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?