] := 4179; `ϕ` := .1; rho[f] := 997.1; rho[s] := 8933; k[s] := 400; k[f] := .613; k := (k[s]+2*k[f]-2*`ϕ`*(k[f]-k[s]))/(k[s]+2*k[f]+`ϕ`*(k[f]-k[s])); Br := .1; M := 1; N := 1
> 

func := proc (v) options operator, arrow; rhs((dsolve({equ1, equ2, subs(`ε` = v, [Bcs])[]}, numeric))(0)[3])/(1-`ϕ`)^2.5 end proc; plot(func, -1 .. 1, title = typeset((diff(f(eta), eta, eta))*versus*`ε`/(1-'`ϕ`')^2.5), titlefont = [times, italic, 18])

 
> 

func2 := proc (v) options operator, arrow; rhs((dsolve({equ1, equ2, subs(`ε` = v, [Bcs])[]}, numeric))(0)[5]) end proc; plot(func2, -1 .. 1, title = typeset((diff(theta(eta), eta))*versus*`ε`), titlefont = [times, italic, 18])

 
> 

``


 

Download plot.mw

 
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