Magneto-bioconvection flow of a Casson thin film with nanoparticles over an unsteady stretching sheet : HAM and GDQ computation

Vasu, B; Ray, AK; Beg, OA; Gorla, RSR

Abstract

Purpose – To numerically investigate the two-dimensional unsteady laminar
magnetohydrodynamic (MHD) bioconvection flow and heat transfer of an electrically-conducting non-Newtonian Casson thin film with uniform thickness over a horizontal elastic sheet emerging from a slit in the presence of viscous dissipation. The composite effects of variable heat, mass, nanoparticle volume fraction and gyrotactic micro-organism flux are considered as is hydrodynamic (wall) slip. The Buongiorno nanoscale model is deployed which features Brownian motion and thermophoretic effects. The model studies the manufacturing fluid dynamics of smart magnetic bio-nano-polymer coatings.

Design/Methodology/Approach – The coupled non-linear partial differential boundary-layer equations governing the flow, heat and nano-particle and micro-organism mass transfer are reduced to a set of coupled non-dimensional equations using the appropriate transformations and then solved as an nonlinear boundary value problem with the semi-numerical Liao homotopy analysis method (HAM).Validation with a generalized differential quadrature (GDQ) numerical technique is included.

Findings – An increase in velocity slip results in a significant decrement in skin friction coefficient and Sherwood number whereas it generates a substantial enhancement in Nusselt number and motile micro-organism number density. The computations reveal that the bioconvection Schmidt number decreases the micro-organism concentration and boundary-layer thickness which is attributable to a rise in viscous diffusion rate. Increasing bioconvection Péclet number substantially elevates the temperatures in the regime, thermal boundary layer thickness, nanoparticle concentration values and nano-particle species boundary layer thickness. The computations demonstrate the excellent versatility of HAM and GDQ in solving nonlinear multi-physical nanobioconvection flows in thermal sciences and furthermore are relevant to application in the synthesis of smart biopolymers, microbial fuel cell coatings etc.

Originality/Value – The originality of the study is to address the simultaneous effects of unsteady and variable surface fluxes on Casson nanofluid transport of gyrotactic bio-convection thin film over a stretching sheet in the presence of a transverse magnetic field. Validation of HAM with a generalized differential quadrature (GDQ) numerical technique is included.

Keywords – Magneto-hydrodynamics, Bioconvection, Nanofluid, Brownian motion, Homotopy analysis method (HAM), Generalized differential quadrature (GDQ)

Citation

Vasu, B., Ray, A., Beg, O., & Gorla, R. (2019). Magneto-bioconvection flow of a Casson thin film with nanoparticles over an unsteady stretching sheet : HAM and GDQ computation. International Journal of Numerical Methods for Heat and Fluid Flow, 29(11), 4277-4309. https://doi.org/10.1108/HFF-02-2019-0158

• Journal Article Type: Article
• Acceptance Date: Apr 11, 2019
• Online Publication Date: Jun 24, 2019
• Publication Date: Nov 4, 2019
• Deposit Date: Apr 16, 2019
• Publicly Available Date: Jun 24, 2020
• Journal: International Journal of Numerical Methods for Heat & Fluid Flow
• Print ISSN: 0961-5539
• Publisher: Emerald
• Volume: 29
• Issue: 11
• Pages: 4277-4309
• DOI: https://doi.org/10.1108/HFF-02-2019-0158
• Publisher URL: https://doi.org/10.1108/HFF-02-2019-0158
• Related Public URLs: https://www.emeraldinsight.com/loi/hff