An analytical solution to the extended Navier–Stokes equations using the Lambert W function

Microchannel gas flows are of importance in a wide range of microelectro mechanical devices. In these flows, the mean free path of the gas can be comparable to the characteristic length of the microchannel, leading to strong diffusion‐enhanced transport of momentum. Numerical solutions to the extended Navier–Stokes equations (ENSE) have successfully modeled such microchannel flows. Analytical solutions to the ENSE for the pressure and velocity fields using the Lambert W function are derived. We find that diffusive contributions to the total transport are only dominant for low average pressures and low pressure drops across the microchannel. For large inlet pressures, we show that the expressions involving the Lambert W function predict steep gradients in the pressure and velocity localized near the channel exit. We extract a characteristic length for this boundary layer. Our analytical results are validated by numerical and experimental results available in the literature. © 2014 American Institute of Chemical Engineers AIChE J, 60: 1413–1423, 2014     

Examining the Suitability of the Reaction Engineering Approach (REA) to Modeling Local Evaporation/Condensation Rates of Materials with Various Thicknesses

The reaction engineering approach (REA) is examined here to investigate its suitability as the local evaporation rate to be used in multiphase drying. For this purpose, REA is first implemented to model the convective drying of materials with various thicknesses. The relative activation energy, as the fingerprint of REA, generated from one size of a material is used to model the convective drying of the same material with different thicknesses. Because the results indicate that REA parameters can model the drying of materials with various thicknesses, REA can be scaled down to describe the local evaporation rate (at the microscale as affected by local composition and temperature). The relative activation energy is used to describe the global drying rate in modeling the local evaporation rate. REA is combined with a system of equations of conservation of heat and mass transfer in order to yield the spatial reaction engineering approach (S-REA) as a nonequilibrium multiphase drying model. By using S-REA, the spatial profiles of moisture content, concentration of water vapor, temperature, and local evaporation rate can be generated, which can assist in comprehending the transport phenomena.     

Design and assessment of delay timer alarm systems for nonlinear chemical processes

In process and manufacturing industries, alarm systems play a critical role in ensuring safe and efficient operations. The objective of a standard industrial alarm system is to detect undesirable deviations in process variables as soon as they occur. Fault detection and diagnosis systems often need to be alerted by an industrial alarm system; however, poorly designed alarms often lead to alarm flooding and other undesirable events. In this article, we consider the problem of industrial alarm design for processes represented by stochastic nonlinear time‐series models. The alarm design for such complex processes faces three important challenges: (1) industrial processes exhibit highly nonlinear behavior; (2) state variables are not precisely known (modeling error); and (3) process signals are not necessarily Gaussian, stationary or uncorrelated. In this article, a procedure for designing a delay timer alarm configuration is proposed for the process states. The proposed design is based on minimization of the rate of false and missed alarm rates—two common performance measures for alarm systems. To ensure the alarm design is robust to any non‐stationary process behavior, an expected‐case and a worst‐case alarm designs are proposed. Finally, the efficacy of the proposed alarm design is illustrated on a non‐stationary chemical reactor problem. © 2017 American Institute of Chemical Engineers AIChE J, 63: 77–90, 2018     

Superconducting State Parameters of (Ni33Zr67)1?xMx (M = Ti, V, Co, Cu) Ternary Amorphous Superconductors

The theoretical investigations of the superconducting state parameters (SSP) viz. electron-phonon coupling strength λ, Coulomb pseudopotential μ ^∗, transition temperature T _C , isotope effect exponent α and effective interaction strength N _O V of (Ni₃₃Zr₆₇)_1−x M _x (M=Ti,V,Co,Cu) ternary amorphous superconductors have been reported using Ashcroft’s empty core (EMC) model potential. Five different types of local field correction functions proposed by Hartree (H), Taylor (T), Ichimaru-Utsumi (IU), Farid et al. (F) and Sarkar et al. (S) are used in the present investigation to study the screening influence on the aforesaid properties. The T _C obtained from Sarkar et al. (S) local field correction function are found in excellent agreement with available theoretical data. Quadratic T _C equation has been proposed, which provides successfully the T _C values of ternary amorphous alloys under consideration. Also, the present results are found to be in qualitative agreement with other such earlier reported data, which confirms the superconducting phase in the superconductors.     

Biaxial tensile behavior of spunbonded nonwoven geotextiles

Geotextiles can be successfully employed for any geotechnical application when they are able to sustain pre-defined levels of tensile stresses. The biaxial tensile test has an advantage over other tensile test methods in that it does not allow “necking” during deformation which simulates the operational conditions of geotextiles under confined stresses. In this study, the model for uniaxial tensile behavior of nonwovens has been modified to investigate the biaxial tensile behavior of spunbonded geotextiles. The model has included the effect of fiber re-orientation, stress-strain behavior of constituent fibers, and physical characteristics of nonwovens when the geotextile specimen is laterally constrained. A comparison is made between predicted and experimental stress-strain curves obtained from previous work (Bais-Singh and Goswami, 1998). Theoretical findings of biaxial tensile behavior obtained using the layer theory are also critically discussed. In addition, it has been revealed that fiber re-orientation is a key factor in translating the random spunbonded nonwoven geotextiles to anisotropic structures under defined biaxial tensile stresses.     

Phase-field theory of grain growth in the presence of mobile second-phase particles

We have developed a phase-field model for grain growth in the presence of mobile second-phase particles. In this model, each grain and particle is represented by a unique order parameter. The grain boundaries sweep the mobile particles during grain growth. The particle velocity is taken to be proportional to the driving force arising from the curvature of the phase boundary in the neighborhood of the particle. The proportionality factor is the constitutive parameter representing the mobility of the particle. We first study the model in a one-dimensional axisymmetric setting and compare the results with theoretical calculations. We then study the interaction of a bicrystal grain boundary with a dilute distribution of particles. Finally we show the effect of particles on polycrystalline grain growth.     

Effect of ash on maximum thickness of plastic layer of coals

A study of the effect of ash yield on the maximum thickness of the plastic layer (MTPL) of some coking coals (as measured by the Sapozhnikov plastometer) has revealed that with an increase in the former the latter in general decre?es. A rectilinear relation approximately exists between the ash percentage (dry basis) and log MTPL values of coals. For the samples studied, a multiple correlation incorporating the rank factor was found to be unnecessary. Higher Fe₂O₃ and SO₃ contents from the coal were found to be associated with higher MTPL values.     

Structuring Optimizing Transformations and Proving Them Sound

A compiler optimization is sound if the optimized program that it produces is semantically equivalent to the input program. The proofs of semantic equivalence are usually tedious. To reduce the efforts required, we identify a set of common transformation primitives that can be composed sequentially to obtain specifications of optimizing transformations. We also identify the conditions under which the transformation primitives preserve semantics and prove their sufficiency. Consequently, proving the soundness of an optimization reduces to showing that the soundness conditions of the underlying transformation primitives are satisfied.The program analysis required for optimization is defined over the input program whereas the soundness conditions of a transformation primitive need to be shown on the version of the program on which it is applied. We express both in a temporal logic. We also develop a logic called temporal transformation logic to correlate temporal properties over a program (seen as a Kripke structure) and its transformation.An interesting possibility created by this approach is a novel scheme for validating optimizer implementations. An optimizer can be instrumented to generate a trace of its transformations in terms of the transformation primitives. Conformance of the trace with the optimizer can be checked through simulation. If soundness conditions of the underlying primitives are satisfied by the trace then it preserves semantics.     

Superconducting State Parameters of 5d-Transition Metals Based Binary Alloys

The theoretical study of the superconducting state parameters (SSP) viz. electron–phonon coupling strength λ, Coulomb pseudopotential μ ^*, transition temperature T _C , isotope effect exponent α and effective interaction strength N _O V of 5d-transition metals based binary alloys have been made extensively in the present work using a model potential for the first time. A considerable influence of various exchange and correlation functions on λ and μ ^* is found from the present study. The present results of the SSP are found in qualitative agreement with the available experimental data wherever it exists.