The novelty of this study is to develop the oscillation, amplitude and periodical behavior of thermal and concentration boundary layers of transient Darcian nanofluid flow over stationary circular cylinder. For the improvement of cutting forces, lubrication and cooling in machining operations, workpiece cutting temperature and tool durability, the nanofluids have significant role with the effects of thermophoretic nanoparticles and rate of reactions. The aim of current work is to deduce the oscillations, amplitude, and frequency analysis of mass and heat transmission of Darcian nanoparticles motion around porous stretchable cylinder with thermal radiation and heat generation effects. For physical and thermo parameters, the governing mathematical equations are transformed into convenient equations. The smooth and similar programing algorithm is developed in FORTRAN language (Lahey‐95) by using primitive and oscillatory stokes transformations. The primitive steady and oscillating model is solved numerically by using Gaussian elimination and implicit finite difference techniques. The steady outcomes of velocity, temperature, and concentration distributions are plotted for various physical parameters within defined boundary values. The range of parameters such as , , , , , and is used. The steady results are again used to display the oscillatory skin friction, oscillating heating rate, and oscillating mass transport around and positions of stretching porous cylinder. The increasing amplitude of velocity and temperature slip distribution grows well as diffusion‐convection parameter and thermal radiation increases at both angles. The slip temperature and slip concentration grows significantly as convective parameter increases. The impact of thermophoresis and rate of reactions enhances the oscillations and amplitudes of mass and heat transmission around stretchable cylinder as porous effect decreases. It is very important in nanofluid lubrications, drilling, rotating, milling, and cutting tools machines.
