Thermal analysis of the bio-convective magnetised retardation-type nanofluid flow over a bidirectional sinusoidal moving surface having radiative effects

Abstract

The nonlinear unsteady flows restricted by moving surfaces have gained particular significance in numerous technological, engineering, industrial, mechanical and biological processes. The flow caused by oscillatory stretched surfaces has attracted particular attention due to its fascinating properties, such as in fluidic oscillators, oscillating jets, oscillation problems, etc. Nanofluids have recently gained much attention due to their potential in numerous applications across various industries. The primary use of the nanomaterials is to increase the effectiveness of heat transfer in various systems. Due to the importance of biomaterial’s in different industrial, technological and engineering systems, the process of bioconvection in nanomaterials has attained reputation in recent years. To lead this exploration, an unsteady bio-convective flow of Oldroyd-B nanomaterial across a bi-directional oscillatory stretched surface is investigated here. Heat generation and thermic radiation have been employed to inspect heat transfer attributes. Furthermore, the effects of magnetic force, chemical reaction and activation energy were employed for the whole analysis. Apposite makeovers were used to convert the deduced nonlinear system to non-dimensional expressions. To yield the series solution, an analytic procedure, namely the homotopy analysis technique (HAM) was adopted. Various graphs were plotted to deliberate the effects of the associated variables on concentration, micro-organism, velocities and temperature profiles. Numeric data were organised in different tables to discuss the importance of different variables on the motile density, local Nusselt and local Sherwood numbers. It has been observed that bidirectional velocities display opposite trends for relaxation and retardation variables. It has further been perceived that amplitudes of velocities periodically decelerate for increase in Hartman number. Greater estimations of heat generation, Brownian motion, thermophoresis and thermic radiation effectively improve the temperature within the nanofluid whereas it diminishes by varying the Prandtl number. Concentration profile declined with Schmidt number, reaction rate and temperature difference variables, while opposite scenario occurred for thermophoresis and activation energy parameters. Moreover, distribution of micro-organisms’ increases for Hartmann number but drops because of greater estimates of the micro-organisms concentration difference, bio-convective Peclet and Lewis numbers.