kill(all)$

maxima : convection -diffusion (constraint =continuity equation),version 1.0
peter.vlasschaert@gmail.com,18/10/2022

load packages
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load(lrats)$

convection - diffusion , constraint : continuity  (x-direction)
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ρ = density fluid
u = velocity x-direction fluid
Φ = function ( see below ,Φ(x))
Γ = diffusion coef.

diff(ρ*u);

depends([u,ρ],x);

→ flow satisfy : continuity

p1:'diff(ρ*u,x)=diff(ρ*u,x);

equation :

p1a: lhs(p1) =0;
p1b: rhs(p1) =0;

depends(Φ,x);

→ advection term

p2:diff(ρ*u*Φ,x);

apply : continuity equation {p1a or p1b}

p2a:lratsubst([p1b],p2);

→ diffusion term :

p3: 'diff(Γ*'diff(Φ,x),x);

final : incompressible flow,satisfy continuity equation
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time independent. (x-direction)

→ combine : advection = diffusion.

p4:p2a-p3=0;

Γ = diffusion coef. = constant

declare(Γ, constant);

p4a:ev(p4,nouns);

will be used : to solve boundary value problem.
see : website
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maxima : convection -diffusion problem (exact : solution),version 1.0
ode2 : p4a                  
bc : Φ(0) = 1  ...  (1)
       Φ(L) = 0 .... (2)
bc : (b)oundary (c)ondition
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