Nonlinear radiation heat transfer effects in the natural convective boundary layer flow of nanofluid past a vertical plate: a numerical study

Meraj Mustafa; Ammar Mushtaq; Tasawar Hayat; Bashir Ahmad

doi:10.1371/journal.pone.0103946

Nonlinear radiation heat transfer effects in the natural convective boundary layer flow of nanofluid past a vertical plate: a numerical study

PLoS One. 2014 Sep 24;9(9):e103946. doi: 10.1371/journal.pone.0103946. eCollection 2014.

Authors

Meraj Mustafa¹, Ammar Mushtaq², Tasawar Hayat³, Bashir Ahmad⁴

Affiliations

¹ School of Natural Sciences (SNS), National University of Sciences and Technology (NUST), Islamabad, Pakistan.
² Research Centre for Modeling and Simulation (RCMS), National University of Sciences and Technology (NUST), Islamabad, Pakistan.
³ Department of Mathematics, Quaid-I-Azam University, Islamabad, Pakistan; Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia.
⁴ Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia.

Abstract

The problem of natural convective boundary layer flow of nanofluid past a vertical plate is discussed in the presence of nonlinear radiative heat flux. The effects of magnetic field, Joule heating and viscous dissipation are also taken into consideration. The governing partial differential equations are transformed into a system of coupled nonlinear ordinary differential equations via similarity transformations and then solved numerically using the Runge-Kutta fourth-fifth order method with shooting technique. The results reveal an existence of point of inflection for the temperature distribution for sufficiently large wall to ambient temperature ratio. Temperature and thermal boundary layer thickness increase as Brownian motion and thermophoretic effects intensify. Moreover temperature increases and heat transfer from the plate decreases with an increase in the radiation parameter.

Publication types

Research Support, Non-U.S. Gov't

MeSH terms

Algorithms
Computer Simulation
Convection*
Hydrodynamics*
Magnetic Fields
Models, Theoretical
Solar Energy*
Temperature
Thermal Conductivity*

Grants and funding

This paper is funded by the Deanship of Scientific Research (DSR), King Abdulaziz University, Jeddah, under grant no. 78-130-35-HiCi. The authors, therefore, acknowledge technical and financial support of KAU. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.