Numerical investigation of magnetohydrodynamic flow and heat transfer of copper–water nanofluid in a channel with non-parallel walls considering different shapes of nanoparticles

Syed Tauseef Mohyud-Din,Umar Khan,Saleh M Hassan

doi:10.1177/1687814016637318

Abstract

This article presents the magnetohydrodynamic flow and heat transfer of water-based nanofluid in divergent and convergent channels. Equations governing the flow are transformed to a set of ordinary differential equations by employing suitable similarity transforms. Resulting system is solved using a strong numerical procedure called Runge–Kutta–Fehlberg method. Results are compared with existing solutions available in the literature and an excellent agreement is seen. Three shapes of nanoparticles, namely, platelet-, cylinder-, and brick-shaped particles, are considered to perform the analysis. Influence of emerging parameters such as channel opening, Reynolds number, magnetic parameter, Eckert number, and the nanoparticle volume fraction are heighted with the help of graphs coupled with comprehensive discussions. The magnetic field can be used as a controlling parameter to reduce the backflow regions for the divergent channel case. Temperature of the fluid can be controlled with the help of strong magnetic field. It is also observed that platelet-shaped particles have higher temperature values as compared to cylinder- and brick-shaped particles.

Highlights

In 1915, Jeffery[1] and Hamel[2] formulated a problem for the flow between non-parallel walls
Throughout this article, our focus is on water-based nanofluid, and copper is taken as the nanoparticle
Lower values of temperature are observed for rising magnetic number. This means that stronger the magnetic field, lower will be the temperature of the fluid for divergent channel case

Summary

Introduction

In 1915, Jeffery[1] and Hamel[2] formulated a problem for the flow between non-parallel walls. Many studies are available in the literature that used all these models to investigate the flow and heat transfer of nanofluids in different geometries.[20,21,22,23,24,25,26,27,28,29,30,31,32,33]. Literature survey proves that there is no single study available in the literature that used Hamilton and Crosser’s model to study the flow and heat transfer of nanofluids in divergent and convergent channels. The equations governing the flow under the effect of magnetic field are transformed into non-linear system of ordinary differential equations. The model for the effective thermal conductivity of the nanofluid considered here is Hamilton and Crosser’s model.

Solution procedure

Results and discussions

Conclusion