Mathematical Models for Ice Accretion on Conductors using Free Streamline Theory: Part I: Single Conductor

It is the purpose of this paper to develop theoretical modelsof rime ice accretion and snow loading on a single conductor.The ice-accretion kinetics are formulated in terms of separatedor free streamline airflow, assuming that the conductor doesnot twist under the eccentric ice loading on the windward side. The new results for rime ice accretion lead to interesting comparisonsof the predicted rate of axial growth for attached and separatedpotential flow, respectively. A new ice-accretion model is thenproposed for snow loading and here account is taken of the factthat the length of dendritic snowflakes is comparable with thediameter of the conductor.     

Synthesis, Structure and Alkali Metal Ion Binding Properties of a Podand Polyether Derived from Calix[4]arene, 5,11,17,23-tetra-tert-butyl-25,27-di(phenylmethoxy)-26,28-di(2‘-methoxyethoxy)-calix[4]arene

The ligand 5,11,17,23-tetra-t-butyl-25,27-di(phenylmethoxy)-26,28-di(2-methoxy-ethoxy)calix[4]arene,designed as an analogue of some calixcrown speciesin order to evaluate possible origins of their selectivity in alkali metal ion binding, has been synthesised and structurally characterised by X-ray crystallography. The crystals are monoclinic, P21/n, a = 15.940(6), b = 19.388(5), c = 20.020(5) Å, = 109.10(2) deg., Z = 4, conventional R on |F| being 0.073 for 3454 independent, observed (I > 3(I)) reflections. 1H-NMR studies in 1:1 CD3CN/CDCl3solvent have shown that the ligand exerts a strong preference for the lighteralkali metal ions (Li+ and Na+) contrary to the binding behaviour of knowncalixcrowns. This may reflect interactions restricted to the lower rim donor atoms without concomitant interaction with the calixarene -electrons, perhaps because the latter interactions are substituted by those with the benzyl group -electrons.     

Lattice Forces in Heavy Metal Picrates: Structural Characterization of Lead and Mercury Species

Structure determinations for the dimethylsulfoxide (dmso) solvate of lead(II) picrate (picrate = pic = 2,4,6-trinitrophenoxide), formally a centrosymmetric dimer, [Pb₂(dmso)₄(pic)₄], and for unsolvated mercury(I) picrate, a polymer of conventional mercurous dimers, [Hg₂(pic)₂] _n , show that, despite considerable differences in the form of the metal unit, there are remarkable similarities in the mode of coordination of the bridging picrate ligands. In both lattices, parallel arrays of picrate rings can be discerned but appear to be associated with short N…O, O…O or O…C contacts rather than C…C. In the Pb compound, there is also evidence of intramolecular contacts to dmso-S.     

Nucleophilic Substitution Reactions of Meta‐ and Para‐Substituted Benzylamines with Benzyl Bromide in Methanol Medium

The rates of reactions of para‐ and meta‐substituted benzylamines with benzyl bromide were measured using conductivity technique in methanol medium. The reaction followed a total second‐order path. The end product of the reaction is identified as dibenzylamine (X‐C₆H₄CH₂NHCH₂C₆H₅) (where X = 4‐OCH₃, 4‐CH₃, H, 4‐Cl, 4‐CF₃, 3‐CF₃, 4‐NO₂). Electron‐withdrawing groups such as chloro, trifluoromethyl, and nitro in the benzylamine moiety decrease the rate of the reaction, whereas the electron‐donating groups, such as methoxy and methyl, increase the rate compared to the unsubstituted compound. A mechanism involving formation of an S_N2‐type transition state between the amine nucleophiles and the benzyl bromide and its subsequent decomposition is proposed. Hammett's reaction constant ρ of the reaction decreases with an increase in temperature. Activation parameters were calculated and discussed.     

LINE FORCE RECEPTANCE OF AN ELASTIC CYLINDRICAL SHELL WITH HEAVY EXTERIOR FLUID LOADING

A time-harmonic line force is applied to an infinite elastic cylindrical shell immersed in compressible fluid. The force may also have axial harmonic dependence. The formal solution for the shell displacement is obtained as the sum of circumferential harmonics and evaluated in the asymptotic limit of heavy exterior fluid-loading. The resulting asymptotic expressions for the elements of the receptance matrix, either at the line of application of the force, or elsewhere on the shell surface, are simple trigonometric functions of the shell and fluid parameters, and show excellent agreement with numerical evaluation of the circumferential harmonic series over a wide frequency range.     

Approximate Predictions of Ice Accretion on an Overhead Transmission Line which Rotates with Constant Angular Velocity

An airflow carrying either freezing-fog droplets or wet snowimpinging on an overhead transmission line causes ice to accreteon the windward side of the conductor. In the vicinity of theconductor anchors (at the towers), axial growth, in the formof a spike of ice growing outward into the wind, is observed.Near the centre of the span this eccentric ice loading causesthe conductor to twist so that cylindrical-sleeve growth isobserved. For small-diameter conductors of low torsional stiffnessthe conductor rotation can amount to many complete revolutions.It is useful to obtain some understanding of this mode of iceaccretion prior to undertaking any investigation of the aeroelasticsystem under icing conditions and it has direct relevance toice loading on small-diameter conductors. To this end, a simple‘icing-clock’ model for sleeve growth in which theconductor rotates with constant angular velocity is proposed,enablinganalytical results on the mechanics of the ice evolution processto be obtained.