Bioconvective flow of a fluid between a co-axial cylinder with the impact of activation energy: application of Hermite collocation method

Purpose: This study examines the impact of non-linear thermal radiation on the bioconvection flow of fluid induced by the stretching of the inner cylinder enclosed by the stationary outer cylinder in the presence of a non-uniform heat source/sink and activation energy. The current scenario presents various obstacles, including the incorporation of radiation and non-uniform heat source/sink, necessitating thorough analysis to capture variations in heating/cooling. The activation energy adds even more intricacy to the system. Design/methodology/approach: The outer cylinder stays fixed while the inner cylinder expands horizontally in the axial direction. The flow is induced by the stretching of the inner cylinder enclosed by the stationary outer cylinder. The energy equation is developed by considering the impact of non-linear thermal radiation and non-uniform heat source/sink. The concentration equation involves the effect of the chemical reaction and activation energy. Applying the appropriate similarity variables converts the governing partial differential equations (PDEs) to non-dimensional ordinary differential equations (ODEs). The Probabilists’ Hermite polynomial-based collocation scheme (PHPBCS) is utilized to solve the resultant ODEs. Findings: The analysis shows that the rise in values of the radiation parameter increases the temperature profile about drastically. The density of motile bacteria falls with an increase in Peclet number. An upsurge in the thermophoresis parameter values increases the thermal and concentration profiles. Originality/value: The literature study indicates that no attempt has been made to examine the bioconvection flow of fluid induced by the stretching of the inner cylinder enclosed by the stationary outer cylinder in the presence of a non-uniform heat source/sink and activation energy. Moreover, the Probabilists Hermite polynomial-based collocation scheme is also utilized to solve the dimensionless equations, which is a novel aspect that is not discussed earlier for these effects.