# Brinkman-Forchheimer flow of SWCNT and MWCNT magneto-nanoliquids in a microchannel with multiple slips and Joule heating aspects

Shashikumar N.S. (Department of Studies and Research in Mathematics, Kuvempu University, Shimoga, India)
Gireesha B.J. (Department of Studies and Research in Mathematics, Kuvempu University, Shimoga, India)
B. Mahanthesh (Department of Mathematics, Christ University, Bengaluru, India)
Prasannakumara B.C. (Department of Mathematics, Government First Grade College, Koppa, India)

ISSN: 1573-6105

Article publication date: 14 June 2018

Issue publication date: 8 October 2018

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## Abstract

### Purpose

The microfluidics has a wide range of applications, such as micro heat exchanger, micropumps, micromixers, cooling systems for microelectronic devices, fuel cells and microturbines. However, the enhancement of thermal energy is one of the challenges in these applications. Therefore, the purpose of this paper is to enhance heat transfer in a microchannel flow by utilizing carbon nanotubes (CNTs). MHD Brinkman-Forchheimer flow in a planar microchannel with multiple slips is considered. Aspects of viscous and Joule heating are also deployed. The consequences are presented in two different carbon nanofluids.

### Design/methodology/approach

The governing equations are modeled with the help of conservation equations of flow and energy under the steady-state situation. The governing equations are non-dimensionalized through dimensionless variables. The dimensionless expressions are treated via Runge-Kutta-Fehlberg-based shooting scheme. Pertinent results of velocity, skin friction coefficient, temperature and Nusselt number for assorted values of physical parameters are comprehensively discussed. Also, a closed-form solution is obtained for momentum equation for a particular case. Numerical results agree perfectly with the analytical results.

### Findings

It is established that multiple slip effect is favorable for velocity and temperature fields. The velocity field of multi-walled carbon nanotubes (MWCNTs) nanofluid is lower than single-walled carbon nanotubes (SWCNTs)-nanofluid, while thermal field, Nusselt number and drag force are higher in the case of MWCNT-nanofluid than SWCNT-nanofluid. The impact of nanotubes (SWCNTs and MWCNTs) is constructive for thermal boundary layer growth.

### Practical implications

This study may provide useful information to improve the thermal management of microelectromechanical systems.

### Originality/value

The effects of CNTs in microchannel flow by utilizing viscous dissipation and Joule heating are first time investigated. The results for SWCNTs and MWCNTs have been compared.

## Acknowledgements

Authors would like to thank the anonymous reviewers for their valuable comments and useful suggestions. In addition, the author (Mahanthesh B.) would like to express gratitude to the Management of the Christ University, Bengaluru, India for providing funding support through MRP entitled “Study on convective heat transfer of nanoliquids”.

## Citation

N.S., S., B.J., G., Mahanthesh, B. and B.C., P. (2018), "Brinkman-Forchheimer flow of SWCNT and MWCNT magneto-nanoliquids in a microchannel with multiple slips and Joule heating aspects", Multidiscipline Modeling in Materials and Structures, Vol. 14 No. 4, pp. 769-786. https://doi.org/10.1108/MMMS-01-2018-0005

## Publisher

:

Emerald Publishing Limited