## Analysis of Bioconvective Unsteady Darcy Forchhemier Nanofluid Flow with Arrhenius Chemical Reaction and Activation Energy Over a Permeable Stretching Surface

Published: 2024-01-23

Page: 22-48

Matilukuro, O. M. *

Department of Mathematics and Statistics, Federal University Wukari, Taraba State, Nigeria.

Olanrewaju, P. O.

Department of Mathematics and Statistics, Federal University Wukari, Taraba State, Nigeria.

Amoo, S. A.

Department of Mathematics and Statistics, Federal University Wukari, Taraba State, Nigeria.

Nwaokolo, M. A.

Department of Mathematics and Statistics, Federal University Wukari, Taraba State, Nigeria.

Ayisa. S. A.

Department of Mathematics and Statistics, Federal University Wukari, Taraba State, Nigeria.

*Author to whom correspondence should be addressed.

### Abstract

Darcy-Forchheimer nanofluids can be used to improve the efficiency of oil recovery from oil reservoirs. The nanoparticles in the nanofluid can help to reduce the viscosity of the oil and increase the permeability of the rock, making it easier for oil to flow to the wells. Analysis of Bioconvective Unsteady Darcy Forchhemier Nanofluid Flow with Arrhenius Chemical Reaction and Activation Energy over A Permeable Stretching Surface was considered. The flow equations are partial differential equations (PDEs), which we translate into ordinary differential equations (ODEs) by applying appropriate similarity transformations. The Runge-Kutta-Gill method and the shooting method were used to solve these ODEs numerically. A number of tables and graphs were used to show how the evolving parameter alterations affected the flow fields. The outcome demonstrate that: The chemical reaction, Thermophoresis and Brownian motion parameter reduces the mass concentration, while large values of activation energy have the opposite effect. The mounting values of Radiation parameter (Rd) and bioconvection Lewis numbers reduce the motile microorganism profile. We noticed that as we increase the values of the unsteadiness parameter the velocity distribution profile as well as the energy distribution profile increases. As Porosity (Pr) parameter increases, energy distribution profile decreases along the boundary region. The combined effects of the controlling fluid flow parameters have greater influence on the Skin Friction, Nusselt number, Sherwood number and the microorganism motile rate transfer across the channel plate of the fluid flow model. .Interestingly, the effect of embedded fluid flow parameters on the skin friction, heat transfer rate and mass transfer rate were established for engineering/industrial purpose.

Keywords: Activation energy, magnetohydrodynamics, porous medium, darcy forchhemier

#### How to Cite

Matilukuro, O. M., Olanrewaju, P. O., Amoo, S. A., Nwaokolo, M. A., & Ayisa. S. A. (2024). Analysis of Bioconvective Unsteady Darcy Forchhemier Nanofluid Flow with Arrhenius Chemical Reaction and Activation Energy Over a Permeable Stretching Surface. Asian Journal of Pure and Applied Mathematics, 6(1), 22–48. Retrieved from https://globalpresshub.com/index.php/AJPAM/article/view/1932

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