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Numerical simulation for Darcy-Forchheimer flow of carbon nanotubes due to convectively heated nonlinear curved stretching surface

Muhammad Ijaz Khan (Department of Mathematics, Quaid-i-Azam University, Islamabad, Pakistan)
Khursheed Muhammad (Department of Mathematics, Quaid-i-Azam University, Islamabad, Pakistan)
Tasawar Hayat (Department of Mathematics, Quaid-i-Azam University, Islamabad, Pakistan and Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia)
Shahid Farooq (Department of Mathematics, Quaid-i-Azam University, Islamabad, Pakistan)
Ahmed Alsaedi (Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia)

International Journal of Numerical Methods for Heat & Fluid Flow

ISSN: 0961-5539

Article publication date: 28 June 2019

Issue publication date: 11 September 2019

Abstract

Purpose

This paper aims to discuss the salient aspects of the Darcy–Forchheimer flow of viscous liquid in carbon nanotubes (CNTs). CNTs are considered as nanofluid, and water is taken as the continuous phase liquid. The flow features are discussed via curved surface. Water is taken as the base liquid. Flow is generated via nonlinear stretching. Energy expression is modeled subject to heat generation/absorption. Furthermore, convective conditions are considered at the boundary. The Xue model is used in the mathematical modeling which describes the features of nanomaterials. Both types of CNTs are considered, i.e. single-walled CNTs and multi-walled CNTs.

Design/methodology/approach

Appropriate transformations are used to convert the flow expressions into dimensionless differential equations. The bvp4c method is used for solution development.

Findings

Velocity enhances via higher estimations of nanoparticles volume fraction while decays for higher Forchheimer number, curvature parameter, behavior index and porosity parameter. Furthermore, thermal field is an increasing function of nanoparticle volume fraction, behavior index, Forchheimer number and porosity parameter.

Originality/value

Here, the authors have discussed two-dimensional CNTs-based nanomaterial Darcy–Forchheimer flow of viscous fluid over a curved surface. The authors believe that all the outcomes and numerical techniques are original and have not been published elsewhere.

Keywords

Citation

Khan, M.I., Muhammad, K., Hayat, T., Farooq, S. and Alsaedi, A. (2019), "Numerical simulation for Darcy-Forchheimer flow of carbon nanotubes due to convectively heated nonlinear curved stretching surface", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 29 No. 9, pp. 3290-3304. https://doi.org/10.1108/HFF-01-2019-0016

Publisher

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Emerald Publishing Limited

Copyright © 2019, Emerald Publishing Limited