Numerical analysis of thermal and entropy transport in unsteady MHD bioconvective Carreau fluid flow over a phase-dependent oscillating plate using Crank–Nicolson method

Purpose This study aims to present a numerical analysis of thermal and entropy analysis of unsteady magnetohydrodynamic bioconvective flow of a Carreau fluid over an oscillating plate with combined sinusoidal and cosinusoidal motions. The main objectives of this research are capturing phase-dependent flow responses through combined oscillations; providing a unified analysis of Carreau fluid MHD flow with motile microorganisms; and examining the relative contributions of thermal, solutal and bioconvective buoyancy forces to flow behavior. Design/methodology/approach An implicit Crank–Nicolson scheme has been used to solve the governing equations. Findings The authors found that near the wall, phase-dependent cosine oscillations impact the momentum enhancement by nearly 70% as compared to sine oscillations. The reduction in species transport has been observed due to the increment in the Lewis number and chemical reaction parameters. On the other hand, the Peclet and bioconvection Lewis number enhance the microorganism cluster due to this sharp concentration gradients are generated. The elasticity parameter Weissenberg number We reduces the heat transfer rate by about 8% and flow resistance by 14% in shear-thinning fluids, on the other hand, in shear thickening fluids both heat transfer and skin friction is increased by 13% and 22%, respectively. Originality/value The authors believe that the present findings are beneficial in biomedical devices, drug delivery systems, microfluidic and lab-on-a-chip devices, bio-reactors, polymer processing, food and chemical industries and magnetic flow control systems.