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The current determination is committed to characterize the boundary layer flow of Williamson nanofluid prompted by nonlinear strained superficial under heat and mass transport mechanisms. Buongiorno model is presented to view the influence of nanoparticles in fluid flow. Scrutiny has been conceded under the action of the transversely smeared magnetic field. Heat and mass relocation exploration are conducted in the companionship of radiation effects and actinic compensation.

Similarity variable is designated to transmute nonlinear partial differential equations of conservation laws of mass, momentum, energy and species into ordinary dimensional expressions. These constitutive and complicated ordinary differential expressions assessing the flow situation are handled efficaciously by manipulating Runge–Kutta–Fehlberg procedure (RK-5) with shooting routine.

The graphical demonstration is deliberated to scrutinize the variation in velocity, temperature and concentration profiles with respect to flow regulating parameters. Numerical data are displayed through tables in order to surmise variation in skin friction coefficient and Nusselt number. The augmenting values of fluid parameter and magnetic parameter reduces the horizontal fluid velocity, whereas normal velocity upsurges for mounting values of stretching ratio parameter. Moreover, mounting values of radiation parameter and thermophoresis parameter upsurges the temperature profile, whereas, growing values of Prandtl number lessen the temperature field.

The current exploration is used in many industrial and engineering applications in order to discuss the transport phenomenon.

Flow over a nonlinear stretched surface has numerous applications in the industry. The present attempt examines the combined influence of various physical characteristics for the flow of Williamson fluid and no such attempt exist in the available literature.

The purpose of this paper is to address the entropy analysis of the 3D flow of Maxwell nanofluid containing gyrotactic microorganism in the presence of homogeneous–heterogeneous reactions with improved heat conduction and mass diffusion models over a stretched surface. Improved models are supported out by utilizing Cattaneo–Christov heat flux and generalized Fick’s law, respectively.

Governing equations which present the given flow phenomenon are modeled in the form of PDEs by applying boundary layer analysis and then suitable makeovers are engaged to transfigure prevailing partial differential equations into a set of ordinary differential equations. Transformed equations are handled via optimal homotopy analysis process in computational tool Mathematica and also a special case of already published work is substantiated and found to be in excellent settlement.

The bearing of innumerable convoluted physical parameters on velocity, temperature, concentration, reaction rate, the concentration of motile microorganism and entropy generation are presented and deliberated through graphs. Moreover, the convergence of the homotopic solution is presented in tabular form which confirms the reliability of the proposed scheme. It is perceived that mounting values of the magnetic parameter and Brinkman number boosts the irreversibility analysis and Bejan number diminishes for these parameters. Moreover, the growing values of Prandtl and Schmidt numbers reduce the temperature and concentration fields, respectively.

The work contained in this paper has applications in a different industry.

The work contained in this paper is original work and it is good for the researcher in the field of applied mathematics.