Effect of variable thermal conductivity and viscosity on single phase convective heat transfer in slip flow

For a variety of fields in which micro-mechanical systems and electronic components are used, fluid flow and heat transfer at the microscale needs to be understood and modeled with an acceptable reliability. In general, models are prepared by making some extensions to the conventional theories by including the scaling effects that become important for microscale. Some of these effects are; axial conduction, viscous dissipation, and rarefaction. In addition to these effects, temperature variable thermal conductivity and viscosity may become important in microscale gas flows due to the high temperature gradients that may exist in the fluid. For this purpose, simultaneously developing, single phase, laminar and incompressible air flow in a microtube and in the micro gap between parallel plates is numerically analyzed. Navier–Stokes and energy equations are solved and the variation of Nusselt number along the channel is presented in tabular and graphical forms as a function of Knudsen, Peclet, and Brinkman numbers, including temperature variable thermal conductivity and viscosity.     

Primes in tuples II

We prove that

$ \mathop{ \lim \inf}\limits_{n \rightarrow \infty} \frac{p_{n+1}-p_{n}}{\sqrt{\log p_{n}} \left(\log \log p_{n}\right)^{2}}< \infty, $

where p _n denotes the nth prime. Since on average p _n+1?p _n is asymptotically log _n , this shows that we can always find pairs of primes much closer together than the average. We actually prove a more general result concerning the set of values taken on by the differences p?p′ between primes which includes the small gap result above.

     

Experimental investigation and numerical analysis: fracture mechanics and microstructural development in Ni55.8Ti superalloy under mixed-mode loading at different temperatures

Meccanica - Shape memory alloys (SMAs) and specifically NiTi superalloys have gained significant attention in different industries for their excellent mechanical properties and superior material...     

A relation between quasi-cyclic codes and 2-D cyclic codes

We consider a q-ary quasi-cyclic code C of length m? and index ?, where both m and ? are relatively prime to q. If the constituents of C are cyclic codes, we show that C can also be viewed as a 2-D cyclic code of size $m\times ?$ over ${\mathbb{F}}_q$. In case m and ? are also coprime to each other, we easily observe that the code C must be equivalent to a cyclic code, which was proved earlier by Lim.     

Density Functional Study of Physical and Chemical Properties of Nano Size Boron Clusters: Bn (n=13～20)

采用密度泛函理论B3LYP与6-311++G方法研究了硼簇B_n(n=13～20)的电子和几何结构、总能量、结合能、谐波频率、点对称性、电荷分布、偶极矩、化学键以及最高分子占据轨道和最低分子占轨道能量差．此外,借助第一和第二能级差确定最稳定的硼簇尺寸．研究表明硼簇几乎所有的物理性质有尺寸依赖性,双环管状结构的B₂₀具有最高平均结合能．内有一原子的二十面体结构的B₁₃不具有稳定构型,这种结构转变为开放式笼状．B₂₀出现二维到三维的结构转变．Mulliken分析表明电荷分布有x-z和y-z平面对称．硼簇的平面稳定性可以通过离域键(π键和α键)以及多中心键来解释．     

4-(2-Methoxy-4-(prop-1-enyl)phenoxy)phthalonitrile; synthesis,characterization, Hirshfeld surface analysis and chemical activity studies

This work deals with experimental and theoretical study of the 4-(2-methoxy-4-(prop-1-enyl)phenoxy)phthalonitrile (MPPP). The MPPP was synthesized and characterized by FT-IR and NMR, and X-ray single-crystal determination. Hirshfeld surface analysis revealed the nature of intermolecular contacts, the fingerprint plots and molecular surface contours provided the information about the percentage contribution and bond interactions. The structural data of the molecule in the ground state was calculated using the DFT employing B3LYP/6-311++G(d,p) basis set. The energetic behavior of the organic dye sensitizer MPPP in solvent media was examined. In addition, chemical activity, NLO, net charges by MPA & NPA, MEP and Fukui function analysis were investigated. Based on vibrational analysis, the thermodynamic properties were calculated at different temperatures and corresponding relations between the properties and temperature were obtained.     

Experimental and Computational Studies on the 1:1 Complex of Anthranilic Acid with P-Toluenesulfonic Acid

Abstract

The proton-transfer compound (3) was synthesized in good yields by the reaction of anthranilic acid with p-toluenesulfonic acid. It was characterized by elemental analysis, infrared spectroscopy, and X-ray single-crystal determination. The crystal structure analysis of 2-carboxyanilinium p-toulenesulfonate (3) has revealed a one-dimensional hydrogen-bonded network structure, involving the tosylate anion, the carboxyl group, and the ammonium group. The H(N)···O distances range from 1.97 to 2.23 Å. The molecular geometry and vibrational frequencies of 3 were calculated using the ab-initio method (HF) with the 6–31G(d) and 6–31+G(d,p) basis sets. The computed results indicate that the optimized geometry reproduces the crystal structure well, and the assignments of fundamental vibrations also agree well with the theoretical frequencies. The intermolecular proton transfer process between the ionic (3) and nonionic (4) structures was also investigated with the theoretical computations. The nonionic form (4) is energetically more stable than the ionic form (3) and TS(3→4) by 9.76 and 7.01 kcal/mol, respectively, including the zero-point vibrational energy correction at the HF/6–31+G(d,p) level. In addition, the atomic charges, the molecular electrostatic potentials, the nucleus-independent chemical shifts, and the frontier molecular orbitals of 3 were carried out at the HF/6–31+G(d,p) level of theory.

Supplementary materials are available for this article. Go to the publisher's online edition of Phosphorus, Sulfer, and Silicon and the Related Elements for the following free supplemental files: Additional figures and tables