- #1
big dream
a microchannel of length 2L and width h in the thermal cycling region. the temperature profile
...(1)
the cyclic temperature profile leads to a time dependent density
...(2)
using the mass conservation equation i.e.
...(3)
and momentum balance equation i.e.
...(4)
we have to find the exact solution of u, v & p
The attempt at a solution
equ(1) →
equ(2) →
length scales are normalised as
so equ(2) becomes
no slip & no penetration boundary condition at the walls (y=0,h) ; and constant pressure at channel entrance(x=-L) and exit(x=L). for small reynolds number eq(3) becomes
this equation normalised as
as
and from
we can get
&
is it the right process?
the cyclic temperature profile leads to a time dependent density
using the mass conservation equation i.e.
and momentum balance equation i.e.
we have to find the exact solution of u, v & p
The attempt at a solution
equ(1) →
equ(2) →
length scales are normalised as
so equ(2) becomes
no slip & no penetration boundary condition at the walls (y=0,h) ; and constant pressure at channel entrance(x=-L) and exit(x=L). for small reynolds number eq(3) becomes
this equation normalised as
as
and from
we can get
&
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