A Taguchi approach for determination of optimum design parameters for a heat exchanger having circular-cross sectional pin fins

The present work submits an investigation about the optimal values of design parameters and performance analysis for a heat exchanger having cylindrical pin fins positioned in a rectangular channel. The experiments covered the following range: Reynolds number 13,500–42,000, the clearance ratio (C/H) 0, 0.33 and 1, the interfin spacing ratio (S _y /D) 1.208, 1.944 and 3.417. In the experimentation, Taguchi method was employed, and Nusselt number and friction factor were considered as performance parameters. While the optimum parameters were determined, due to the goals (above aims) more than one being, the trade-off among goals was considered. First of all, each goal was optimized, separately. Then, all goals were optimized together, considering the priority of goals, and the optimum results were found to be Reynolds number of 42,000, fin height of 50 mm and pitch of 3.417. The performance analysis also was made under a constant pumping power constraint, and the results showed that the use of cylindrical pin fins may lead to an advantage on the basis of heat transfer enhancement.     

Dynamic Phase Transitions and Compensation Temperatures in a Mixed Spin-3/2 and Spin-5/2 Ising System

We examine the dynamic phase transitions and the dynamic compensation temperatures, within a mean-field approach, in the mixed spin-3/2 and spin-5/2 Ising system with a crystal-field interaction under a time-varying magnetic field on a hexagonal lattice by using Glauber-type stochastic dynamics. The model system consists of two interpenetrating sublattices with σ=3/2 and S=5/2. The Hamiltonian model includes intersublattice, intrasublattice, and crystal-field interactions. The intersublattice interaction is considered antiferromagnetic and to be a simple but interesting model of a ferrimagnetic system. We employ the Glauber transition rates to construct the mean-field dynamic equations, and we solve these equations in order to find the phases in the system. We also investigate the thermal behavior of the dynamic sublattice magnetizations and the dynamic total magnetization to obtain the dynamic phase transition points and compensation temperatures as well as to characterize the nature (continuous and discontinuous) of transitions. We also calculate the dynamic phase diagrams including the compensation temperatures in five different planes. According to the values of Hamiltonian parameters, five different fundamental phases, three different mixed phases, and six different types of compensation behaviors in the Néel classification nomenclature exist in the system.     

Dynamic phase transition and dynamic phase diagrams in the spin-5/2 Blume–Capel model under a time-dependent oscillating external field

We calculate the dynamic phase transition (DPT) temperatures and present the dynamic phase diagrams in the kinetic spin-5/2 Blume–Capel model under the presence of a time-dependent oscillating external magnetic field. First, we employ the Glauber transition rates to construct the mean-field dynamic equation. Then, we study the time variation of the average magnetization to find the phases in the system. We also investigate the behaviour of the dynamic magnetization to characterize the nature (continuous and discontinuous) of transition and to obtain the DPT points. We present the dynamic phase diagrams in two different planes. The phase diagrams include the ferromagnetic-5/2 (f_5/2), the ferromagnetic-1/2 (f_1/2) and paramagnetic (p) fundamental phases. In addition to these fundamental phases, we find 10 mixed phases, depending on the interaction parameters. The phase diagrams display many special points, such as a dynamic tricritical point, a double critical end point, a triple point and a quadruple point.     

Dynamic magnetic properties of the kinetic cylindrical Ising nanotube

The nature (time variation) of response magnetizations m(wt) of the kinetic cylindrical Ising nanotube in the presence of a periodically varying external magnetic field h(wt) is studied by employing the effective-field theory (EFT) with correlations as well as the Glauber-type stochastic dynamics. We have determined the time variations of m(wt) and h(wt) for various temperatures, and investigated the dynamic magnetic hysteresis behavior. Temperature dependence of the dynamic magnetizations, hysteresis loop areas and correlations are investigated in order to characterize the nature (first- or second-order) of the dynamic transitions as well as to obtain the dynamic phase transition temperatures. We also present the dynamic phase diagrams in the three different planes and compare the results of the equilibrium and nonequilibrium states. The phase diagrams exhibit dynamic tricritical, isolated critical, multicritical and triple points. The results are in good agreement with some experimental and theoretical results.     

Numerical solutions of integro-differential equations and application of a population model with an improved Legendre method

In this paper, an improved Legendre collocation method is presented for a class of integro-differential equations which involves a population model. This improvement is made by using the residual function of the operator equation. The error differential equation, gained by residual function, has been solved by the Legendre collocation method (LCM). By summing the approximate solution of the error differential equation with the approximate solution of the problem, a better approximate solution is obtained. We give the illustrative examples to demonstrate the efficiency of the method. Also we compare our results with the results of the known some methods. In addition, an application of the population model is made.     

Effective-field theory of the Ising model with three alternative layers on the honeycomb and square lattices

The Ising model with three alternative layers on the honeycomb and square lattices is studied by using the effective-field theory with correlations. We consider that the nearest-neighbor spins of each layer are coupled ferromagnetically and the adjacent spins of the nearest-neighbor layers are coupled either ferromagnetically or anti-ferromagnetically depending on the sign of the bilinear exchange interactions. We investigate the thermal variations of the magnetizations and present the phase diagrams. The phase diagrams contain the paramagnetic, ferromagnetic and anti-ferromagnetic phases, and the system also exhibits a tricritical behavior.     

Temperature dependency of thermal conductivity of solid phases for fatty acids

Thermal conductivity variations with temperature of solid phases for lauric acid (LA), myristic acid (MA), pivalic acid (PA), and stearic acid (SA) have been measured with radial heat-flow method. Temperature dependencies of the thermal conductivity for same organic materials have been obtained by linear regression analysis. From graphs of thermal conductivity versus temperature, the thermal conductivity of solid phase at their melting temperature and temperature coefficients of thermal conductivity for LA, MA, PA, and SA have been found to be 0.37, 0.39, 0.23, and 0.35 W K^?1 m^?1 and 0.00935, 0.00446, 0.01095, and 0.00295 K^?1, respectively. The ratios of thermal conductivity of liquid phase to thermal conductivity of solid phase for LA, MA, PA, and SA have also been measured to be 0.52, 0.48, 0.25, and 0.59, respectively, with a Bridgman-type directional solidification apparatus.     

On a Submersion Between Reinhart Lightlike Manifolds and Semi-Riemannian Manifolds

In this paper, we introduce a new submersion, namely, screen lightlike submersion between a lightlike manifold and a semi-Riemannian manifold. We give an example and obtain a characterization for lightlike manifold to be Reinhart under such submersion. Then, we investigate the geometry of a screen lightlike submersion when the total manifold is a Reinhart lightlike manifold. Received: March 6, 2007 Revised: October 4, 2007 and November 2, 2007 Accepted: December 6, 2007     

On the solutions of a higher‐order difference equation in terms of generalized Fibonacci sequences

This paper deals with the solutions, stability character, and asymptotic behavior of the difference equation where and the initial values x_?k,x_{?k + 1},…,x₀ are nonzero real numbers, such that their solutions are associated to Horadam numbers. Copyright © 2015 John Wiley & Sons, Ltd.     

Dehydrophenylnitrenes: matrix isolation and photochemical rearrangements

The photochemistry of 3-iodo-2,4,5,6-tetrafluorophenyl azide 8 and 3,5-diiodo-2,4,6-trifluorophenyl azide 9 was studied by IR and EPR spectroscopy in cryogenic argon and neon matrices. Both compounds form the corresponding nitrenes as primary photoproducts in photostationary equilibria with their azirine and ketenimine isomers. In contrast to fluorinated phenylnitrenes, ring-opened products are obtained upon short-wavelength irradiation of the iodine-containing systems, indicative of C-I bond cleavage in the nitrenes or didehydroazepines under these conditions. Neither 3-dehydrophenylnitrene 6 nor 3,5-didehydrophenylnitrene 7 could be detected directly. The structures of the acyclic photoproducts were identified by extensive comparison with DFT calculated spectra. Mechanistic aspects of the rearrangements leading to the observed products and the electronic properties of the title intermediates are discussed on the basis of DFT as well as high-level ab initio calculations. The computations indicate strong through-bond coupling of the exocyclic orbital in the meta position with the singly occupied in-plane nitrene orbital in the monoradical nitrenes. In contrast to the ortho or para isomers, this interaction results in low-spin ground states for meta nitrene radicals and a weakening of the C1-C2 bond causing the kinetic instability of these species even under low-temperature conditions. 3,5-Didehydrophenylnitrenes, on the other hand, in which a strong C3-C5 interaction reduces coupling of the radical sites with the nitrene unit, might be accessible synthetic targets if the intermediate formation of labile monoradicals could be circumvented.