Advanced Search

Question: Cannot solve with dsolve the self similarity problem for external natural convection (boundary layer and Boussinesq approximation)

Question:Cannot solve with dsolve the self similarity problem for external natural convection (boundary layer and Boussinesq approximation)

jetboo 45 Maple 2021
ode homework dsolve numeric differential-equations
February 08 2023
0

Hello,

I am trying to solve the self similarity problem for external natural convection which is the following coupled problem

  •     3/4*F(eta)*Theta(eta)'  = Theta(eta)''
  •     1/2 (F(eta)')^2 - 3/4 F(eta)*F(eta)'' = Pr*(Theta(eta) - F(eta)''')

where Pr is a constant and  ()' denotes differentiation with respect to eta. The boundary conditions are:

  •     at eta = 0, F = 0, F'=0, Theta = 1
  •     at eta -> infinity, F' = 0, Theta = 0

I tried the following but I cannot obtain a solution

``

> 

Pr:=1

1

 (1)
> 

etamax := infinity

infinity

 (2)

``

> 

eq:= 3/4*F(eta)*diff(theta(eta),eta) = diff(theta(eta),eta,eta),1/Pr*(1/2*diff(F(eta),eta)^2 - 3/4*F(eta)*diff(F(eta),eta,eta)) = -diff(F(eta),eta,eta,eta) + theta(eta)

(3/4)*F(eta)*(diff(theta(eta), eta)) = diff(diff(theta(eta), eta), eta), (1/2)*(diff(F(eta), eta))^2-(3/4)*F(eta)*(diff(diff(F(eta), eta), eta)) = -(diff(diff(diff(F(eta), eta), eta), eta))+theta(eta)

 (3)

NULL

> 

 

NULL

> 

bcs := F(0) = 0, theta(0)=1, D(F)(0)=0,theta(etamax)=0,D(F)(etamax)=0

F(0) = 0, theta(0) = 1, (D(F))(0) = 0, theta(infinity) = 0, (D(F))(infinity) = 0

 (4)

NULL

> 

sol:=dsolve([eq,bcs],[F(eta),theta(eta)])

``

Download wip.mw
Please Wait...