Joules and Newtonian heating effects on stagnation point flow over a stretching surface by means of genetic algorithm and Nelder-Mead method

Abstract

Purpose

The purpose of this paper is to study the Joules heating effects on stagnation point flow of Newtonian and non-Newtonian fluids over a stretching cylinder by means of genetic algorithm (GA). The main emphasis is to find the analytical and numerical solutions for the said mathematical model. The work undertaken is a blend of numerical and analytical studies. Effects of active parameters such as: Hartmann number, Prandtl number, Eckert number, Nusselt number, Skin friction and dimensionless fluids parameters on the flow and heat transfer characteristics have been examined by graphs and tables. Compression is also made with the existing benchmark results.

Design/methodology/approach

Analytical solutions of non-linear coupled equations are developed by optimal homotopy analysis method (OHAM). A very effective and higher order numerical scheme hybrid GA and Nelder-Mead optimization Algorithms are used for numerical investigations.

Findings

An excellent agreement with the existing results in limiting sense is noted. It is observed that the radial velocity is an increasing function of dimensionless material parameters α ₁, α ₂ and β. Temperature increases by increasing the values of M, Pr, Ec and γ. Non-Newtonian parameter β has similar effects on skin friction coefficient and Nusselt number. The wall heat transfer rate is a decreasing function of A and ß whereas it increases by increasing conjugate parameter γ.

Originality/value

The problem under consideration has been widely studied by many investigators due to its importance and engineering applications. But most of the studies as the authors have documented are for Newtonian or viscous fluids. But no such analysis is available in the literature which can describe the Joules heating effects on stagnation point flow of Newtonian and non-Newtonian fluids over a stretching cylinder by means of GA.

Citation

Nawaz, M., Zeeshan, A., Ellahi, R., Abbasbandy, S. and Rashidi, S. (2015), "Joules and Newtonian heating effects on stagnation point flow over a stretching surface by means of genetic algorithm and Nelder-Mead method", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 25 No. 3, pp. 665-684. https://doi.org/10.1108/HFF-04-2014-0103