Abstract: To achieve reliable solutions, today-s numerical and
experimental activities need developing more accurate methods and
utilizing expensive facilities, respectfully in microchannels. The analytical
study can be considered as an alternative approach to alleviate
the preceding difficulties. Among the analytical solutions, those with
high robustness and low complexities are certainly more attractive.
The perturbation theory has been used by many researchers to analyze
microflows. In present work, a compressible microflow with constant
heat flux boundary condition is analyzed. The flow is assumed to be
fully developed and steady. The Mach and Reynolds numbers are also
assumed to be very small. For this case, the creeping phenomenon
may have some effect on the velocity profile. To achieve robustness
solution it is assumed that the flow is quasi-isothermal. In this study,
the creeping term which appears in the slip boundary condition
is formulated by different mathematical formulas. The difference
between this work and the previous ones is that the creeping term
is taken into account and presented in non-dimensionalized form.
The results obtained from perturbation theory are presented based
on four non-dimensionalized parameters including the Reynolds,
Mach, Prandtl and Brinkman numbers. The axial velocity, normal
velocity and pressure profiles are obtained. Solutions for velocities
and pressure for two cases with different Br numbers are compared
with each other and the results show that the effect of creeping
phenomenon on the velocity profile becomes more important when
Br number is less than O(ε).
Abstract: The effect of streamwise conduction on the thermal
characteristics of forced convection for nanofluidic flow in
rectangular microchannel heat sinks under isothermal wall has been
investigated. By applying the fin approach, models with and without
streamwise conduction term in the energy equation were developed
for hydrodynamically and thermally fully-developed flow. These two
models were solved to obtain closed form analytical solutions for the
nanofluid and solid wall temperature distributions and the analysis
emphasized details of the variations induced by the streamwise
conduction on the nanofluid heat transport characteristics. The effects
of the Peclet number, nanoparticle volume fraction, thermal
conductivity ratio on the thermal characteristics of forced convection
in microchannel heat sinks are analyzed. Due to the anomalous
increase in the effective thermal conductivity of nanofluid compared
to its base fluid, the effect of streamwise conduction is expected to be
more significant. This study reveals the significance of the effect of
streamwise conduction under certain conditions of which the
streamwise conduction should not be neglected in the forced
convective heat transfer analysis of microchannel heat sinks.