]> 2012 5 4 104
An Analytical Approximation for Boundary Layer Flow Convection Heat and Mass Transfer Over a Flat Plate An Analytical Approximation for Boundary Layer Flow Convection Heat and Mass Transfer Over a Flat Plate en en In this article, Laplace transform and new homotopy perturbation methods are adopted to study the problem of forced convection over a horizontal flat plate analytically. The problem is a system of nonlinear ordinary differential equations which arises in boundary layer flow. The solutions approximated by the proposed method are shown to be precise as compared to the corresponding results obtained by numerical method. A high accuracy of new method is evident. 241 257 Hossein Aminikhah Ali Jamalian Laplace transform New homotopy perturbation method Blasius equation. Article.1.pdf  H. Blasius , The Boundary Layers in Fluid with Little Friction (in German) Zeitschrift fur Mathematik und Physik, English translation available as NACATM 1256, 56 (1) (1950), 908-1 ## J. H. He, Homotopy perturbation technique, Comput Meth Appl Mech Eng, 178 (1999), 257-262 ## J. H. He, A coupling method of homotopy technique and perturbation technique for nonlinear problems, Int J Non-linear Mech, 35 (2000), 37-43 ## J. H. He, New interpretation of homotopy perturbation method, Int J Mod Phys B, 20 (2006), 2561-8 ## J. H. He, Recent development of homotopy perturbation method , Topol. Meth Nonlinear Anal, 31 (2008), 205-9 ## J. H. He, The homotopy perturbation method for nonlinear oscillators with discontinuities, Appl Math Comput, 151 (2004), 287-92 ## J. H. He, Application of homotopy perturbation method to nonlinear wave equations, Chaos Soliton Fract, 26 (2005), 695-700 ## J. H. He, Limit cycle and bifurcation of nonlinear problems, Chaos Soliton Fract, 26 (2005), 827-33 ## A. Rajabi, D. D. Ganji , Application of homotopy perturbation method in nonlinear heat conduction and convection equations, Phys Lett A, 360 (2007), 570-3 ## D. D. Ganji, A. Sadighi, Application of homotopy perturbation and variational iteration methods to nonlinear heat transfer and porous media equations, J Comput Appl Math, 207 (2007), 24-34 ## D. D. Ganji , The application of Hes homotopy perturbation method to nonlinear equations arising in heat transfer, Phys Lett A, 355 (2006), 337-41 ## G. A. Afrouzi, D. D. Ganji, H. Hosseinzadeh, R. A. Talarposhti, Fourth order Volterra integro differential equations using modifed homotopy-perturbation method, The Journal of Mathematics and Computer Science, 3 (2011), 179-191 ## Mohamed I. A. Othman, A. M. S. Mahdy, R. M. Farouk , Numerical Solution of 12th Order Boundary Value Problems by Using Homotopy Perturbation Method, The Journal of Mathematics and Computer Science, 1 (2010), 14-27 ## J. Singh, D. Kumar, Sushila, S. Gupta, APPLICATION OF HOMOTOPY PERTURBATION TRANSFORM METHOD TO LINEAR AND NON-LINEAR SPACE-TIME FRACTIONAL REACTIONDIFFUSION EQUATIONS, The Journal of Mathematics and Computer Science, 5 (2012), 40-52 ## S. Abbasbandy, A numerical solution of Blasius equation by Adomians decomposition method and comparison with homotopy perturbation method, Chaos Soliton Fract, 31 (2007), 257-60 ## J. Biazar, H. Ghazvini , Exact solutions for nonlinear Schrodinger equations by He's homo-topy perturbation method, Phys Lett A, 366 (2007), 79-84 ## S. Abbasbandy , Numerical solutions of the integral equations: homotopy perturbation and Adomians decomposition method, Appl Math Comput, 173 (2006), 493-500 ## JH. He, Homotopy perturbation method for solving boundary value problems, Phys Lett A, 350 (2006), 87-8 ## Q. Wang, Homotopy perturbation method for fractional KdV-Burgers equation, Chaos Soliton Fract, 35 (2008), 843-850 ## E. Yusufoglu, Homotopy perturbation method for solving a nonlinear system of second order boundary value problems, Int J Nonlinear Sci Numer Simul, 8 (2007), 353-8 ## Y. Khan, N. Faraz, A. Yildirim, Q. Wu, A Series Solution of the Long Porous Slider, Tribology Transactions, 54, 2 (2011), 187-191 ## M. Esmaeilpour, D. D. Ganji, Application of He’s homotopy perturbation method to boundary layer flow and convection heat transfer over a flat plate, Physics Letters A , 372 (2007), 33-38 ## L. Howarth, On the Solution of the Laminar Boundary-Layer Equations, Proceedings of the Royal Society of London, A , 164 (1983), 547-579 ## H. Aminikhah, Analytical Approximation to the Solution of Nonlinear Blasius’ Viscous Flow Equation by LTNHPM, ISRN Mathematical Analysis, Article ID 957473, doi:10.5402/2012/957473. , 2012 (2012), 1-10 ## H. Aminikhah, M. Hemmatnezhad, An efficient method for quadratic Riccati differential equation, Commun. Nonlinear Sci. Numer. Simul. , 15 (2010), 835-839 ## H. Aminikhah, A. Jamalian, A new efficient method for solving the nonlinear Fokker–Planck equation, Scientia Iranica, In Press, Available online 3 July 2012. (2012) ## H. Aminikhah, F. Mehrdoust, A. Jamalian, A New Efficient Method for Nonlinear Fisher-Type Equations, Journal of Applied Mathematics , Article ID 586454, doi:10.1155/2012/586454. , 2012 (2012), 1-18 ## R. Byron Bird, Warren E. Stewart, Edwin N. Lightfoot , Transport Phenomena, John Wiley& Sons (ASIA) Pte Ltd, 627. ()
Solution of Fredholm Integro-differential Equations System by Modified Decomposition Method Solution of Fredholm Integro-differential Equations System by Modified Decomposition Method en en In this paper, the technique of modified decomposition method is used to solve a system of linear integro-differential equations with initial conditions. Moreover, two particular examples are discussed to show relability and the performance of the modified decomposition method. 258 264 M. Rabbani B. Zarali Modified decomposition method System of Fredholm integro-differential equations. Article.2.pdf  G. Adomian , Solving Frontier problem of Physics: The Decomposition Method , Kluwer Academic press, (1994) ## A. Arikoglu, I. Ozkol , Solutions of Integral and Integro-Differential Equation Systems by Using Differential Transform Method, Computers Mathematics with Applications, 56 (2008), 2411-2417 ## T. Badredine, K. Abbaoui, Y. Cherruault , Convergence of Adomian’s method applied to integral equations, Kybernetes, 28(5) (1999), 557-564 ## J. Biazar, Solution of systems of integro-differential equation by Adomian decomposition method, Appl. Math. Comput, 168 (2003), 1232-1238 ## J. Biazar, H. Ghazvini, M. Eslami, Hes Homotopy perturbation method for systems of integro-differential Equations, Chaos, Solitions and Fractals, 39 (2009), 1253-1258 ## Y. Cherruault, convergence of Adomian method , kybernetes, 18 (1989), 31-38 ## S. Hyder Ali Muttaqi Shah, S. H. Sandilo, Modified Decompositin method for nonlinear Volterra-Fredholm integro-differential equation , Journal of Basic and Applied Sciences, 6 (2010), 13-16 ## K. Maleknejad, F. Mirzaee, S. Abbasbandy, Solving linear Integro-differential equations system by using rationalized Haar functions method, Applied Mathematics & Computation, (2003), - ## K. Maleknejad, M. Tavassoli Kajani, Solving Linear integro-differential equation system by Galerkin methods with Hybrid functions, Applied Mathematics and Computation, 159 (2004), 603-612 ## J. Pour-Mahmoud, M. Y. Rahimi-Ardabili, S. Shahmorad , Numerical solution of the system of Fredholm integro-differential equations by the Tau method, Applied Mathematics and Computation, 168 (2005), 465-478 ## AM. Wazwaz, A reliable modification of Adomian’s decomposition method , Appl Math Comput, (1999) ## AM. Wazwaz, A reliable treatment for mixed Volterra-Fredholm integral equations , Appl Math Comput, (2002) ## AM. Wazwaz, A first course In integral equations , World Scientific, Singapore (1997)
Neighborhood Number in Graphs Neighborhood Number in Graphs en en A set $$S$$ of points in graph $$G$$ is a neighborhood set if $$G=\cup_{\nu\in S}\langle N[\nu]\rangle$$ where $$\langle N[\nu]\rangle$$ is the subgraph of $$G$$ induced by $$\nu$$ and all points adjacent to $$\nu$$. The neighborhood number, denoted $$n_0(G)$$, of $$G$$ is the minimum cardinality of a neighborhood set of $$G$$. In this paper, we study the neighborhood number of certain graphs. 265 270 Z. Tahmasbzadehbaee N. S. Soner D. A. Mojdeh Neighborhood set Neighborhood number Jahangir graph Harary graphs Circulant graph. Article.3.pdf  J. C. Bermond, F. Comellas, D. F. Hsu, Distributed loop computer networks: a survey, J. Paralled Distrib. Comput. , 24 (1995), 2-10 ## F. Boesch, R. Tindell , Circulants and their connectivity, J. Graph Theory, 8 (1984), 487-499 ## S. Ghobadi, N. D. Soner, D. A. Mojdeh, Vertex neighborhood critical graphs, International Journal of Mathematics and Analysis, 9(1-6) (2008), 89-95 ## E. Sampathkumar, P. S. Neeralagi, Independent, Perfect and Connected neighborhood number of a graph, Journal of Combinatorics, Information & System Sciences, 19(3-4) (1994), 139-145 ## E. Sampathkumar, P. S. Neeralagi, The neighborhood number of a graph, Indian J. Pure Appl. Math., 16(2) (1985), 126-132 ## D. B. West , Introduction to graph theory (Second Edition), Prentice Hall, USA (2001)
Mathematical Modeling of Thermosyphon Heat Exchanger for Energy Saving Mathematical Modeling of Thermosyphon Heat Exchanger for Energy Saving en en Waste heat recovery is very important, because not only it reduces the expenditure of heat generation, but also it is of high priority in environmental consideration, such as reduction in greenhouse gases. One of the devices is used in waste heat recovery is thermosyphon heat exchanger (THE). In this paper, theoretical research has been carried out to investigate the thermal performance of an air to air thermosyphon heat exchanger. This purpose is done by solving simultaneous principles equations. It was found that with implementation of targeted subsides plan in Islamic Republic of Iran, saving in gas oil consumption is very considerable by using this device. 271 279 Mohammad Reza Sarmasti Emami Mathematical Modeling Thermosyphon Heat Exchanger Energy Saving Article.4.pdf  S. W. Chi, Heat Pipe Theory and Practice, McGraw Hill, New York (1976) ## M. R. Sarmasti Emami, Energy Recovery in Poultry Plants by Heat Pipe Heat Exchangers, the 6th International Chemical Engineering Congress and Exhibition, 16-20 November, Iran (2009) ## M. R. Sarmasti Emami, S. H. Noie, R. Shokri, Simulation and economical investigation of application of heat pipe heat exchanger in air condition systems, 10th National conference of Chemical Engineering, Zahedan, Iran (2005) ## , , www.worldwatch.org. , () ## J. O. Tan, C.Y. Liu, Predicting the Performance of a Heat Pipe Heat Exchanger using the Effectiveness NTU Method, Int. J. Heat Fluid Flow, 11(4) (1990), 1-376 ## B. J. Haung, J.T. Tsuei, A Method of Analysis for Heat Pipe Heat Exchangers, Int. J. Heat Mass Transfer, 28(3) (1985), 1-553 ## A. Faghri, Heat pipe Science and Technology, Taylor & Francis, USA (1995) ## F. P. Incropera, D. P. DeWitt, Fundamentals of Heat and Mass Transfer, 5th ed., John Wiley and Sons, New York, (2002), 1-640 ## E. Azad, F. Geoola, A Design Procedure for Gravity-Assisted Heat Pipe Heat Exchanger, Heat Recovery System, Elsevier Science, (1984), 1-101 ## P. D. Dunn, D. A. Reay, Heat pipes, 3rd ed., Pergamon Press, Oxford, U.K. (1994) ## A. Faghri , Heat pipe science and Technology, Taylor & Francis , Washington, D.C. (1995) ## Z. R. Gorbis, G. A. Savchenkov, Low Temperature Tow-phase Closed Thermosyphon Investigation, proc. 2nd International Heat pipe Conf. Bologna, Italy, (1967), 37-45 ## M. Shiraishi, M. Yoneya, A. Yabe, Visual study of operating limit in the Tow-Phase closed thermosyphone, proc. 5th international Heat Pipe Conf., 14-17 May, Tsukuba, Japan, (1984), 11-17
Solving Nonlinear System of Mixed Volterra-fredholm Integral Equations by Using Variational Iteration Method Solving Nonlinear System of Mixed Volterra-fredholm Integral Equations by Using Variational Iteration Method en en In this paper for solving nonlinear system of mixed Volterra-Fredholm integral equations by using variational iteration method, we have used differentiation for converting problem to suitable form such that it can be useful for constructing a correction functional with general lagrange multiplier. The optimum of lagrange multiplier can be found by variational theorem and by choosing of restrict variations properly. By substituting of optimum lagrange multiplier in correction functional, we obtain convergent sequences of functions and by appropriate choosing initial approximation, we can get approximate of the exact solution of the problem with few iterations. Some applications of nonlinear mixed Volterra-Fredholm integral equations arise in mathematical modeling of the Spatio-temporal development of an epidemic. So nonlinear system of mixed Volterra-Fredholm integral equations is important and useful. The above method independent of small parameter in comparison with similar works such as perturbation method. Also this method does not require discretization or linearization. Accuracy of numerical results show that the method is very effective and it is better than Adomian decomposition method since it has faster convergence and it is more simple. Also this method has a closed form and avoids the round of errors for finding approximation of the exact solution. The looking forward the proposed method can be used for solving various kinds of nonlinear problems. 280 287 M. Rabbani R. Jamali Nonlinear system of mixed Integral equation Variational method Volterra-Fredholm lagrange multiplier Article.5.pdf  A. Yildirim, Homotopy perturbation method for the mixed Voltera-Fredholm integral equations, chaos,solitons and fractals, 42 (2009), 2760-2764 ## M. A. Abdou, A. A. Soliman, Variational iteration method for solving Burger's and coupled Burger's equations, J.comput.Appl.Math, 181 (2005), 245-251 ## S. Abbasbandy, E. Shivanian, Application of integro-differential equations, Math.comput.Appl., 14 (2009), 147-158 ## G. Adomian, A rieview of the decomposition method and some recent results for nonlinear equations, Math.comput.Modeling, 13(7) (1990), 17-34 ## J. Biazar, H. Ghazvini, He's variational iteration method for solving linear and nonlinear systems of ordinary differential equations , Applied mathematics and computation, 191 (2007), 287-297 ## N. Bildik, M. Inc, Modified decomposition method for nonlinear Voltera-Fredholm integral equations, Chaos,Solitons and Fractals, 33 (2007), 308-311 ## H. Brunner, On the numerical solution of nonlinear Voltera-Fredholm integral equation by collocation methods, SIAM J.Number.Anal, 27(4) (1990), 987-100 ## M. Dehghan, M. Tatari, The use of He's variational iteration method for solving the Fokker-Planck equation, Phys.scripta, 74 (2006), 310-316 ## O. Diekman, Thresholds and traveling waves for geographical spread of infection, J.Math.Biol, 6 (1978), 109-130 ## M. Dehghan, F. Shakeri, Approximate solution of a differential equation arising in astrophysics using the variational iteration method , New Astronomy, 13 (2008), 53-59 ## B. A. Finlayson, The method of weighted residuals and variational principles , Academic press, Newyork (1972) ## L. Hacia, An approximate solution for integral equations of mixed type, Zamm.z.Angew.Math.Mech, 76 (1996), 415-416 ## J. H. He, A new approach to nonlinear partial differential equations, Communications in Nonlinear science and Numerical simulation, 2 (1997), 230-235 ## J. H. He, Nonlinear oscillation with fractional derivative and it's approximation, Int,conf. on vibration Engineering 98, Dalian, China (1998) ## J. H. He, Variational iteration method for nonlinear and it's applications, Mechanics and practice (in chinese), 20, (1) (1998), 30-32 ## J. H. He, Variational Iteration method - a kind of nonlinear analytical technique:Some examples, Int.Journal of Nonlinear Mechanics, 34 (1999), 699-708 ## M. Inokuti , General use of the Lagrange multiplier in in nonlinear mathematical physics, in: S. Nemat-nasser(Ed.), Variational Method in Mechanics of solids, Progamon press, oxford, (1978), 156-162 ## Xu. Lan, Variational iteration method for solving integral equations, computers and Mathematics with Applications, 54 (2007), 1071-1078 ## K. Maleknejad, M. R. Fadaei Yami, A computational method for system of volterra-Fredholm integral equations, Applied Math and comput, 13 (2006), 589-595 ## S. Monani, S. Abuasad, Application of He's variational iteration method to helmhots equation, Chaos, Solutin and Fractals, 27 (2006), 1119-1123 ## B. G. Pachmatta, On Mixed Volterra-Fredholm type integral equation, Indian J. Pure Appl.Math, 17 (1986), 488-496 ## M. Tatari, M. Dehghan, On the Convergence of He's Variational Iteration Method, J.comput.Appl.Math, 207 (2007), 121-128 ## A. M. Wazwaz, A. Reliable , Treatment for Mixed Volterra-Fredholm in Integral Equations, Appl.Math.comput., 127 (2002), 405-414 ## A. M. Wazwaz, A Reliable Modification of Adomian's Decomposition Method, Appl.Math.comput, 102 (1999), 77-86
Comparison Differential Transform Method with Homotopy Perturbation Method for Nonlinear Integral Equations Comparison Differential Transform Method with Homotopy Perturbation Method for Nonlinear Integral Equations en en In this study, an application of differential transform method (DTM) is applied to solve the second kind of nonlinear integral equations such that Volterra and Fredholm integral equations. If the equation considered has a solution in terms of the series expansion of known function, this powerful method catches the exact solution. Comparison is made between the homotopy perturbation and differential transform method. The results reveal that the differential transform method is very effective and simple. 288 296 Malihe Bagheri Mahnaz Bagheri Ebrahim Miralikatouli differential transform method Integral equation Volterra and Fredholm integral quations Article.6.pdf  J. Biazar, E. Babolian, R. Islam, Solution of a system of Volterra integral equations of the first kind by Adomian method, Appl. Math. Comput, 139 (2003), 249-258 ## K. Maleknejad, M. Tavassoli Kajani, solving linear integro-differential equation system by Galerkin methods with hybrid functions, Appl. Math. Comput. , 159 (2004), 603-612 ## K. Maleknejad, F. Mirzaee, S. Abbasbandy, solving linear integro-differential equations system by using rationalized Haar functions method, Appl. Math. Comput. , 155 (2004), 317-328 ## J. Biazar, H. Ghazvini, M. Eslami , He’s homotopy perturbation method for system of integral equations , Chaos solitons. Fractal, (2007), 1-06 ## S. Q. Wang, J. H. He, Variational iteration method for solving integro-differential equations, Phys. Lett.A., 367 (2007), 188-191 ## J. H. He, Homotopy technique and a perturbation technique for non-linear problems, Int J. Non linear Mech., 35 (2000), 37-43 ## N. Bildik, A. Konuralp, Two-dimensional differential transform method, Adomian’s decomposition method, and variational iteration method for partial differential equations, Int.J. Comput. Math., 83 (2006), 973-987 ## J. H. He, New interpretation of homotopy perturbation method, Internat. J. Modern Phys. B., 20 (2006), 2561-2568 ## J. H. He, Some asymptotic methods for strongly nonlinear equations, Internat. J. Modern Phys. B., 20 (2006), 1141-1199 ## J. K. Zhou, Differential Transform and its Application for Electrical Circuits, Huazhong University Press, Wuhan, China (1968) ## O. Ozdemir, M.O. Kaya, Flapwise bending vibration analysis of a rotating tapered cantilever Bernoulli-Euler bean by differential transform method , J. Sound Vid., 289 (2006), 413-420 ## A. Arikoglu, I. Ozkol , Solution of difference equations by using differential transform method, Appl. Math. Comput. , 174 (2006), 1216-1228 ## A. Arikoglu, I. Ozkol, Solution of differential-difference equations by using differential transform method, Appl. Math. Comput., 181 (2006), 153-162 ## A. Arikoglu, I. Ozkol , Solution of fractial differential equations by using differential transform method, Chaos Solitone. Fract. , 34 (2007), 1473-1481 ## D. D. Ganji, G. A. Afrouzi, H. Hosseinzadeh, R. A. Talarposhti , Application of homotopy-perturbation method to the second kind of nonlinear integral equations, Phys. Lett.A. , 371 (2007), 20-25 ## Z. Odibat, Differential Transform method for solving Volterra integral equations with separable kernels, Mathematics computational modeling, 48 (2008), 1144-1149