  We study hydrodynamics, heat transfer and entropy generation in
pressure-driven microchannel flow of a power-law fluid. Specifically, we
address the effect of asymmetry in the slip boundary condition at the channel
walls. Constant, uniform but unequal heat fluxes are imposed at the walls in
this thermally developed flow. The effect of asymmetric slip on the velocity
profile, on the wall shear stress, on the temperature distribution, on the
Bejan number profiles, and on the average entropy generation and the Nusselt
number are established through the numerical evaluation of exact analytical
expressions derived. Specifically, due to asymmetric slip, the fluid momentum
flux and thermal energy flux are enhanced along the wall with larger slip,
which in turn shifts the location of the velocity's maximum to an off-center
location closer to the said wall. Asymmetric slip is also shown to redistribute
the peaks and plateaus of the Bejan number profile across the microchannel,
showing a sharp transition between entropy generation due to heat transfer and
due to fluid flow at an off-center-line location. In the presence of asymmetric
slip, the difference in the imposed heat fluxes leads to starkly different
Bejan number profiles depending on which wall is hotter, and whether the fluid
is shear-thinning or shear-thickening. Overall, slip is shown to promote
uniformity in both the velocity field and the temperature field, thereby
reducing irreversibility in this flow.
