Role of bioconvection on the dynamics of chemically active Casson nanofluid flowing via an inclined porous stretching sheet with convective conditions

ABSTRACT

Nanofluids are emerging as a revolutionary replacement for traditional cooling agents. In addition to this, the motile microorganism helps to stabilize the nanofluid. In this direction, the present investigation addressed Casson fluid flow immersed with gyrotactic microorganisms due to an inclined surface. This flow is controlled by incorporating magnetic forces and restricted to passing through porous media. The influence of the chemical activities and heat convection is examined to complete the mathematical description of the flow situation. The total energy involvement is obtained by the addition of resistive heating and viscous dissipation terms in the energy equation. The current flow situation of equations of said physical condition is renovated into the ordinary differential equations (ODEs) with the implementation of proper similarity variables. The numerical solution is developed with the Runge-Kutta scheme. Graphical illustration for respective physical parameters is obtained via MATLAB. The numerical discussion of the present work is validated with previously published literature. The flow motion is controlled by strengthening the magnetic strength. Boost in the Schmidt number and bioconvection Schmidt number reduces the boundary layer thickness.

KEYWORDS:

• Thermal radiation
• chemical reaction
• magnetohydrodynamics
• gyrotactic microorganisms

Nomenclature

$a$	=	Stretching constants [1/s]
$b$	=	Chemotaxis constant
$B$	=	Magnetic flux [T]
$B_0$	=	Magnetic flux strength
$B_1$	=	Biot number due to heat transfer
$C$	=	Concentration [kg/m2]
$C_f$	=	Skin friction
$C_w$	=	Surface concentration [kg/m2]
C${ }_{\mathrm{\infty }}$	=	Ambient concentration [mol/m3]
$C_p$	=	Specific heat at constant pressure [J/Kg K]
$D_B$	=	Brownian coefficient [m2/s]
$D_T$	=	Thermophoresis coefficient [m2/s]
$D_n$	=	Diffusivity of microorganisms
$Ec$	=	Eckert number
$g$	=	Gravitational acceleration [m/s−2]
$G$	=	Chemical reaction parameter
$Gr$	=	Grashof number
$k_f$	=	Thermal conductivity [Wm−1K−1]
$k^{\ast }$	=	Mean absorption coefficient
$K_p$	=	Porosity index
$K_r$	=	Coefficient of chemical reaction
$M$	=	Magnetic parameter
$N$	=	Concentration of microorganisms
$N^{\ast }$	=	The ratio of buoyancy forces
$Nb$	=	Brownian motion
$Nt$	=	Thermophoresis parameter
$N{u}_x$	=	Nusselt number
$N{n}_x$	=	Nanoparticle Sherwood number
$Pe$	=	Bioconvection Peclet number
$Pr$	=	Prandtl number
$q_r$	=	Radiative heat flux [W/m2]
$q_w$	=	Heat flux [W/m2]
$q_m$	=	Mass flux
$q_n$	=	Motile microorganism flux
$Q_0$	=	Coefficient of heat generation /absorption
$Q$	=	Heat generation /absorption
$R$	=	Thermal radiation parameter
${Re}_x$	=	Local Reynolds number
$Rb$	=	Bioconvection Rayleigh number
$S{c}_1$	=	Schmidt number
$S{c}_2$	=	Bioconvection Schmidt number
$S{h}_x$	=	Sherwood number
$T$	=	Fluid temperature [K]
$T_w$	=	The temperature at the wall [K]
$T_{\mathrm{\infty }}$	=	Ambient temperature [K]
$u,v$	=	Velocity components [m/s]
$u_w$	=	Stretching velocity [m/s]
$Wc$	=	A maximum speed of swimming cell [m/s]
$x,y$	=	The distance along the surface [m]

Greek symbols

$\alpha$	=	The angle of inclination [rad]
$\beta$	=	Casson fluid parameter
${\beta }^{\ast }$	=	Coefficient of volumetric expansion
$\gamma$	=	The average volume of microorganisms
$\lambda$	=	Mixed convection parameter
$\rho$	=	Fluid density [kg/m3]
${\rho }_p$	=	Microorganism’s density
$\bar{\sigma }$	=	Electrical conductivity
${\sigma }^{\ast }$	=	Stefan-Boltzmann constant [Wm−2K−4]
$\eta$	=	Similarity invariants
$\theta$	=	Non-dimensional temperature
$\varphi$	=	Non-dimensional concentration
$\chi$	=	The non-dimensional concentration of microorganisms
$\nu$	=	Kinematic viscosity [m2/s]
$\tau$	=	The effective heat capacitance ratio
${\tau }_w$	=	Shear stress
$\mu$	=	Coefficient of viscosity [kg/m s]

Subscripts

$w$	=	Quantities at wall
$\mathrm{\infty }$	=	Quantities at the surface

Disclosure statement

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

Additional information

Notes on contributors

Pooja P. Humane

Pooja P. Humane received her M.Sc. degree in Mathematics from Shivaji University, Kolhapur, India, in 2013. She is working as a research scholar in the Department of Mathematics, Shivaji University, Kolhapur. Her research interest includes boundary value problems, heat and mass transfer, nanofluids and hybrid nanofluid, similarity techniques, and magnetohydrodynamics. She has published more than 10 International articles through various reputed journals as author/co-author.

Vishwambhar S. Patil

Dr. Vishwambhar S. Patil is working as an Associate Professor and Head in the Department of Mathematics, Government College of Engineering Karad, India. He obtained his Ph.D. degree from the North Maharashtra University, Jalgaon, India in the year 2011. His area of interest includes Similarity Analysis, Magnetohydrodynamics, Non-Newtonian fluids, nanofluid and hybrid nanofluids, and heat and mass transfer Mechanics. He has published more than 28 International articles through various reputed journals as author/co-author.

MD. Shamshuddin

Dr. MD. Shamshuddin has completed his Masters in Mathematics from Osmania University in the year 2002, and also completed his M. Phil from Sri Venkateswara University in the year 2010. He received his prestigious Ph.D. degree in Applied Mathematics at GITAM Deemed to be University, Andhra Pradesh in the year 2019. He has published more than 111 International repute articles through various journals and Conferences. Currently, his research interest is in fluid mechanics, magneto fluid dynamics, micropolar fluid, nanofluid and hybrid nanofluid, and heat and mass transfer with its applications. He is a seasoned researcher with a strong mentality and sound analytical mind, and he has contributed tremendously in his core areas of research. He has reviewed several research articles for many journals and publishers.

Govind R Rajput

Dr. Govind R Rajput is working as an Assistant Professor and Head in the Department of Applied Sciences and Humanities, Mukesh Patel School of Technology Management and Engineering, Shirpur campus, India. He obtained his Ph.D. degree from the North Maharashtra University, Jalgaon, India in the year 2018. His area of interest includes Non-Newtonian fluids, nanofluid and hybrid nanofluid, and heat and mass transfer. He has published more than 21 International articles through various reputed journals as author/co-author.

Amar B Patil

Amar Patil received his M.Sc. degree in Mathematics from Shivaji University, Kolhapur, India, in 2006 and qualified SET exam in 2018. Currently; he is working as a research scholar in the Department of Mathematics, Shivaji University, Kolhapur. His research interest includes Magnetohydrodynamics, micropolar fluid, nanofluid, and heat and mass transfer of non-Newtonian fluids. He has published more than 10 International articles through various reputed journals as author/co-author.