DS N 3 : Modélisation électrocinétique d`ondes thermiques

◦3

d= 15,0λ
R= 8,00 Ω
U0= 6,00
T0= 293 20,0◦
z−−→
grad T

~
jQ
z > 0~ jQ(z= 0) R U0d
~
jQ
T(z)
T(z)T(L)
z1= 8 z2= 16
T1= 46,4◦T2= 41,4◦
λ
Dm
c
U(t)
T(z, t)
λ cp= 380 −1−1
ρ= 8870 −3
D2−1
D
r
c

r c
D
D= 1,19.10−4 2 −1
∆t
z1
z2=z1+ ∆z
L= 50
z z + dz
U(t) =
U0cos(Ωt)
T(z, t) = T(z)+
θm(z) cos(ωt +ϕ(z))
T(z1, t)T(z2, t)
z1= 8 z2= 16
θm(z1)θm(z2)ϕ(z2)−
ϕ(z1)
p(t) = P0+P0cos(ωt)P0U0R ω
Ω
θ(z, t) = T(z, t)−T(z)
θm(z)ϕ(z)
θ(z, t)θ(z, t) = Aexp(j(ωt −Kz))
K

K
K=1−j
δ=±1
δ λ ρ cpω
δ r c ω
θm(z)ϕ(z)θm(z= 0) = θ0
θ0
R C