International Journal of Research and Scientific Innovation (IJRSI) | Volume IV Issue XI, November 2017 | ISSN 2321–2705

Solution of Flow and Heat Transfer of an Elastico-viscous Liquid Between Two Co-axial Cylinders by Artificial Neural Network

U. K. Tripathy#1 and S. M. Patel[*2]
[#1] Retd. Professor & Head Dept of Mathematics, V.S.S.University, Burla-768017, Sambalpur, India.
[*2]Lecturer, Department of Mathematics, Sundargarh Engineering School, Sundargarh. 7700073, India
[*]Corresponding Author: S. M. Patel

Abstract: In this paper an approximate analysis of free convective flow of a non-Newtonian liquid between two co-axial cylinders has been carried out by two techniques. The equation of motion and energy including viscous dissipative terms are a pair of simultaneous non-linear ordinary differential equations. These equations under appropriate boundary conditions have been solved by the fourth order Runge-Kutta method and the back propagation neural networks method. The truncation errors involved in Runge-Kutta method of solution have been determined for one set of values of parameters and have been noted to be O(10-5 ). It has been observed that the elastic parameter has greater influence on the velocity field than on the temperature field. The effect of other parameters Pr (Prandatl number), E (Eckert number) etc. on flow and temperature field. The solution has been compared with the results obtained from the ANN model. This study so far reveals that skin friction, Nusselt number both at outer and inner cylinder can alternatively be modeled using the ANN within a reasonable accuracy. The results obtained from the ANN model are in very good agreement with the numerical results. The designed ANN model can be considered and useful alternative and one of the best techniques for solving non-Newtonian fluid flow problems.

Key words: artificial neural network, back-error propagation, non-Newtonian fluid, skin friction, Nusselt number.

I. INTRODUCTION

The free convective viscous flow between vertical heated plates was investigated by [1], [2],[3],[4],[5]. Likewise [6], [7] have studied the free convective viscous flow through a vertical circular pipe when it is heated or cooled uniformly. The magnetohydrodynamic (MHD) flow of non-Newtonian fluids was examined by [8]. The same problems including the effect of frictional heating and distributed sources or sinks was considered by [9]. In the past years free convective laminar flow of a non-Newtonian liquid has gained substantial importance and has attracted the attention of several researchers.

Read More