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Integral equations play a crucial role in many scientific and engineering problems, though solving them is often challenging. This paper addresses the solution of multi-dimensional systems of mixed Volterra-Fredholm integral equations (SMVF-IEs) by means of a Legendre-Gauss-Lobatto collocation method. The one-dimensional case is addressed first. Afterwards, the method is extended to two-dimensional linear and nonlinear SMVF-IEs. Several numerical examples reveal the effectiveness of the approach and show its superiority in comparison to other alternative techniques for treating SMVF-IEs. [ABSTRACT FROM AUTHOR]

The passive feature of natural convection encourages continuous investigation on this field. This research work studies the natural convection inside a cavity of wavy vertical surfaces, including a heat source block standing on the base of cavity. The employed liquid is a hybrid water–Cu–Al 2 O 3 nanofluid. The vertical wavy surfaces are fixed at low temperature, while the heat source remains constant at a higher temperature. The Galerkin finite element method is applied to obtain the numerical solutions. Besides the common visualization tools, the heatlines tool is used in this paper as well. It is found from the outcomes that the Nusselt number is purely proportional to the length of the heat source. In addition, the hybrid water–Cu–Al 2 O 3 nanofluid exhibits a higher Nusselt number than that corresponding to a pure water and as well as other regular nanofluids. The percentages of the average heat transfer gained by the hybrid nanofluid at ϕ = 0.02 are 13.7% and 5% higher than those for pure water and other nanofluids. [ABSTRACT FROM AUTHOR]

One of the problems in the numerical analysis of solutions is the nonlinear variable-order fractional convection-diffusion equations for nonsmooth solutions. We offer a numerical technique based on the shifted Legendre Gauss-Lobatto collocation and the shifted Chebyshev Gauss-Radau collocation to solve the problem. The technique with shifted Legendre Gauss-Lobatto and shifted Chebyshev Gauss-Radau nodes is applied to diminish nonlinear variable-order fractional convection-diffusion equations to an easily-solvable system of algebraic equations. Besides, we give numerical test examples to show that the approach can preserve the nonsmooth solution of the underlying problems. [ABSTRACT FROM AUTHOR]

An analysis is presented to investigate the effect of thermophoresis particle deposition and variable viscosity on Darcy mixed convective heat and mass transfer of a viscous, incompressible fluid past a porous wedge in the presence of chemical reaction. The wall of the wedge is embedded in a uniform Darcian porous medium in order to allow for possible fluid wall suction or injection. The viscosity of the fluid is assumed to be a inverse linear function of temperature. The results are analyzed for the effect of different physical parameters, such as variable viscosity, magnetic, chemical reaction and thermophoresis parameters, on the flow, the heat and mass transfer characteristics.

This work is concerned with magnetohydrodynamic viscous flow due to a shrinking sheet in the presence of suction. The cases of two dimensional and axisymmetric shrinking are discussed. The governing boundary layer equations are written into a dimensionless form by similarity transformations. The transformed coupled nonlinear ordinary differential equations are numercally solved by using an advanced numeric technique. Favorability comparisons with previously published work are presented. numerical results for the dimensionless velocity, temperature and concentration profiles are obtained and displayed graphically for pertinent parameters to show interesting aspects of the solution.

In the present study, an analysis is carried out to study the variable viscosity and chemical reaction effects on MHD flow, heat, and mass transfer characteristics in a viscous fluid over a porous wedge in the presence of heat radiation. The wall of the wedge is embedded in a uniform Darcian porous medium in order to allow for possible fluid wall suction or injection. The governing boundary layer equations are written into a dimensionless form by similarity transformations. The transformed coupled nonlinear ordinary differential equations are solved numerically by using the R. K. Gill and shooting methods. The effects of different parameters on the dimensionless velocity, temperature, and concentration profiles are shown graphically. Comparisons with previously published works are performed and excellent agreement between the results is obtained. The results are presented graphically and the conclusion is drawn that the flow field and other quantities of physical interest are significantly influenced by these parameters.

The capacity analysis under mixed traffic flow conditions considers a dynamic problem. Traffic microsimulation models have been a very effective tool for such problem. Calibration and validation of microsimulation models are essential steps to ensure the reliability of the models. This paper suggests the use of measurable variables for calibrating micro-simulation models. Therefore, the objective of this paper is to estimate the roadway capacity through micro-simulation models calibrated using spot speed distributions. The micro-simulation software VISSIM was used to model and analyze the two-lane and multi-lane roads. The models were calibrated and validated using the data collected in Menoufia Governorate, Egypt. The K-S test was performed to ensure that simulated speed distributions matched the observed distributions. It was found that the models were successfully calibrated and validated. Finally, roadway capacity was estimated based on field data and micro-simulation models through the flow rate-density relationship. The results showed a good match between the field and simulated capacity. [ABSTRACT FROM AUTHOR]

This article reports TL response for different glass modifier and doping concentration. Alkali oxides (Na2O and Li2O) and alkali earth oxide (CaO) will be used as a glass modifier for strontium borate based glass. The samples were prepared by melt quenching technique. Dy2O3 concentrations ranging from 0.00 to 0.70 mol% and exposure doses of 1 to 9 Gy will be varied. All glass samples exhibit the prominent peak temperature positioned at 186 oC to 232 oC. From all the samples, one of the samples shows an excellent linearity dose response, higher TL and show good reproducibility after 5 cycles exposure which is sodium strontium borate doped with 0.1 mol% Dy2O3 (optimum concentration).