Eur. Phys. J. Plus (2016) 131: 314
https://doi.org/10.1140/epjp/i2016-16314-1

Regular Article

Non-Darcy effect on boundary layer flow of TiO₂-water/kerosene nanofluid over an extensible sheet

¹ Dept. of Mathematics, A.B.N. Seal College, Cooch Behar, Pin: 736101, West Bengal, India
² Department of Mathematics, Jadavpur University, Kolkata 700032, W.B., India

^* e-mail: tausifdropbox@gmail.com

Received: 30 June 2016
Accepted: 3 August 2016
Published online: 12 September 2016

Abstract

An analytical and numerical enquiry has been executed to measure up to the numerical data and graphical figures of two different types of nanofluid boundary layer flow in a non-Darcy porous medium with TiO₂ nanoparticles in the fluid. The current surface is continuously protracted under a fixed law and the base liquids are water and kerosene. A mathematical model of the stream has been developed and after renovating the non-linear partial differential equations into a system of ODE, it has been solved both analytically by Differential Transformation Method (DTM) in cooperation with Padé Approximant and numerically by Runge-Kutta 4th order shooting technique. The aggregate of the relations between various flow parameters with the skin friction and the heat transfer rate of two different fluids have been gauged by correlation coefficients and the impact of the relation has been verified using Fisher’s t-Test. One of the most interesting verdicts of the progress survey is that the rate of heat transfer rate in the TiO₂ -kerosene nanofluid is almost 83-88% higher than that of TiO₂ -water nanofluid. Also the relation between various pertinent parameters with the Nusselt number and the skin friction coefficient are highly significant and they can be regulated according to our requirement by controlling these parameters of the flow.