Bioconvection analysis of EMHD and dissipative Williamson nanofluid over a three dimensional Riga plate with Joule heating effect

ABSTRACT

The current study investigates the weakly hydromagnetic and bioconvection nanofluid flow of Williamson fluid, which conveys gyrotactic microorganisms, over a three-dimensional Riga surface. The primary objective is to stabilize biological, mechanical, and thermal systems through the introduction of exponentially decaying rheology in both the momentum and energy equations, known as the electro-magneto-hydrodynamic actuator (EMHD). As such, the working fluid is assumed to be dissipative, with significant consideration given to the magnetic Reynolds number and a higher-order reaction rate. To simplify the phenomenon of suspended nanoparticles’ bioconvection, an appropriate similarity transformation is applied, converting the system of partial differential equations (PDEs) into systems of ordinary differential equations (ODEs). To analyze the governing flow parameters, the numerical approach, Galerkin Weighted Residual Method (GWRM), is employed. The results are presented through tables and graphs, providing valuable insights. The findings of the study highlight that Hartmann number improves the weak movement of the Williamson fluid, thermophoresis number positively affects all flow distributions. Moreover, the temperature field is influenced by Brownian motion, leading to inflation, while the concentration field experiences a decrease due to a lower number of fluid particles available for reaction. Furthermore, higher buoyancy forces indicate significant fluid movement, resulting in a reduction in the Williamson fluid chemical reaction rate.

KEYWORDS:

• Gyrotactic microorganisms
• Williamson fluid
• Galerkin method
• Nanoscience
• EMHD
• Riga plate

Nomenclature

$j_0$	=	current density [$A/L^2$]
$M_0$	=	surface magnetic property [$Wb/L^2$]
$\mu$	=	variable fluid viscosity [$kg{L}^{-1}{s}^{-1}$]
$C$	=	fluid concentration [$mol.$]
$\rho$	=	fluid density [$Kg{m}^{-3}$]
$\nu$	=	kinematic viscosity [$L^2/s$]
${\beta }_4$	=	material constant [-]
${\beta }_1$	=	viscosity parameter
$N_t$	=	Thermophoresis number [-]
$Sc$	=	Schmidt number [-]
$\mathbf{K}$	=	Williamson fluid parameter [-]
$Gn$	=	Gyrotatic Grashof number [-]
$Ec$	=	Local Eckert number [-]
$\lambda$	=	chemical reaction parameter [-]
$T_w$	=	temperature density [K]
$C_w$	=	concentration density [$mol.L^{-3}$]
$C_{\mathrm{\infty }}$	=	free stream concentration [$mol.L^{-3}$]
$w$	=	velocity component in the $z-$ [$L{s}^{-1}$]
$u$	=	velocity component in the $x-$ direction [$L{S}^{-1}$]
$K_r$	=	rate of reaction [$S^{-1}$]
${\rho }_f$	=	density of the fluid [$Kg/L^3$]
$r_0$	=	diameter of the magnets [L]
$D_o$	=	mass diffusivity[$L^2/s$]
$T$	=	fluid temperature [$K$]
$C_p$	=	specific heat capacity [$J/kg.K$]
$Ha$	=	modified Hartman number [-]
${\beta }_2$	=	thermal conductivity [$W{L}^{-1}{K}^{-1}$]
$N_b$	=	Brownian motion [-]
${\beta }_5$	=	stretching ratio [-]
$Pr$	=	Prandtl number [-]
$Gr$	=	thermal Grashof number [-]
$\chi$	=	bioconvection constant [-]
$Le$	=	Lewis number [-]
$Pe$	=	Peclet number [-]
$N_w$	=	motile density [$mol.K{g}^{-1}$]
$T_{\mathrm{\infty }}$	=	free stream temperature [$K$]
$N_{\mathrm{\infty }}$	=	free Stream motile microorganisms [$mol.K{g}^{-1}$]
$v$	=	velocity component in the $y-$ direction [$L{S}^{-1}$]
$x,y,z$	=	cartesian coordinate system [L]

Acknowledgments

The authors appreciates and acknowledge the reviewers for their constructive comments. Thanks you for your time.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Notes on contributors

Mojeed T. Akolade

Mojeed T. Akolade is a doctoral student at the Department of Mathematics, University of Ilorin, Ilorin, Nigeria, and an Assistant Lecturer at the Department of Mathematical and Computing Science, Thomas Adewumi University, Oko, Kwara State, Nigeria. His research interest includes, fluid mechanics, thermodynamics analysis, squeezing flow, non-Newtonian fluid flow, sensitivity analysis, numerical, and statistical analysis of fluid flow problems, and has authored and co-authored numerous journal articles.

Tayyaba Akhtar

Tayyaba Akhtar is from the historic town, Sangla Hill located in the Nankana Sahib district of Punjab, Pakistan. She has been working as a visiting Lecturer in the Department of Mathematics since 2022 to present. She graduated from the reputed institute Government College University, Faisalabad, Pakistan. Her research interests are Numerical Simulation, Heat and mass flows, radiations Porous Media, MHD flow, Microorganism, Nanofluids, and differential equations. She participated in many national/international conferences/seminars.

Mohamed M. Awad

Prof. Dr. Mohamed M. Awad is an associate professor at the Mechanical Power Engineering Department, Faculty of Engineering, Mansoura University, Egypt. He was also a recipient of the ASME International Petroleum Technology Institute (IPTI) Award in 2005 and 2006. He won a silver medal at the 45th International Exhibition of Inventions, Geneva, Swiss, 29 March - 2 April 2017. Currently, he is the Regional Editor of Africa and Australia, the Editorial Board, of the Journal of Thermal Engineering, Yildiz Technical University Press, Turkey & Editorial Board Member of the International Journal of Oil, Gas and Coal Engineering & Editorial Board Member of International Journal of Petroleum Technology. He received his Ph.D. from Memorial University of Newfoundland in 2007 and his undergraduate degree and his master’s degree from Mansoura University, Egypt, in 1996 and 2000, respectively. His research focus is on the development of robust models for characterizing transport phenomena using fundamental theory. These models are validated using experimental and/or numerical results. He is the author of 3 book chapters. He has published more than 65 papers in refereed journals and conference proceedings in these areas. Presently, his research is focused on the modeling of complex fluid dynamics and heat transfer problems in internal flows. These include transport in porous media, compact heat exchangers, two-phase flow, microchannel flows, non-Newtonian flows, and thermal design/optimization of energy systems. He is a member of the American Society of Mechanical Engineers (ASME).

Yusuf O. Tijani

Yusuf O. Tijani is an avid lover of research and teaching.

Adeshina T. Adeosun

Adeshina T. Adeosun obtained a Master of Science degree in Analytical Dynamics from the University of Ilorin, Nigeria. He later got a Ph.D. in Fluid Mechanics from the same University, and a now a Lecturer at the Department of Mathematics, Federal College of Education, Iwo, Nigeria. His research interest is in Computational Fluid Dynamics and Modelling.