Darcy–Brinkman–Forchheimer Model for Nano-Bioconvection Stratified MHD Flow through an Elastic Surface: A Successive Relaxation Approach

Anwar Shahid,Mohamed S Mohamed,Muhammad Mubashir Bhatti,Mohammad Hossein Doranehgard

doi:10.3390/math9192514

Abstract

The present study deals with the Darcy–Brinkman–Forchheimer model for bioconvection-stratified nanofluid flow through a porous elastic surface. The mathematical modeling for MHD nanofluid flow with motile gyrotactic microorganisms is formulated under the influence of an inclined magnetic field, Brownian motion, thermophoresis, viscous dissipation, Joule heating, and stratifi-cation. In addition, the momentum equation is formulated using the Darcy–Brinkman–Forchheimer model. Using similarity transforms, governing partial differential equations are reconstructed into ordinary differential equations. The spectral relaxation method (SRM) is used to solve the nonlinear coupled differential equations. The SRM is a straightforward technique to develop, because it is based on decoupling the system of equations and then integrating the coupled system using the Chebyshev pseudo-spectral method to obtain the required results. The numerical interpretation of SRM is admirable because it establishes a system of equations that sequentially solve by providing the results of the first equation into the next equation. The numerical results of temperature, velocity, concentration, and motile microorganism density profiles are presented with graphical curves and tables for all the governing parametric quantities. A numerical comparison of the SRM with the previously investigated work is also shown in tables, which demonstrate excellent agreement.

Highlights

In 1995, Choi and Eastman [1] developed the concept of a “nanofluid”, which refers to the suspension of nanometer-sized particles in a base fluid containing nanoparticles with diameters smaller than 100 nm
Choi and Eastman [1] proved that nanofluids enhance the thermal conductivity of the base fluids
The mathematical modeling for MHD nanofluid flow with motile gyrotactic microorganisms is formulated under the influence of an inclined magnetic field, Brownian motion, thermophoresis, viscous dissipation, Joule heating, and stratification

Summary

Introduction

In 1995, Choi and Eastman [1] developed the concept of a “nanofluid”, which refers to the suspension of nanometer-sized particles in a base fluid containing nanoparticles with diameters smaller than 100 nm. Choi and Eastman [1] proved that nanofluids enhance the thermal conductivity of the base fluids. Nanofluids have received a lot of attention in engineering sectors because of their thermal enhancing features. Nanofluids have various applications, including as productive energy sources, solar cells, and vehicle engines, as well as in electronic circuits to enhance the cooling process [2]. Tiwari and Das [4] used a solid volume fraction of fragments to offer an alternative modelling approach for assessing enhancement in the thermal conductivity of nanofluids. Kakaç and Pramuanjaroenkij [5]

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Conclusion