In this article, unsteady boundary layer flow formed over a vertical surface due to impulsive mo-tion and buoyancy is investigated. The mathematical model which properly accounts for space and temperature-dependent internal heat source in a flowing fluid is incorporated into the energy equa-tion. This model is presented in this study as a term which accounts for two different forms of internal heat generation during the short time period and long time period. Due to the fluid flow under consideration, the influence of thermal-diffusion and diffusion-thermo are incorporated into the governing equation since it may not be realistic to assume that both effects are of smaller order of magnitude than the effects described by Fourier’s or Fick’s law. The corresponding effect of in-ternal heat source on viscosity is considered, the viscosity is assumed to vary as a linear function of temperature. The flow model is described in terms of a highly coupled and nonlinear system of partial differential equations. The governing equations are nondimensionalized by using suitable similarity transformation which unraveled the behavior of the fluid flow at short time and long time periods. The dimensionless system of non-linear coupled partial differential equations (PDEs) is solved using BIVARIATE SPECTRAL RELAXATION METHOD (BSRM). A parametric study of selected parameters is conducted and results of the surface shear stress, heat transfer and mass transfer at the wall are illustrated graphically and physical aspects of the problem are discussed.

Recently, it has been observed that a new METHOD for generating continuous distributions, T 􀀀 X family, can be quite effectively used to analyze the data in one dimension. The aim of this study is to generalize this METHOD to two dimensional space so that the marginals would have T 􀀀 X distributions. So, several examples and properties of this family have been presented. As an application, a special distribution of this family, called BIVARIATE Weibull-Rayleigh-Rayleigh, is fitted to a data set and is shown to have a better fit.

In this paper, the fuzzy BIVARIATE Chebyshev METHOD is proposed for solving the fuzzy Volterra-Fredholm integral equations (FVFIE). FVFTE is converted to a dual fuzzy linear system that can be solved by the proposed METHOD in [10]. And finally, the METHOD is explained with illustrative examples.

Dynamic RELAXATION METHOD is an iterative procedure for solving the simultaneous system of equations. This technique is used in the static and dynamic nonlinear structural analysis. One of the most important parameters in this approach is fictitious damping factor. If this factor is selected more accurately, convergence rate will rise. In this paper, inverse vector iteration METHOD is utilized to find the damping factor in the dynamic RELAXATION iterations, and a new formulation is proposed. The geometric nonlinear analysis of several plane and space trusses and also structural frames are performed using the suggested METHOD. The numerical results indicate that the convergence rate improves compared with the conventional dynamic RELAXATION procedure so that the number of iterations and the analysis time decrease significantly. Consequently, the authors' technique makes the solving process faster and more capable.

Overally location problem could be classified as desirable facility location and undesirable facility location. In the undesirable facility location problem contrary to desirable location, facilities are located far from service receiver facilities as much as possible. The problem of locating such facilities is discussed in this paper. This research is focused on the “ not in my backyard” (NIMBY) which refers to the social phenomena in which residents are opposed to locate undesirable facilities around their houses. Examples of such facilities include electric transmission lines and recycling centers. Due to the opposition typically encountered in constructing an undesirable facility, the facility planner should understand the nature of the NIMBY phenomena and consider it as a key factor in the determining facility location. A integer linear model of this problem and a Lagrange RELAXATION METHOD are proposed in this research. This METHOD relaxes up the hard constraints and adds the constraints to the objective function with a Lagrangian multiplier. To show that the Lagrangian RELAXATION METHOD is computationally powerful exact solution algorithm and is capable to solve the medium-size problems, the performance of the proposed algorithm is examined by applying it to several test problems.

Dynamic RELAXATION is an iterative technique, which is used as an equation solver. In this paper, a new time step will be formulated for Dynamic RELAXATION METHOD. The suggested technique is based on the minimization of residual force in each iteration. Mathematical theories and numerical examples are used to verify efficiency of the formulation. By using optimum time step, mathematical convergence rank of DR algorithm will be infinite and two in linear and nonlinear analyses, respectively. To investigate the capability of the proposed formulation, isotropic plates and frame structure by linear and geometrical nonlinear behaviors are analyzed. This study shows that optimum time step reduces number of convergence iterations.Therefore, the cost and the computational time will be reduced. As a result, the suggested formulation for optimum time step has higher mathematical and numerical efficiency than other common METHODs, such as constant time step. Therefore, the convergence rate of DR iterations will considerably improve.

This study investigates a time-domain METHOD for modeling general transient elastodynamic problems using the SPECTRAL-based finite element METHOD (SEM) which is based upon a conforming mesh of two-dimensional quadrilaterals. Employing the Galerkin weighted residual METHOD, detailed formulation of the SEM is derived in which various aspects involving in elastodynamic problems are discussed. The accuracy and efficiency of the METHOD is fully demonstrated by comparing results obtained from the SEM with those reported in other studies. For this purpose, a set of wave propagation and structural dynamic problems, subjected to various load forms such as triangular load, Heaviside step load, sinusoidal impulsive load, and ramped load are modeled using the SEM. Furthermore, support motion boundary conditions are examined using the SEM. Each problem is successfully modeled using a very small number of degrees of freedom in comparison with other numerical METHODs. The numerical results agree very well with the analytical solutions as well the results from other numerical METHODs.

The common dynamic RELAXATION algorithm (DR) does not have the ability to trace the static path. In these techniques, the jumps occur at the limit points. A variable load factor is used to fix this defect. Here, a new procedure is suggested to calculate the load factor. The authors’ relationship is achieved by minimizing external work and residual energy, simultaneously. It should be stated that the proposed load factor depends only on the DR artificial parameters. To show the ability of the new formulation, several truss and shell structures with nonlinear geometrically behavior are analyzed. All used METHODs are ranked by the number of iterations, numbers of convergence points and total duration analysis. Numerical solutions show the high efficiency of the new METHOD. In other words, the authors' technique, in addition to good accuracy, has higher convergence rate, in comparison to the other strategies. On the other hand, the time duration of the proposed METHOD to trace the static paths has been reduced appropriately compared to other techniques.