# Heat transmission in Darcy-Forchheimer flow of Sutterby nanofluid containing gyrotactic microorganisms

Ambreen A. Khan (Department of Mathematics and Statistics, International Islamic University, Islamabad, Pakistan)
Alina Arshad (Department of Mathematics and Statistics, International Islamic University, Islamabad, Pakistan)
R. Ellahi (Center for Modeling and Computer Simulation, Research Institute, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia; Department of Mathematics and Statistics, International Islamic University, Islamabad, Pakistan and Department of Mechanical Engineering, University of California Riverside, Riverside, California, USA)
Sadiq M. Sait (Center for Communications and IT Research, Research Institute, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia)

ISSN: 0961-5539

Article publication date: 16 June 2022

Issue publication date: 3 January 2023

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## Abstract

### Purpose

This paper aims to deal with the heat transmission of Sutterby fluid-containing gyrotactic microorganism by incorporating non-Darcy resistance law. The mathematical modeling is based on nanoparticle concentration, energy, momentum and motile microorganism equations.

### Design/methodology/approach

The governing nonlinear coupled equations are first rendered into nonlinear ordinary equations using appropriate transformation and are then solved analytically by using the optimal homotopy.

### Findings

Graphical illustration of results depict the behavior of flow involved physical parameters on temperature, gyrotactic microorganism, concentration and velocity. Additionally, local Nusselt number and skin friction coefficient are computed numerically and validated through comparison with existing literature as a special case of proposed model. It is found that the temperature profile decreases by increasing values of Brownian-motion parameter and Prandtl number. An increase in thermophoresis parameter and Schmidt number results in decrease in concentration of nanoparticles. Bioconvection Peclet number corresponds to decreasing behavior of nondimensional gyrotactic microorganism field is observed. Finally, a comparison with the existing literature is made, and an excellent agreement is seen.

### Originality/value

To the best of the authors’ knowledge, this study is reported for the first time.

## Citation

Khan, A.A., Arshad, A., Ellahi, R. and Sait, S.M. (2023), "Heat transmission in Darcy-Forchheimer flow of Sutterby nanofluid containing gyrotactic microorganisms", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 33 No. 1, pp. 135-152. https://doi.org/10.1108/HFF-03-2022-0194

## Publisher

:

Emerald Publishing Limited