Abstract:
evaluation of mechanical and interfacial properties of friction welded alumina-mild steel rods with the use of al6061 sheet are presented in this work. sem, edx analysis, hardness and bending strength tests were conducted. the bonds were attained through interfacial interlocking and intermetalllic phase formation with average bending strengths in the range of 40 to 200 mpa and insignificant hardness change in the parent alumina and mild steel. a preliminary simulation was made to predict the deformation, stress, strain and temperature distribution during the joining operation using a fully coupled thermo-mechanical fe model. the aluminum alloy metal being rubbed was simulated using a phenomenological johnson-cook viscoplasticity material model, which suited for materials subjected to large strains, high strain rates and high temperatures. the highest stress, strain and deformation are found to be within the heat affected zone of the weld close to the periphery rubbing surface region and correspond to the highest temperature profiles observed.

Abstract:
In this paper, an estimate of the expected maximum water levels associated with tide and tsunami interaction is computed along the coastal belts of Penang Island in Peninsular Malaysia. For this purpose, a nonlinear Polar coordinate shallow water model of the Indonesian tsunami of 2004 by Roy et al. (2007b) is used. Appropriate tidal condition is generated in the domain by applying tidal forcing through the western open sea boundary. For studying tide and tsunami interaction, the 2004 Indonesian tsunami is introduced in the previously generated tidal oscillation. The expected maximum possible water level along the coastal belts of Penang Island is estimated based on the interaction of tide and tsunami for different tidal conditions (high and low tidal periods). It is seen that the surge level is very sensitive towards the coastal belts due to interaction during high tide. The west coast of Penang Island is found to be vulnerable for stronger surge due to interaction. The influence of tidal wave on the tsunami wave height towards Penang Island is also investigated. The tide was found to have a significant effect in tsunami enhancement in the coastal regions.

Abstract:
The computation of the roots of positive definite matrices arises in nuclear magnetic resonance, control theory, lattice quantum chromo-dynamics (QCD), and several other areas of applications. The Cauchy integral theorem which arises in complex analysis can be used for computing f(A), in particular the roots of A, where A is a square matrix. The Cauchy integral can be approximated by using the trapezoid rule. In this paper, we aim to give a brief overview of the computation of roots of positive definite matrices by employing integral representation. Some numerical experiments are given to illustrate the theoretical results.

Abstract:
The pulsatile flow of blood through stenosed arteries is analyzed by assuming the blood as a two-fluid model with the suspension of all the erythrocytes in the core region as a non-Newtonian fluid and the plasma in the peripheral layer as a Newtonian fluid. The non-Newtonian fluid in the core region of the artery is assumed as a (i) Herschel-Bulkley fluid and (ii) Casson fluid. Perturbation method is used to solve the resulting system of non-linear partial differential equations. Expressions for various flow quantities are obtained for the two-fluid Casson model. Expressions of the flow quantities obtained by Sankar and Lee (2006) for the two-fluid Herschel-Bulkley model are used to get the data for comparison. It is found that the plug flow velocity and velocity distribution of the two-fluid Casson model are considerably higher than those of the two-fluid Herschel-Bulkley model. It is also observed that the pressure drop, plug core radius, wall shear stress and the resistance to flow are significantly very low for the two-fluid Casson model than those of the two-fluid Herschel-Bulkley model. Hence, the two-fluid Casson model would be more useful than the two-fluid Herschel-Bulkley model to analyze the blood flow through stenosed arteries.

Abstract:
Numerical solutions of one-dimensional heat and advection-diffusion equations are obtained by collocation method based on cubic B-spline. Usual finite difference scheme is used for time and space integrations. Cubic B-spline is applied as interpolation function. The stability analysis of the scheme is examined by the Von Neumann approach. The efficiency of the method is illustrated by some test problems. The numerical results are found to be in good agreement with the exact solution.

Abstract:
An incompressible Newtonian fluid is forced through the porous of a circular slider which is moving laterally on a horizontal plan. In this paper, we introduce and apply the one step Optimal Homotopy Analysis Method (one step OHAM) to the problem of the circular porous slider where a fluid is injected through the porous bottom. The effects of mass injection and lateral velocity on the heat generated by viscous dissipation are investigated by solving the governing boundary layer equations using one step optimal homotopy technique. The approximate solution for the coupled nonlinear ordinary differential equations resulting from the momentum equation is obtained and discussed for different values of the Reynolds number of the velocity field. The solution obtained is also displayed graphically for various values of the Reynolds number and it is shown that the one step OHAM is capable of finding the approximate solution of circular porous slider. 1. Introduction An interesting subject in mathematical physics is the study and analysis of flow between plates [1–6]. An analytical overview of study of porous bearing has been carried out by Morgan and Cameron in [3]. Gorla [7] discussed the fluid dynamical and heat transfer of the circular porous slider bearing. The study of the effects of the Reynolds number on circular porous slider has been investigated in [8] by using the Variational Iteration Method (VIM) which is one of the semi analytical methods. The fluid dynamics in a slider bearing have been discussed in [9] by using the series expansion and asymptotic expansion. Wang [9], in fact, discussed the numerical solution for the porous slider for the large Reynolds number. As it is well known the numerical methods such as finite difference and finite element are time consuming and may be difficult due to stability constraints. Toward this end, in this paper, we introduce and apply an effective method (so-called one step Homotopy Analysis Method) that provides accurate solution and has advantage over the finite difference and finite element methods. Semi analytical schemes such as Variational Iteration Method (VIM), Adomian Decomposition Method (ADM), Homotopy Perturbation Method (HPM), and Homotopy Analysis Method (HAM) have been widely employed to solve various linear and nonlinear ordinary and partial differential equations. One of the advantages of the semi approximate analytical methods is that these methods generate an infinite series solution and, unlike finite difference methods, semi approximate analytical methods do not have the problem of rounding

Abstract:
A new approach is developed to simulate the effect of far field tsunami in a limited area model domain where the coastal and Island boundaries are curvilinear in nature and the bending is high. The model is designed in a boundary fitted curvilinear grid system. To simulate the effect of far field tsunami, it is considered that the tsunami source is located far away from the model domain. The coastal and island boundaries and the other open boundaries of the model domain are represented by some functions so as to generate the boundary fitted grids. To use the regular finite difference scheme a transformation is used so that the physical domain is transformed into a rectangular one. The transformed shallow water equations are then solved in the transformed domain. The response of the tsunami source due to 26 December 2004 Indonesian tsunami is computed along the western open boundary of the model domain. Based on the response of the tsunami source, an appropriate boundary condition is formulated to simulate the effect of far field tsunami along the coastal belt. All simulations show excellent agreement with the observed data.

Abstract:
In this paper, a numerical method for the solution of a strongly coupled reaction-diffusion system, with suitable initial and Neumann boundary conditions, by using cubic B-spline collocation scheme on a uniform grid is presented. The scheme is based on the usual finite difference scheme to discretize the time derivative while cubic B-spline is used as an interpolation function in the space dimension. The scheme is shown to be unconditionally stable using the von Neumann method. The accuracy of the proposed scheme is demonstrated by applying it on a test problem. The performance of this scheme is shown by computing and error norms for different time levels. The numerical results are found to be in good agreement with known exact solutions.

Abstract:
The generalized nonlinear Klien-Gordon equation plays an important role in quantum mechanics. In this paper, a new three-time level implicit approach based on cubic trigonometric B-spline is presented for the approximate solution of this equation with Dirichlet boundary conditions. The usual finite difference approach is used to discretize the time derivative while cubic trigonometric B-spline is applied as an interpolating function in the space dimension. Several examples are discussed to exhibit the feasibility and capability of the approach. The absolute errors and error norms are also computed at different times to assess the performance of the proposed approach and the results were found to be in good agreement with known solutions and with existing schemes in literature.