A nonlinear nonlocal mixed problem for a second order pseudoparabolic equation

We study a nonlocal mixed problem for a nonlinear pseudoparabolic equation, which can, for example, model the heat conduction involving a certain thermodynamic temperature and a conductive temperature. We prove the existence, uniqueness and continuous dependence of a strong solution of the posed problem. We first establish for the associated linear problem a priori estimate and prove that the range of the operator generated by the considered problem is dense. The technique of deriving the a priori estimate is based on constructing a suitable multiplicator. From the resulted energy estimate, it is possible to establish the solvability of the linear problem. Then, by applying an iterative process based on the obtained results for the linear problem, we establish the existence, uniqueness and continuous dependence of the weak solution of the nonlinear problem.     

Solid‐particle erosion in the tube end of the tube sheet of a shell‐and‐tube heat exchanger

Erosion is one of the major problems in many industrial processes, and in particular, in heat exchangers. The effects of flow velocity and sand particle size on the rate of erosion in a typical shell‐and‐tube heat exchanger were investigated numerically using the Lagrangian particle‐tracking method. Erosion and penetration rates were obtained for sand particles of diameters ranging from 10 to 500 µm and for inlet flow velocities ranging from 0.197 to 2.95 m/s. A flow visualization experiment was conducted with the objective of verifying the accuracy of the continuous phase calculation procedure. Comparison with available experimental data of penetration rates was also conducted. These comparisons resulted in a good agreement. The results show that the location and number of eroded tubes depend mainly on the particle size and velocity magnitude at the header inlet. The rate of erosion depends exponentially on the velocity. The particle size shows negligible effect on the erosion rate at high velocity values and the large‐size particles show less erosion rates compared to the small‐size particles at low values of inlet flow velocities. The results indicated that the erosion and penetration rates are insignificant at the lower end of the velocity range. However, these rates were found to increase continuously with the increase of the inlet flow velocity for all particle sizes. The particle size creating the highest erosion rate was found to depend on the flow velocity range. Copyright © 2005 John Wiley & Sons, Ltd.     

Elastic modulus of supercooled liquid and hot solid silicon measured by inelastic X-ray scattering

The dynamical structure factors of supercooled-liquid and hot-solid silicon are measured by inelastic X-ray scattering at the same temperature, 1620 K. Two significant changes in the averaged longitudinal sound velocities and in the longitudinal modulus are observed. First, we observe a different longitudinal modulus in the polycrystalline hot-solid silicon compared to the extrapolated value obtained from the single-crystal measurement. This reduction of the modulus may be a precursor of the semiconductor-to-metal transition. Second, the increase in the longitudinal modulus in the liquid upon supercooling is consistent with an increase in the degree of the directional bonding.     

Numerical investigation of natural convection inside an inclined parallel‐walled channel

Steady two‐dimensional natural convection in an inclined parallel‐walled channel was investigated numerically. The full elliptic forms of conservation equations were solved together and the velocity vectors, temperature contours and local and average Nusselt number distribution were obtained. The comparisons of local and average Nusselt number with published experimental and numerical results indicate very good agreement. Results are presented for a single aspect ratio, L/b=24, over the range of Rayleigh number of 3–1000 and angle of inclination 0–90°. The results indicate that the overall channel average Nusselt number is reduced as the inclination angle is increased. Significant reductions in the overall Nusselt number are exhibited at high angle of channel inclination. Copyright © 2005 John Wiley & Sons, Ltd.     

Thermal changes in the optical properties of SnSxSe2−x crystals

Optical measurements on crystals in the series SnS_xSe_2?x for 0 ? x ? 2, have yielded information on the changes in the ordinary refractive index $\text{Δn}\text{ΔT}$ and the energy gap $\text{ΔEg}\text{ΔT}$ in the temperature range 125–425 K. The coefficient $\text{Δn}\text{ΔT}$ has values +40 to +160 × 10^?6K^?1 and this confirms that covalent bonding predominantly exists in these materials. The coefficient $\text{ΔEg}\text{ΔT}$ remains fairly consistent for all values of x with an average value of -8.0×10^-4eV K^-1.     

Synthesis of 7-oxopyrrolo[3,2-B]pyridine-6-carboxylic acid derivatives as potential antimicrobial agents

A route for the synthesis of various derivatives of 7-oxopyrrolo[3,2-b]pyridine-6-carboxylic acid from 2-methyl-3-carbomethoxy-4-aminopyrrole is reported.     

Styrene cis—trans photoisomerisation treated through a Heisenberg non-empirical hamiltonian

Using a recently proposed non-empirical Heisenberg hamiltonian, the ground and excited covalent surfaces of the styrene molecule are calculated as functions of the external double-bond twisting angle θ, including full bond-length optimisation. The lowest excited singlet surface exhibits a barrier at 0 ?~ 45° resulting from a weakly avoided crossing of two neutral diabatic surfaces. The isomerisation should proceed from the twisted funnel. This model and the calculated transition energies are in good agreement with experiment.