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A New Solution for Natural Convection of Darcian Fluid about a Vertical Full Cone Embedded in Porous Media Prescribed Wall Temperature by using a Hybrid Neural Network-Particle Swarm Optimization Method

Authors: M.A.Behrang, M. Ghalambaz, E. Assareh, A.R. Noghrehabadi


Fluid flow and heat transfer of vertical full cone embedded in porous media is studied in this paper. Nonlinear differential equation arising from similarity solution of inverted cone (subjected to wall temperature boundary conditions) embedded in porous medium is solved using a hybrid neural network- particle swarm optimization method. To aim this purpose, a trial solution of the differential equation is defined as sum of two parts. The first part satisfies the initial/ boundary conditions and does contain an adjustable parameter and the second part which is constructed so as not to affect the initial/boundary conditions and involves adjustable parameters (the weights and biases) for a multi-layer perceptron neural network. Particle swarm optimization (PSO) is applied to find adjustable parameters of trial solution (in first and second part). The obtained solution in comparison with the numerical ones represents a remarkable accuracy.

Keywords: Porous Media, Particle Swarm Optimization (PSO), Ordinary Differential Equations (ODE), Neural Network (NN)

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[1] A.R. Sohouli, D. Domairry, M. Famouri, A. Mohsenzadeh. Analytical solution of natural convection of Darcian fluid about a vertical full cone embedded in porous media prescribed wall temperature by means of HAM. International Communications in Heat and Mass Transfer. 2008; 35: 1380-1384.
[2] D.A. Nield, A. Bejan, Convection in Porous Media, third ed., Springer-Verlag, New York, 2006.
[3] P. Cheng, I.D. Chang, On buoyancy induced flows in a saturated porous medium adjacent to impermeable horizontal surfaces, International Journal Heat Mass Transfer. 1976; 19: 1267-1272.
[4] J. H. Merkin, Free convection boundary layers in a saturated porous medium with lateral mass flux, International Journal Heat Mass Transfer. 1978; 21: 1499-1504.
[5] J. H. Merkin, Free convection boundary layers on axisymmetric and two-dimensional bodies of arbitrary shape in a saturated porous medium, International Journal Heat Mass Transfer. 1979; 22: 1461- 1462.
[6] R.H. Nilson, Natural convective boundary layer on two-dimensional and axisymmetric surfaces in high-Pr fluids or in fluid saturated porous media, ASME J. Heat Transfer. 1981; 103: 803-807.
[7] P. Cheng, T.T. Le, I. Pop, Natural convection of a Darcian fluid about a cone, International Communications Heat Mass Transfer. 1985; 12: 705-717.
[8] I. Pop, T. Y. Na, Naturnal convection of a Darcian fluid about a wavy cone, International Communications Heat Mass Transfer. 1994; 21: 891-899.
[9] I. Pop, P. Cheng, An integral solution for free convection of a Darcian fluid about a cone with curvature effects, International Communications Heat Mass Transfer. 1986; 13: 433-438.
[10] Ching-Yang Cheng, An integral approach for heat and mass transfer by natural convection from truncated cones in porous media with variable wall temperature and concentration, International Communications Heat Mass Transfer. 2000; 27: 537-548.
[11] K.A. Yih, The effect of uniform lateral mass flux on free convection about a vertical cone embedded in a saturated porous medium, International Communications Heat Mass Transfer. 1997; 24: 1195- 1205.
[12] I. Pop, T. Y. Na, Natural convection over a frustum of a wavy cone in a porous medium, Mech. Res. Comm. 1995; 22: 181-190.
[13] A. Malek, R.S. Beidokhti, Numerical solution for high order differential equations using a hybrid neural networkÔÇöOptimization method. Applied Mathematics and Computation. 2006; 183: 260-271.
[14] H. Lee, I.S. Kang, Neural algorithms for solving differential equations, Journal of Computational Physics 1990; 91: 110-131.
[15] A.J. Meade Jr, A.A. Fernandez, The numerical solution of linear ordinary differential equations by feedforward neural networks, Mathematical and Computer Modelling. 1994; 19 (12): 1-25.
[16] I.E. Lagaris, A. Likas, D.I. Fotiadis. Artificial neural networks for solving ordinary and partitial differential equations. IEEE Transactions on Neural Networks. 1998; 9 (5): 987-1000.
[17] J.A. Khan, R.M.A. Zahoor, I.M. Qureshi, Swarm intelligence for the problem of non-linear ordinary differential equations and its application to well known Wessinger's equation. European Journal of scientific research. 2009; 34(4): 514-525.
[18] Z.Y. Lee, Method of bilaterally bounded to solution blasius equation using particle swarm optimization. Applied Mathematics and Computation 2006; 179: 779-786.
[19] D.T. Pham, E. Koc, A. Ghanbarzadeh, S. Otri. Optimisation of the weights of multi-layered perceptrons using the bees algorithm. Proceedings of 5th International Symposium on Intelligent Manufacturing Systems. Sakarya University, Department of Industrial Engineering, 2006; pp. 38-46, May 29-31.
[20] A.S. Yilmaz, Z. Ozer,. Pitch angle control in wind turbines above the rated wind speed by multi-layer percepteron and Radial basis function neural networks. Expert Systems with Applications. 2009; 36: 9767- 9775.
[21] Pham, D.T., Liu, X. Neural Networks for Identification, Prediction and Control. Springer Verlag, London. 1995.
[22] R.P. Lippmann, An introduction to computing with neural nets, IEEE ASSP Magazine 1987; 4-22.
[23] K. Hornick, M. Stinchcombe, H. white, Multilayer feedforward networks are universal approximators, Neural Networks 1989; 2 (5): 359-366.
[24] M.A. Behrang, E. Assareh, A. Ghanbarzadeh, A.R. Noghrehabadi. The potential of different artificial neural network (ANN) techniques in daily global solar radiation modeling based on meteorological data. Solar Energy 2010; 84: 1468-1480.
[25] Kennedy J, Eberhart R. Particle swarm optimization. Proc Neural Networks. Proceedings,vol.1944. IEEE International Conference on, 1995. p.1942-1948.
[26] Engelbrecht A P. Fundamentals of computational swarm intelligence. Hoboken, N.J.: Wiley, 2005.
[27] Brits R, Engelbrecht AP, van den Bergh F. Locating multiple optima using particle swarm optimization. Applied Mathematics and Computation 2007; 189(2): 1859-1883.
[28] Liu X, Liu H, Duan H. Particle swarm optimization based on dynamic niche technology with applications to conceptual design. Advances in Engineering Software 2007; 38(10): 668-676.
[29] Pan H, Wang L, Liu B. Particle swarm optimization for function optimization in noisy environment. Applied Mathematics and Computation 2006; 181(2): 908-919.
[30] Yang IT.Performing complex project crashing analysis with aid of particle swarm optimization algorithm. International Journal of Project Management 2007; 25(6): 637-646.
[31] Shi Y, Eberhart R. A modified particle swarm optimizer. Proceedings of the IEEE International Conference on Evolutionary Computation. Anchorage, Alaska, 1998a. p.69-73.
[32] Shi Y, Eberhart R. Parameter selection in particle swarm optimization. Proceedings of the Seventh Annual Conference on Evolutionary Programming. New York, 1998b. p.591-600.
[33] E. Assareh, M.A.Behrang, M.R.Assari, A.Ghanbarzadeh. Application of particle swarm optimization (PSO) and genetic algorithm (GA) techniques on demand estimation of oil in Iran. Energy 35 (2010) 5223- 5229.
[34] M.A. Behrang., E. Assareh, M.R. Assari, M.R., and A. Ghanbarzadeh. Assessment of electricity demand in Iran's industrial sector using different intelligent optimization techniques. Applied Artificial Intelligence 2011; 25: 292-304. doi:10.1080/08839514.2011.559572
[35] M.A. Behrang, E. Assareh, A.R. Noghrehabadi, and A. Ghanbarzadeh. New sunshine-based models for predicting global solar radiation using PSO (particle swarm optimization) technique. Energy 2011; 36: 3036- 3049. doi:10.1016/