International Journal of Engineering Mathematics The latest articles from Hindawi © 2017 , Hindawi Limited . All rights reserved. Modelling of the Deformation Diffusion Areas on a Para-Aramid Fabric with B-Spline Curves Mon, 20 Feb 2017 00:00:00 +0000 The geometrical modelling of the planar energy diffusion behaviors of the deformations on a para-aramid fabric has been performed. In the application process of the study, in the experimental period, drop test with bullets of different weights has been applied. The B-spline curve-generating technique has been used in the study. This is an efficient method for geometrical modelling of the deformation diffusion areas formed after the drop test. Proper control points have been chosen to be able to draw the borders of the diffusion areas on the fabric which is deformed, and then the De Casteljau and De Boor algorithms have been used. The Holditch area calculation according to the beams taken at certain fixed lengths has been performed for the B-spline border curve obtained as a closed form. After the calculations, it has been determined that the diffusion area where the bullet with pointed end was dropped on a para-aramid fabric is bigger and the diffusion area where the bullet with rounded end was dropped is smaller when compared with the areas where other bullets with different ends were dropped. Hatice Kuşak Samancı, Filiz Yağcı, and Ali Çalişkan Copyright © 2017 Hatice Kuşak Samancı et al. All rights reserved. Transient Free Convective MHD Flow Past an Exponentially Accelerated Vertical Porous Plate with Variable Temperature through a Porous Medium Tue, 17 Jan 2017 00:00:00 +0000 This paper is concerned with analytical solution of one-dimensional unsteady laminar boundary layer MHD flow of a viscous incompressible fluid past an exponentially accelerated infinite vertical plate in presence of transverse magnetic field. The vertical plate and the medium of flow are considered to be porous. The fluid is assumed to be optically thin and the magnetic Reynolds number is considered small enough to neglect the induced hydromagnetic effects. The governing boundary layer equations are first converted to dimensionless form and then solved by Laplace transform technique. Numerical values of transient velocity, temperature, skin friction, and Nusselt number are illustrated and are presented in graphs for various sets of physical parametric values, namely, Grashof number, accelerating parameter, suction parameter, permeability parameter, radiation parameter, magnetic parameter, and time. It is found that the velocity decreases with increases of the suction parameter for both cases of cooling and heating of the porous plate whereas skin friction increases with increase of suction parameter. Ashish Paul Copyright © 2017 Ashish Paul. All rights reserved. A New Iterative Numerical Continuation Technique for Approximating the Solutions of Scalar Nonlinear Equations Mon, 16 Jan 2017 09:10:23 +0000 The present study concerns the development of a new iterative method applied to a numerical continuation procedure for parameterized scalar nonlinear equations. Combining both a modified Newton’s technique and a stationary-type numerical procedure, the proposed method is able to provide suitable approximate solutions associated with scalar nonlinear equations. A numerical analysis of predictive capabilities of this new iterative algorithm is addressed, assessed, and discussed on some specific examples. Grégory Antoni Copyright © 2017 Grégory Antoni. All rights reserved. Unsteady Natural Convection Flow past an Infinite Cylinder with Thermal and Mass Stratification Wed, 11 Jan 2017 12:39:54 +0000 This paper presents an analytical solution of unsteady one-dimensional free convection flow past an infinite vertical circular cylinder in a stratified fluid medium. The dimensionless coupled linear governing partial differential equations are solved by Laplace transform technique for unit Prandtl number and Schmidt number. Effects of various physical parameters are presented with graphs. Numerical values of boundary layer thickness for different parameters are presented in table. Due to the effects of thermal and mass stratifications, the velocity, temperature, and skin friction, Nusselt number shows oscillatory behaviour at smaller times and then reaches steady state at larger times. Ashish Paul and Rudra Kanta Deka Copyright © 2017 Ashish Paul and Rudra Kanta Deka. All rights reserved. On the Extension of Sarrus’ Rule to Matrices: Development of New Method for the Computation of the Determinant of Matrix Mon, 05 Dec 2016 12:21:03 +0000 The determinant of a matrix is very powerful tool that helps in establishing properties of matrices. Indisputably, its importance in various engineering and applied science problems has made it a mathematical area of increasing significance. From developed and existing methods of finding determinant of a matrix, basketweave method/Sarrus’ rule has been shown to be the simplest, easiest, very fast, accurate, and straightforward method for the computation of the determinant of 3 × 3 matrices. However, its gross limitation is that this method/rule does not work for matrices larger than 3 × 3 and this fact is well established in literatures. Therefore, the state-of-the-art methods for finding the determinants of 4 × 4 matrix and larger matrices are predominantly founded on non-basketweave method/non-Sarrus’ rule. In this work, extension of the simple, easy, accurate, and straightforward approach to the determinant of larger matrices is presented. The paper presents the developments of new method with different schemes based on the basketweave method/Sarrus’ rule for the computation of the determinant of 4 × 4. The potency of the new method is revealed in generalization of the basketweave method/non-Sarrus’ rule for the computation of the determinant of () matrices. The new method is very efficient, very consistence for handy calculations, highly accurate, and fastest compared to other existing methods. M. G. Sobamowo Copyright © 2016 M. G. Sobamowo. All rights reserved. Various Fixed Point Theorems in Complex Valued -Metric Spaces Thu, 03 Nov 2016 11:37:38 +0000 We prove some common fixed point results for a pair of mappings which satisfy generalized contractive conditions with rational expressions having point-dependent control functions as coefficients in complex valued -metric spaces. The results of this paper generalize and extend the several known results in complex valued -metric spaces. Finally, examples are provided to verify the effectiveness and to usability of our main results. Anil Kumar Dubey, Manjula Tripathi, and Ravi Prakash Dubey Copyright © 2016 Anil Kumar Dubey et al. All rights reserved. Reflection of Plane Waves in Generalized Thermoelastic Half Space under the Action of Uniform Magnetic Field Wed, 02 Nov 2016 13:09:41 +0000 Reflection of longitudinal displacement waves in a generalized thermoelastic half space under the action of uniform magnetic field has been investigated. The magnetic field is applied in such a direction that the problem can be considered as a two-dimensional one. The discussion is based on the three theories of generalized thermoelasticity: Lord-Shulman (L-S), Green-Lindsay (G-L), and Green-Naghdi (G-N) with energy dissipation. We compute the possible wave velocities for different models. Amplitude ratios have been presented. The effects of magnetic field on various subjects of interest are discussed and shown graphically. Narottam Maity, S. P. Barik, and P. K. Chaudhuri Copyright © 2016 Narottam Maity et al. All rights reserved. An Efficient and Straightforward Numerical Technique Coupled to Classical Newton’s Method for Enhancing the Accuracy of Approximate Solutions Associated with Scalar Nonlinear Equations Wed, 02 Nov 2016 13:00:47 +0000 This study concerns the development of a straightforward numerical technique associated with Classical Newton’s Method for providing a more accurate approximate solution of scalar nonlinear equations. The proposed procedure is based on some practical geometric rules and requires the knowledge of the local slope of the curve representing the considered nonlinear function. Therefore, this new technique uses, only as input data, the first-order derivative of the nonlinear equation in question. The relevance of this numerical procedure is tested, evaluated, and discussed through some examples. Grégory Antoni Copyright © 2016 Grégory Antoni. All rights reserved. Perturbation Solutions for Hagen-Poiseuille Flow and Heat Transfer of Third-Grade Fluid with Temperature-Dependent Viscosities and Internal Heat Generation Mon, 10 Oct 2016 10:22:34 +0000 Regular perturbation technique is applied to analyze the fluid flow and heat transfer in a pipe containing third-grade fluid with temperature-dependent viscosities and heat generation under slip and no slip conditions. The obtained approximate solutions were used to investigate the effects of slip on the heat transfer characteristics of the laminar flow in a pipe under Reynolds’s and Vogel’s temperature-dependent viscosities. Also, the effects of parameters such as variable viscosity, non-Newtonian parameter, viscous dissipation, and pressure gradient at various values were established. The results of this work were compared with the numerical results found in literature and good agreements were established. The results can be used to advance the analysis and study of the behavior of third-grade fluid flow and steady state heat transfer processes such as those found in coal slurries, polymer solutions, textiles, ceramics, catalytic reactors, and oil recovery applications. B. Y. Ogunmola, A. T. Akinshilo, and M. G. Sobamowo Copyright © 2016 B. Y. Ogunmola et al. All rights reserved. Qualitative Analysis of a Leslie-Gower Predator-Prey System with Nonlinear Harvesting in Predator Mon, 03 Oct 2016 09:27:13 +0000 This paper deals with the study of the stability and the bifurcation analysis of a Leslie-Gower predator-prey model with Michaelis-Menten type predator harvesting. It is shown that the proposed model exhibits the bistability for certain parametric conditions. Dulac’s criterion has been adopted to obtain the sufficient conditions for the global stability of the model. Moreover, the model exhibits different kinds of bifurcations (e.g., the saddle-node bifurcation, the subcritical and supercritical Hopf bifurcations, Bogdanov-Takens bifurcation, and the homoclinic bifurcation) whenever the values of parameters of the model vary. The analytical findings and numerical simulations reveal far richer and complex dynamics in comparison to the models with no harvesting and with constant-yield predator harvesting. Manoj Kumar Singh, B. S. Bhadauria, and Brajesh Kumar Singh Copyright © 2016 Manoj Kumar Singh et al. All rights reserved. Sensitivity Studies and Parameters Identification for Noisy 3D Moving AWJM Model Tue, 06 Sep 2016 14:05:58 +0000 This work focuses on the identification of optimal model parameters related to Abrasive Waterjet Milling (AWJM) process. The evenly movement as well as variations of the jet feed speed was taken into account and studied in terms of 3D time dependent AWJM model. This gives us the opportunity to predict the shape of the milled trench surfaces. The required trench profile could be obtained with high precision in lack of knowledge about the model parameters and based only on the experimental measurements. We use the adjoint approach to identify the AWJM model parameters. The complexity of inverse problem paired with significant amount of unknowns makes it reasonable to use automatic differentiation software to obtain the adjoint statement. The interest in investigating this problem is caused by needs of industrial milling applications to predict the behavior of the process. This study proposes the possibility of identifying the AWJM model parameters with sufficiently high accuracy and predicting the shapes formation relying on self-generated data or on experimental measurements for both evenly jets movement and arbitrary changes of feed speed. We provide the results acceptable in the production and estimate the suitable parameters taking into account different types of model and measurement errors. Didier Auroux and Vladimir Groza Copyright © 2016 Didier Auroux and Vladimir Groza. All rights reserved. A New Accurate and Efficient Iterative Numerical Method for Solving the Scalar and Vector Nonlinear Equations: Approach Based on Geometric Considerations Sun, 07 Aug 2016 08:10:36 +0000 This paper deals with a new numerical iterative method for finding the approximate solutions associated with both scalar and vector nonlinear equations. The iterative method proposed here is an extended version of the numerical procedure originally developed in previous works. The present study proposes to show that this new root-finding algorithm combined with a stationary-type iterative method (e.g., Gauss-Seidel or Jacobi) is able to provide a longer accurate solution than classical Newton-Raphson method. A numerical analysis of the developed iterative method is addressed and discussed on some specific equations and systems. Grégory Antoni Copyright © 2016 Grégory Antoni. All rights reserved. On Stability of Vector Nonlinear Integrodifferential Equations Wed, 25 May 2016 13:58:22 +0000 Let be a bounded domain in a real Euclidean space. We consider the equation , where and are matrix-valued functions and is a nonlinear mapping. Conditions for the exponential stability of the steady state are established. Our approach is based on a norm estimate for operator commutators. Michael Gil’ Copyright © 2016 Michael Gil’. All rights reserved. Numerical Solution of the Blasius Viscous Flow Problem by Quartic B-Spline Method Mon, 11 Apr 2016 11:27:38 +0000 A numerical method is proposed to study the laminar boundary layer about a flat plate in a uniform stream of fluid. The presented method is based on the quartic B-spline approximations with minimizing the error -norm. Theoretical considerations are discussed. The computed results are compared with some numerical results to show the efficiency of the proposed approach. Hossein Aminikhah and Somayyeh Kazemi Copyright © 2016 Hossein Aminikhah and Somayyeh Kazemi. All rights reserved. New Improvement of the Expansion Methods for Solving the Generalized Fitzhugh-Nagumo Equation with Time-Dependent Coefficients Wed, 16 Dec 2015 14:24:10 +0000 An improvement of the expansion methods, namely, the improved -expansion method, for solving nonlinear second-order partial differential equation, is proposed. The implementation of the new approach is demonstrated by solving the generalized Fitzhugh-Nagumo equation with time-dependent coefficients. As a result, many new and more general exact travelling wave solutions are obtained including periodic function solutions, soliton-like solutions, and trigonometric function solutions. The exact particular solutions contain four types: hyperbolic function solution, trigonometric function solution, exponential solution, and rational solution. We obtained further solutions comparing this method with other methods. The results demonstrate that the new -expansion method is more efficient than the Ansatz method and Tanh method applied by Triki and Wazwaz (2013). Recently, this method is developed for searching exact travelling wave solutions of nonlinear partial differential equations. Abundant exact travelling wave solutions including solitons, kink, and periodic and rational solutions have been found. These solutions might play an important role in engineering fields. It is shown that this method, with the help of symbolic computation, provides a straightforward and powerful mathematical tool for solving the nonlinear physics. Jalil Manafian and Mehrdad Lakestani Copyright © 2015 Jalil Manafian and Mehrdad Lakestani. All rights reserved. Effects of Temperature and Stirring on Mass Transfer to Maximize Biodiesel Production from Jatropha curcas Oil: A Mathematical Study Tue, 27 Oct 2015 14:02:39 +0000 Biodiesel, the most promising renewable and alternative energy, is produced through transesterification of vegetable oils. One of the most cost effective sources of biodiesel is Jatropha curcas oil. Transesterification of Jatropha oil depends significantly on reaction parameters such as reaction time, temperature, molar ratio, catalyst amount, and stirrer speed. Among these parameters temperature and stirring have noteworthy effect on mass transfer. In this research article, we have shown the simultaneous effect of temperature and stirring on mass transfer by considering a mathematical model. The optimal profiles of temperature and stirring are determined as a combined parameter, for which maximum biodiesel can be obtained. Further, we have shown that this pair exists and is unique for the optimality of the system. Fahad Al Basir and Priti Kumar Roy Copyright © 2015 Fahad Al Basir and Priti Kumar Roy. All rights reserved. Successive Complementary Expansion Method for Solving Troesch’s Problem as a Singular Perturbation Problem Tue, 27 Oct 2015 06:32:42 +0000 A simple and efficient method that is called Successive Complementary Expansion Method (SCEM) is applied for approximation to an unstable two-point boundary value problem which is known as Troesch’s problem. In this approach, Troesch’s problem is considered as a singular perturbation problem. We convert the hyperbolic-type nonlinearity into a polynomial-type nonlinearity using an appropriate transformation, and then we use a basic zoom transformation for the boundary layer and finally obtain a nonlinear ordinary differential equation that contains SCEM complementary approximation. We see that SCEM gives highly accurate approximations to the solution of Troesch’s problem for various parameter values. Moreover, the results are compared with Adomian Decomposition Method (ADM) and Homotopy Perturbation Method (HPM) by using tables. Süleyman Cengizci and Aytekin Eryılmaz Copyright © 2015 Süleyman Cengizci and Aytekin Eryılmaz. All rights reserved. An Efficient Method to Find Solutions for Transcendental Equations with Several Roots Thu, 15 Oct 2015 13:06:26 +0000 This paper presents a method for obtaining a solution for all the roots of a transcendental equation within a bounded region by finding a polynomial equation with the same roots as the transcendental equation. The proposed method is developed using Cauchy’s integral theorem for complex variables and transforms the problem of finding the roots of a transcendental equation into an equivalent problem of finding roots of a polynomial equation with exactly the same roots. The interesting result is that the coefficients of the polynomial form a vector which lies in the null space of a Hankel matrix made up of the Fourier series coefficients of the inverse of the original transcendental equation. Then the explicit solution can be readily obtained using the complex fast Fourier transform. To conclude, the authors present an example by solving for the first three eigenvalues of the 1D transient heat conduction problem. Rogelio Luck, Gregory J. Zdaniuk, and Heejin Cho Copyright © 2015 Rogelio Luck et al. All rights reserved. Mixed Convection Flow of Magnetic Viscoelastic Polymer from a Nonisothermal Wedge with Biot Number Effects Mon, 12 Oct 2015 12:55:18 +0000 Magnetic polymers are finding increasing applications in diverse fields of chemical and mechanical engineering. In this paper, we investigate the nonlinear steady boundary layer flow and heat transfer of such fluids from a nonisothermal wedge. The incompressible Eyring-Powell non-Newtonian fluid model is employed and a magnetohydrodynamic body force is included in the simulation. The transformed conservation equations are solved numerically subject to physically appropriate boundary conditions using a second-order accurate implicit finite difference Keller Box technique. The numerical code is validated with previous studies. The influence of a number of emerging nondimensional parameters, namely, the Eyring-Powell rheological fluid parameter (), local non-Newtonian parameter based on length scale (), Prandtl number (Pr), Biot number (), pressure gradient parameter (), magnetic parameter (), mixed convection parameter (), and dimensionless tangential coordinate (), on velocity and temperature evolution in the boundary layer regime is examined in detail. Furthermore, the effects of these parameters on surface heat transfer rate and local skin friction are also investigated. S. Abdul Gaffar, V. Ramachandra Prasad, Bhuvana Vijaya, and O. Anwar Beg Copyright © 2015 S. Abdul Gaffar et al. All rights reserved. Robust Adaptive Exponential Synchronization of Two Different Stochastic Perturbed Chaotic Systems with Structural Perturbations Tue, 29 Sep 2015 07:49:15 +0000 The robust adaptive exponential synchronization problem of stochastic chaotic systems with structural perturbations is investigated in mean square. The stochastic disturbances are assumed to be Brownian motions that act on the slave system and the norm-bounded uncertainties exist in all parameters after decoupling. The stochastic disturbances could reflect more realistic dynamical behaviors of the coupled chaotic system presented within a noisy environment. By using a combination of the Lyapunov functional method, the robust analysis tool, the stochastic analysis techniques, and adaptive control laws, we derive several sufficient conditions that ensure the coupled chaotic systems to be robustly exponentially synchronized in the mean square for all admissible parameter uncertainties. This approach cannot only make the outputs of both master and slave systems reach synchronization with the passage of time between both systems but also attenuate the effects of the perturbation on the overall error system to a prescribed level. The main results are shown to be general enough to cover many existing ones reported in the literature. A. Soup Tewa Kammogne and H. B. Fotsin Copyright © 2015 A. Soup Tewa Kammogne and H. B. Fotsin. All rights reserved. Block Backward Differentiation Formulas for Fractional Differential Equations Tue, 29 Sep 2015 07:39:16 +0000 This paper concerns the numerical approximation of Fractional Initial Value Problems (FIVPs). This is achieved by constructing -step continuous BDFs. These continuous schemes are developed via the interpolation and collocation approach and are used to obtain the discrete -step BDF and () additional methods which are applied as numerical integrators in a block-by-block mode for the integration of FIVP. The properties of the methods are established and regions of absolute stability of the methods are plotted in the complex plane. Numerical tests including large systems arising form the semidiscretization of one-dimensional fractional Burger’s equation show that the methods are highly accurate and efficient. T. A. Biala and S. N. Jator Copyright © 2015 T. A. Biala and S. N. Jator. All rights reserved. Homotopy Simulation of Nonlinear Unsteady Rotating Nanofluid Flow from a Spinning Body Sun, 27 Sep 2015 09:04:28 +0000 The development of new applications of nanofluids in chemical engineering and other technologies has stimulated significant interest in computational simulations. Motivated by coating applications of nanomaterials, we investigate the transient nanofluid flow from a time-dependent spinning sphere using laminar boundary layer theory. The free stream velocity varies continuously with time. The unsteady conservations equations are normalized with appropriate similarity transformations and rendered into a ninth-order system of nonlinear coupled, multidegree ordinary differential equations. The transformed nonlinear boundary value problem is solved using the homotopy analysis method (HAM), a semicomputational procedure achieving fast convergence. Computations are verified with an Adomian decomposition method (ADM). The influence of acceleration parameter, rotational body force parameter, Brownian motion number, thermophoresis number, Lewis number, and Prandtl number on surface shear stress, heat, and mass (nanoparticle volume fraction) transfer rates is evaluated. The influence on boundary layer behavior is also investigated. HAM demonstrates excellent stability and leads to highly accurate solutions. O. Anwar Bég, F. Mabood, and M. Nazrul Islam Copyright © 2015 O. Anwar Bég et al. All rights reserved. Improving the Performance of Metaheuristics: An Approach Combining Response Surface Methodology and Racing Algorithms Wed, 16 Sep 2015 09:36:25 +0000 The setup of heuristics and metaheuristics, that is, the fine-tuning of their parameters, exercises a great influence in both the solution process, and in the quality of results of optimization problems. The search for the best fit of these algorithms is an important task and a major research challenge in the field of metaheuristics. The fine-tuning process requires a robust statistical approach, in order to aid in the process understanding and also in the effective settings, as well as an efficient algorithm which can summarize the search process. This paper aims to present an approach combining design of experiments (DOE) techniques and racing algorithms to improve the performance of different algorithms to solve classical optimization problems. The results comparison considering the default metaheuristics and ones using the settings suggested by the fine-tuning procedure will be presented. Broadly, the statistical results suggest that the fine-tuning process improves the quality of solutions for different instances of the studied problems. Therefore, by means of this study it can be concluded that the use of DOE techniques combined with racing algorithms may be a promising and powerful tool to assist in the investigation, and in the fine-tuning of different algorithms. However, additional studies must be conducted to verify the effectiveness of the proposed methodology. Eduardo Batista de Moraes Barbosa, Edson Luiz França Senne, and Messias Borges Silva Copyright © 2015 Eduardo Batista de Moraes Barbosa et al. All rights reserved. Rational-Like Solutions of a Differential-Difference Equation Related to Ablowitz-Ladik Spectral Problem Thu, 03 Sep 2015 14:00:43 +0000 By using the Casoratian technique, we construct the double Casoratian solutions whose entries satisfy matrix equation of a differential-difference equation related to the Ablowitz-Ladik spectral problem. Soliton solutions and rational-like solutions are obtained from taking special cases in general solutions. Jiang-ping Zhang, Qi Li, and Shou-ting Chen Copyright © 2015 Jiang-ping Zhang et al. All rights reserved. A Wavelet Algorithm for Fourier-Bessel Transform Arising in Optics Mon, 31 Aug 2015 13:00:10 +0000 The aim of the paper is to propose an efficient and stable algorithm that is quite accurate and fast for numerical evaluation of the Fourier-Bessel transform of order , using wavelets. The philosophy behind the proposed algorithm is to replace the part of the integral by its wavelet decomposition obtained by using CAS wavelets thus representing as a Fourier-Bessel series with coefficients depending strongly on the input function . The wavelet method indicates that the approach is easy to implement and thus computationally very attractive. Nagma Irfan and A. H. Siddiqi Copyright © 2015 Nagma Irfan and A. H. Siddiqi. All rights reserved. Global Stability of a Delayed SIRI Epidemic Model with Nonlinear Incidence Sun, 07 Dec 2014 07:38:14 +0000 In this paper we propose the global dynamics of an SIRI epidemic model with latency and a general nonlinear incidence function. The model is based on the susceptible-infective-recovered (SIR) compartmental structure with relapse (SIRI). Sufficient conditions for the global stability of equilibria (the disease-free equilibrium and the endemic equilibrium) are obtained by means of Lyapunov-LaSalle theorem. Also some numerical simulations are given to illustrate this result. Amine Bernoussi, Abdelilah Kaddar, and Said Asserda Copyright © 2014 Amine Bernoussi et al. All rights reserved. Influence of Variable Thermal Conductivity on MHD Boundary Layer Slip Flow of Ethylene-Glycol Based Cu Nanofluids over a Stretching Sheet with Convective Boundary Condition Thu, 06 Nov 2014 12:43:54 +0000 An analysis is carried out to investigate the influence of variable thermal conductivity and partial velocity slip on hydromagnetic two-dimensional boundary layer flow of a nanofluid with Cu nanoparticles over a stretching sheet with convective boundary condition. Using similarity transformation, the governing boundary layer equations along with the appropriate boundary conditions are transformed to a set of ordinary differential equations. Employing Runge-kutta fourth-order method along with shooting technique, the resultant system of equations is solved. The influence of various pertinent parameters such as nanofluid volume fraction parameter, the magnetic parameter, radiation parameter, thermal conductivity parameter, velocity slip parameter, Biot number, and suction or injection parameter on the velocity of the flow field and heat transfer characteristics is computed numerically and illustrated graphically. The present results are compared with the existing results for the case of regular fluid and found an excellent agreement. N. Bhaskar Reddy, T. Poornima, and P. Sreenivasulu Copyright © 2014 N. Bhaskar Reddy et al. All rights reserved. Aligned Magnetic Field, Radiation, and Rotation Effects on Unsteady Hydromagnetic Free Convection Flow Past an Impulsively Moving Vertical Plate in a Porous Medium Tue, 21 Oct 2014 09:06:38 +0000 We analyse the effects of aligned magnetic field, radiation, and rotation on unsteady hydromagnetic free convection flow of a viscous incompressible electrically conducting fluid past an impulsively moving vertical plate in a porous medium in presence of heat source. An exact solution of the governing equations in dimensionless form is obtained by Laplace transform technique in ramped temperature case. To compare the results obtained in this case with that of isothermal plate, the exact solution of the governing equations is also obtained for isothermal plate and results are discussed graphically in both ramped temperature and isothermal cases. Sandeep Naramgari, Sugunamma Vangala, and Mohankrishna Penem Copyright © 2014 Sandeep Naramgari et al. All rights reserved. Quadratic Prediction Models for the Performance Comparison of a Marine Engine Fuelled with Biodiesels B5 and B20 Tue, 30 Sep 2014 08:34:28 +0000 According to Thailand’s renewable energy development plan, biodiesel is one of the interesting alternative energies. In this research, biodiesels B5 and B20 are tested in a marine engine. The experimental results are then compared by using three different techniques including (1) the conventional technique, (2) average of the point-to-point comparisons, and (3) a comparison by using quadratic prediction models. This research aims to present the procedures of these techniques in-depth. The results show that the comparison by using quadratic prediction models can accurately predict ample amounts of results and make the comparison more logical. The results are compatible with those of the conventional technique, while the average of the point-to-point comparisons shows diverse results. These results are also explained on the fuel property basis, confirming that the quadratic prediction model and the conventional technique are practical, but the average of the point-to-point comparison technique presents an inaccurate result. The benefit of this research shows that the quadratic prediction model is more flexible for future science and engineering experimental design, thus reducing cost and time usage. The details of the calculation, results, and discussion are presented in the paper. Chedthawut Poompipatpong Copyright © 2014 Chedthawut Poompipatpong. All rights reserved. A New Approach to Solve Intuitionistic Fuzzy Optimization Problem Using Possibility, Necessity, and Credibility Measures Thu, 25 Sep 2014 13:03:03 +0000 Corresponding to chance constraints, real-life possibility, necessity, and credibility measures on intuitionistic fuzzy set are defined. For the first time the mathematical and graphical representations of different types of measures in trapezoidal intuitionistic fuzzy environment are defined in this paper. We have developed intuitionistic fuzzy chance constraints model (CCM) based on possibility and necessity measures. We have also proposed a new method for solving an intuitionistic fuzzy CCM using chance operators. To validate the proposed method, we have discussed three different approaches to solve the intuitionistic fuzzy linear programming (IFLPP) using possibility, necessity and credibility measures. Numerical and graphical representations of optimal solutions of the given example at different possibility and necessity, levels have been discussed. Dipankar Chakraborty, Dipak Kumar Jana, and Tapan Kumar Roy Copyright © 2014 Dipankar Chakraborty et al. All rights reserved.