Non-linear couette flow with heat transfer using the B-G-K model

In recent years a large number of investigators have devoted their efforts to the study of flow and heat transfer in rarefied gases, using the BGK [1] model or the Boltzmann kinetic equation. The velocity moment method which is based on an expansion of the distribution function as a series of orthogonal polynomials in velocity space, has been applied to the linearized problem of shear flow and heat transfer by Mott-Smith [2] and Wang Chang and Uhlenbeck [3]. Gross, Jackson and Ziering [4] have improved greatly upon this technique by expressing the distribution function in terms of half-range functions and it is this feature which leads to the rapid convergence of the method. The full-range moments method [4] has been modified by Bhatnagar [5] and then applied to plane Couette flow using the B-G-K model. Bhatnagar and Srivastava [6] have also studied the heat transfer in plane Couette flow using the linearized B-G-K equation. On the other hand, the half-range moments method has been applied by Gross and Ziering [7] to heat transfer between parallel plates using Boltzmann equation for hard sphere molecules and by Ziering [83 to shear and heat flow using Maxwell molecular model. Along different lines, a moment method has been applied by Lees and Liu [9] to heat transfer in Couette flow using Maxwell's transfer equation rather than the Boltzmann equation for distribution function. An iteration method has been developed by Willis [10] to apply it to non-linear heat transfer problems using the B-G-K model, with the zeroth iteration being taken as the solution of the collisionless kinetic equation. Krook [11] has also used the moment method to formulate the equivalent continuum equations and has pointed out that if the effects of molecular collisions are described by the B-G-K model, exact numerical solutions of many rarefied gas-dynamic problems can be obtained. Recently, these numerical solutions have been obtained by Anderson [12] for the non-linear heat transfer in Couette flow,

The Raman spectra of organic compounds -Part I. Methyl, ethyl, n-propyl and n-butyl alcohols

The Raman spectra of methyl alcohol, ethyl alcohol, n-propyl alcohol and n-butyl alcohol have been recorded using λ 2537 excitation. 35, 49, 45 and 51 Raman lines respectively have been identified in the spectra of these alcohols, in addition to the rotational 'wings'. In each case, a large number of additional lines have been recorded. The existence of Raman lines with frequency shifts greater than 3800 cm.-1, first reported by Bolla in the spectrum of ethyl alcohol, has been confirmed. Similar high-frequency shift Raman lines have also been recorded in the spectrum of methyl alcohol. They have been assigned as combinations. Proper assignments have been given for the prominent Raman lines appearing in the spectra of these alcohols.

An electron diffraction investigation of the molecular structure of methyl azide

The molecular structure of methyl azide has been studied by the sector-microphotometer and the sector-visual methods of electron diffraction and the parameters determined as follows: C-N = 1.47 ± 0.02 Å., N1-N2 = 1.24 ± 0.01 Å., N2-N3 = 1.12 ± 0.01 Å. and

Isomerisations of substituted β-keto-esters - Part II. Isomerisation of ethyl 1-ethoxycarbonyl 2oxocyclopentyl acetate into 2, 3-diethoxycarbonylcyclohexanone

A mechanism for the isomerisation of ethyl 1-ethoxycarbonyl-2-oxocyclopentylacetate (I) into a cyclohexane β-keto-ester as proceeding through an intermediate bicyclic /gb-diketone (VII) has been considered as an alternative mechanism to one earlier suggested.1 The determination of the structure of the isomerised β-keto-ester as 2, 3-diethoxycarbonylcyclohexanone (V) has provided support for the earlier mechanism.

Methyl 1-methyl-1H-1,2,3-triazole-4-carboxylate

The title molecule, C5H7N3O2, has an almost planar conformation, with a maximum deviation of 0.043 (3) angstrom, except for the methyl H atoms. In the crystal structure, intermolecular C-H center dot center dot center dot O hydrogen bonds link the molecules into layers parallel to the bc plane. Intermolecular pi-pi stacking interactions [centroid-centroid distances = 3.685 (2) and 3.697 (2) angstrom] are observed between the parallel triazole rings.

Crystal And Molecular-Structure Of 8-Acetoxy-6-(2,4-Dimethoxy-5-Bromophenyl)-3-Methyl-Tricyclo[5,2,1,03,8 ]Decan-2-One

The crystal and molecular structure has been determined by the heavy-atom method and refined by the least-squares procedure to R= 8"3 % for 2033 photographically observed reflexions. The compound crystallizes in the space group P]" with two molecules in a unit cell of dimensions a = 11"68 + 0-02, b = 12"91 +0"02, c= 10"43+0"02/~, e= 114"7+ 1, fl=90-2+ 1 and 7,= 118.3+ 1 °. The unit cell also contains one molecule of the solvent, benzene. The 'cage' part of the molecule exhibits a large number of elongated bonds and strained internal valency angles. The bridgehead angle in the bicyclic heptane ring system is 89 °. The acetate group at C(16) and the methyl group at C(15) are cis to each other.

1-[(2-Chloro-8-methylquinolin-3-yl)methyl]pyridin-2(1H)-one

In the title compound, C16H13ClN2O, the quinoline ring system is approximately planar [maximum deviation 0.021 (2) angstrom] and forms a dihedral angle of 85.93 (6)degrees with the pyridone ring. Intermolecular C-H center dot center dot center dot O hydrogen bonding, together with weak C-H center dot center dot center dot pi and pi-pi interactions [centroid-to-centroid distances 3.5533 (9) and 3.7793 (9) angstrom], characterize the crystal structure.

2-Chloro-8-methyl-3-[(pyrimidin-4-yloxy)methyl]quinoline

In the title compound, C15H12ClN3O, the quinoline ring system is essentially planar, with a maximum deviation of 0.017 (1) angstrom. The crystal packing is stabilized by pi-pi stacking interactions between the quinoline rings of adjacent molecule, with a centroid-centroid distance of 3.5913 (8) angstrom. Aweak C-H center dot center dot center dot pi contact is also observed between molecules.

3-[(2-Chloro-6-methylquinolin-3-yl)methyl]quinazolin-4(3H)-one

In the title molecule, C19H14ClN3O, the quinoline and quinazoline ring systems form a dihedral angle of 80.75 (4)degrees. In the crystal, the molecules are linked by pairs of C-H center dot center dot center dot N hydrogen bonds into centrosymmetric dimers, generating R-2(2)(6) ring motifs. The structure is further stabilized by C-H center dot center dot center dot pi interactions and pi-pi stacking interactions [centroid-centroid distances = 3.7869 (8) and 3.8490 (8) angstrom].