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The main purpose of this paper is to implement the piecewise spectral-variational iteration method (PSVIM) to solve the nonlinear Lane-Emden equations arising in mathematical physics and astrophysics.

This method is based on a combination of Chebyshev interpolation and standard variational iteration method (VIM) and matching it to a sequence of subintervals. Unlike the spectral method and the VIM, the proposed PSVIM does not require the solution of any linear or nonlinear system of equations and analytical integration.

Some well-known classes of Lane-Emden type equations are solved as examples to demonstrate the accuracy and easy implementation of this technique.

In this paper, a new and efficient technique is proposed to solve the nonlinear Lane-Emden equations. The proposed method overcomes the difficulties arising in calculating complicated and time-consuming integrals and terms that are not needed in the standard VIM.

The purpose of the present article is to obtain the similarity solution for the shock wave generated by a piston propagating in a self-gravitating nonideal gas under the impact of azimuthal magnetic field for adiabatic and isothermal flows.

The Lie group theoretic method given by Sophus Lie is used to obtain the similarity solution in the present article.

Similarity solution with exponential law shock path is obtained for both ideal and nonideal gas cases. The effects on the flow variables, density ratio at the shock front and shock strength by the variation of the shock Cowling number, adiabatic index of the gas, gravitational parameter and nonidealness parameter are investigated. The shock strength decreases with an increase in the shock Cowling number, nonidealness parameter and adiabatic index, whereas the strength of the shock wave increases with an increase in gravitational parameter.

Propagation of shock wave with spherical geometry in a self-gravitating nonideal gas under the impact of azimuthal magnetic field for adiabatic and isothermal flows has not been studied by any author using the Lie group theoretic method.

The purpose of this manuscript is to study the vibration characteristics of the spherically symmetric solid and hollow spheres poised of a homogeneous thermoelastic material, based on the three dimensional coupled thermoelasticity.

In this paper, matrix Fröbenius series solution is used to derive the frequency equations, for the field functions. Results have been applied on rigidly fixed boundary conditions.

The main finding of this paper is that the frequency of vibration of spherically symmetric sphere (structure is independent of theta and phi) increases with the increase of radius, for solid spheres and for hollow spheres with thickness to mean radius ratio. Deformation in the given materials increases with thickness to mean radius ratio of the hollow sphere.

A numerical simulation has been done with the help of functional iteration method for solid and hollow thermoelastic spheres made of zinc and poly methyl meth acrylate materials for different boundary conditions. The computer simulated results in contempt of frequency, damping of vibration modes and displacement have been obtained graphically and compared with the existed results.

Presents numerical aspects of the program CODE_BRIGHT, which is a simulator for COupled DEformation, BRIne, Gas and Heat transport problems. It solves the equations of mass and energy balance and stress equilibrium and, originally, it was developed for saline media. The governing equations also include a set of constitutive laws and equilibrium conditions. The main peculiarities of saline media are in the dissolution/precipitation phenomena, presence of brine inclusions in the solid salt and creep deformation of the solid matrix.

Computation have been made of the three‐dimensional flow field development, chemical reaction and combustion processes in a typical afterburner system under both isothermal and reacting flow conditions. The calculations are based upon a numerical solution of the time‐averaged transport equations for mass, momentum, turbulence kinetic energy, dissipation rate, enthalpy and species concentrations using a finite‐volume formulation. The physical models include the k—ε turbulence model, the eddy break‐up model, a two‐step reaction model, a droplet vaporization and combustion model and six‐flux radiation model. The mean flow structures are presented in important longitudinal and cross‐sectional planes which show certain striking similarities and contrasting differences for isothermal and reacting flows. The flame stabilizer flow is shown to be dominated by a complex combination of recirculation and vortex patterns. Combustion alters convergence and mixing flow patterns downstream of the flame stabilizer, thus influencing the selection of the fuel injection system. The predicted reacting flow parameters identify a number of design parameters such as fuel injector location, high degree reaction zone, nozzle opening area and the corresponding fuel flow rate.

This paper aims to describe the physical and numerical modeling of a new computational fluid dynamics solver for hypersonic flows in thermo-chemical non-equilibrium. The code uses a blend of numerical techniques to ensure accuracy and robustness and to provide scalability for advanced hypersonic physics and complex three-dimensional (3D) flows.

The solver is based on an edge-based stabilized finite element method (FEM). The chemical and thermal non-equilibrium systems are loosely-coupled to provide flexibility and ease of implementation. Chemical non-equilibrium is modeled using a laminar finite-rate chemical kinetics model while a two-temperature model is used to account for thermodynamic non-equilibrium. The systems are solved implicitly in time to relax numerical stiffness. Investigations are performed on various canonical hypersonic geometries in two-dimensional and 3D.

The comparisons with numerical and experimental results demonstrate the suitability of the code for hypersonic non-equilibrium flows. Although convergence is shown to suffer to some extent from the loosely-coupled implementation, trading a fully-coupled system for a number of smaller ones improves computational time. Furthermore, the specialized numerical discretization offers a great deal of flexibility in the implementation of numerical flux functions and boundary conditions.

The FEM is often disregarded in hypersonics. This paper demonstrates that this method can be used successfully for these types of flows. The present findings will be built upon in a later paper to demonstrate the powerful numerical ability of this type of solver, particularly with respect to robustness on highly stretched unstructured anisotropic grids.

This paper aims to examine how using lattice Boltzmann method (LBM) aids the study of the isothermal‐gas flow with slight rarefaction in long microtubes.

A revised axisymmetric lattice Boltzmann model is proposed to simulate the flow in microtubes. The wall boundary condition combining the bounce‐back and specular‐reflection schemes is used to capture the slip velocity on the wall. Appropriate relation between the Knudsen number and relax‐time constant is defined.

The computed‐slip velocity, average velocity and non‐linear pressure distribution along the microtube are in excellent agreement with analytical solution of the weakly compressible Navier‐Stokes equations. The calculated‐friction factors are also consistent with available experimental data. For simulations of slip flow in microtube, LBM is more accurate and efficient than DSMC method.

The laminar flow in circular microtube is assumed to be axisymmetric. The present LBM is only applied to the simulation of slip flows (0.01 < Kn₀<0.1) in microtube.

Lattice‐BGK method is a very useful tool to investigate the micro slip flows.

A revised axisymmetric D2Q9 lattice Boltzmann model is proposed to simulate the slip flow in axisymmetric microtubes.

Early detection of forest fires offers the chance to put the fire out before it gets out of control. The purpose of this paper is to look into nature and to learn how certain insects detect remote forest fires. A small group of highly specialized insects that have been called pyrophilous is attracted by forest fires and approaches fires sometimes from distances of many kilometers. As a unique feature some of these insects are equipped with infrared (IR) receptors, which in case of two species of jewel beetles (family Buprestidae) are used for fire detection.

The paper has investigated the IR receptors of the pyrophilous beetles with various morphological techniques including scanning electron microscopy, transmission electron microscopy, neuroanatomy and the paper also investigated the thermo-/mechanical properties of the IR receptors by nanoindentation. Data were used for subsequent modeling of a biomimetic technical sensor. Finally, a macroscopic prototype was built and tested.

This biological principle was transferred into a new kind of uncooled technical IR receptor. A simple model for this biological IR sensor is a modified Golay sensor in which the gas has been replaced by a liquid. Here, the absorbed IR radiation results in a pressure increase of the liquid and the deflection of a thin membrane. For the evaluation of this model, analytical formulas are presented, which permits the calculation of the pressure increase in the cavity, the deformation of the membrane and the time constant of an artificial leak to compensate ambient temperature changes. Some organic liquids with high thermal expansion coefficients may improve the deflection of the membrane compared to water.

Results so far obtained suggest that it seems promising to take the photomechanic IR receptors of pyrophilous jewel beetles as models for the building of new uncooled IR sensors. The beetle receptors have been shaped by evolution since thousands of years and, therefore, can be considered as highly optimized sources of inspiration for new technical sensors suitable for remote fire detection.

The purpose of this work is to study the effect of surface-radiation on the phenomenon of natural convection flow of a Newtonian fluid in a non-Darcian porous media cavity. The study is mainly focused on the interaction between the inertial resistance of the fluid layers and the surface radiation.

For numerical simulation of transient vorticity transport and energy equations, the paper uses the alternate direct implicit method. Forward Time Central Space descretization is used for the transient and diffusion terms in the alternate direct implicit method, whereas for the convective terms, the method is modified using second upwind differencing technique. ADI method is adopted here, since this technique is unconditionally stable as a complete sweep and is second-order accurate in time for low velocity changes. The stream function equation is solved using the successive over relaxation technique with residual tolerance of order 10-5.

It was found that despite the reduction of flow, the heat transfer increases as the Forschheimer resistance is increased. Further, with the increase in the Planck number, the heat transfer from the bottom radiating wall increases. Darcy drag parameter did not have a significant impact on flow properties except a slight reduction in the flow. Nevertheless, the increase in temperature ratio has a significant impact on flow properties.

The analysis is valid for unsteady, two-dimensional natural convection flow in a fluid-saturated non-Darcy porous medium enclosed by non-isothermal walls. As a first case, the study is conducted for square cavity. An extension to three-dimensional flow case and the study of Darcy-Forschheimer medium with effect of viscous dissipation is left as a part of future work.

The approach is applicable to the modeling of geothermal systems where the inertial resistance to flow also comes into act with the non-uniform temperature distribution. The method is very useful to analyze solar receiver systems, fire research, electronic cooling, brake housing of an aircraft and many environmental geothermal processes.

The study may be of some interest to engineers interested in heat transfer in ventilated rooms or enclosures, the industrial waste, water and atmospheric pollution.

This paper gives a review of the finite element techniques (FE) applied in the area of material processing. The latest trends in metal forming, non‐metal forming, powder metallurgy and composite material processing are briefly discussed. The range of applications of finite elements on these subjects is extremely wide and cannot be presented in a single paper; therefore the aim of the paper is to give FE researchers/users only an encyclopaedic view of the different possibilities that exist today in the various fields mentioned above. An appendix included at the end of the paper presents a bibliography on finite element applications in material processing for 1994‐1996, where 1,370 references are listed. This bibliography is an updating of the paper written by Brannberg and Mackerle which has been published in Engineering Computations, Vol. 11 No. 5, 1994, pp. 413‐55.