A note on the unsteady boundary layers over a flat plate

The unsteady boundary layer over a semi-infinite flat plate was investigated in this paper. The flow involves the unsteady flow over a flat plate with leading edge accretion or ablation. The momentum boundary layer was further analyzed and it was shown that the leading edge ablation had a similar effect to the wall mass injection or upstream wall movement making the fluid blown away from the wall. The thermal boundary layer of the same flow was also studied. Results show that the leading edge accretion or ablation can greatly change the fluid motion and the heat transfer characteristics.     

The moduli space of flat SU (2) and SO (3) connections over surfaces

All the connected components of the moduli space of flat connections on SU (2) and SO (3) (trivial and non-trivial) bundles over closed oriented surfaces are determined. The symplectic structure and volumes of the non-maximal strata of the moduli space are also determined.     

η-Invariant and Flat Vector Bundles

Abstract We present an alternate definition of the mod Z component of the Atiyah-Patodi-Singer η invariant associated to (not necessary unitary) flat vector bundles, which identifies explicitly its real and imaginary parts. This is done by combining a deformation of flat connections introduced in a previous paper with the analytic continuation procedure appearing in the original article of Atiyah, Patodi and Singer. * Project supported by the Cheung-Kong Scholarship of the Ministry of Education of China and the 973 Project of the Ministry of Science and Technology of China. (Dedicated to the memory of Shiing-Shen Chern)     

微型热驱动热声热机热端换热器的优化设计

该文基于热声环境,采用厘米级扁管和deltaE数值计算对微型热声换热器进行了优化设计。     

Elliptic fibers over non-perfect residue fields

Kodaira and Néron classified and described the geometry of the special fibers of the Néron model of an elliptic curve defined over a discrete valuation ring with a perfect residue field. Tate described an algorithm to determine the special fiber type by manipulating the Weierstrass equation. In the case of non-perfect residue fields, we discover new fiber types which are not on the Kodaira-Néron list. We describe these new types and extend Tate's algorithm to deal with all discrete valuation rings. Specifically, we show how to translate a Weierstrass equation into a form where the reduction type may be easily determined. Having determined the special fiber type, we construct the regular model of the curve with explicit blow-up calculations. We also provide tables that serve as a simple reference for the algorithm and which succinctly summarize the results.     

Boiling heat transfer characteristics of nanofluids in a flat heat pipe evaporator with micro-grooved heating surface

An experimental study was performed to understand the nucleate boiling heat transfer of water–CuO nanoparticles suspension (nanofluids) at different operating pressures and different nanoparticle mass concentrations. The experimental apparatus is a miniature flat heat pipe (MFHP) with micro-grooved heat transfer surface of its evaporator. The experimental results indicate that the operating pressure has great influence on the nucleate boiling characteristics in the MFHP evaporator. The heat transfer coefficient and the critical heat flux (CHF) of nanofluids increase greatly with decreasing pressure as compared with those of water. The heat transfer coefficient and the CHF of nanofluids can increase about 25% and 50%, respectively, at atmospheric pressure whereas about 100% and 150%, respectively, at the pressure of 7.4 kPa. Nanoparticle mass concentration also has significant influence on the boiling heat transfer and the CHF of nanofluids. The heat transfer coefficient and the CHF increase slowly with the increase of the nanoparticle mass concentration at low concentration conditions. However, when the nanoparticle mass concentration is over 1.0 wt%, the CHF enhancement is close to a constant number and the heat transfer coefficient deteriorates. There exists an optimum mass concentration for nanofluids which corresponds to the maximum heat transfer enhancement and this optimum mass concentration is 1.0 wt% at all test pressures. The experiment confirmed that the boiling heat transfer characteristics of the MFHP evaporator can evidently be strengthened by using water/CuO nanofluids.     

Left invariant special Kähler structures

We construct left invariant special Kähler structures on the cotangent bundle of a flat pseudo-Riemannian Lie group. We introduce the twisted cartesian product of two special Kähler Lie algebras according to two linear representations by infinitesimal Kähler transformations. We also exhibit a double extension process of a special Kähler Lie algebra which allows us to get all simply connected special Kähler Lie groups with bi-invariant symplectic connections. All Lie groups constructed by performing this double extension process can be identified with a subgroup of symplectic (or Kähler) affine transformations of its Lie algebra containing a nontrivial 1-parameter subgroup formed by central translations. We show a characterization of left invariant flat special Kähler structures using étale Kähler affine representations, exhibit some immediate consequences of the constructions mentioned above, and give several non-trivial examples.     

Coniveau of classes of flat bundles trivialized on a finite smooth covering of a complex manifold

On a smooth algebraic complex varietyX, we show that the classes of a flat bundle, which is trivialized on a finite cover ofX, with values in the odd-dimensional cohomology of the underlying complex manifold with / (i), are living in the bottom part of Grothendieck's coniveau filtration. This answers positively when the basis is smooth complex a question of Bruno Kahn [K-Theory (1992), conjecture 2].     

Compact flat manifolds with holonomy group

In this paper we construct a family of compact flat manifolds, for all dimensions , with holonomy group isomorphic to and first Betti number zero.

     

Modeling of the EHD effects on hydrodynamics and heat transfer within a flat miniature heat pipe including axial capillary grooves

A numerical model for an electrohydrodynamic (EHD) grooved Flat Miniature Heat Pipe (FMHP) is developed. Two microchannel shapes are considered as axial capillary structures: square and triangle grooves. For both groove shapes, the electric field affects the liquid-vapor radius of curvature which decreases in the condenser and increases in the evaporator under the action of the electric field. The liquid and vapor velocities are also affected by the EHD effects. The electric field effects on the velocities depend on the FMHP zone. It is also demonstrated that the electric field increases the vapor pressure drop; however, it decreases the liquid pressure drop. The liquid-wall and vapor-wall viscous forces as well as the shear liquid-vapor forces are affected by the electric field. The analysis of the electric forces shows that the dielectrophoretic forces which act on the liquid-vapor interface are predominant and their order of magnitude is much higher than the Coulomb forces. Finally, it is also demonstrated that the capillary limit increases with the electric field for both groove shapes.