a microchannel of length 2L and width h in the thermal cycling region. the temperature profile .....(1)(adsbygoogle = window.adsbygoogle || []).push({});

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?

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Velocity in microchannel with temporal temperature variation

Have something to add?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**