Thermally radiative bioconvective nanofluid flow on a wavy cylinder with buongiorno model: A sensitivity analysis using response surface methodology

The significant impact of nanotechnology has turned the ordinary into the excellent in the ever-changing environment of science and technology. Recent times have seen a dramatic transformation as advances in science and technology continue to push us into the domain of nanoscale innovation. Fluid flow over a range of geometries is involved in the physical processes of heat and mass transfer subject to the constraints. These phase change systems are also converted into the latest technology by improving the thermal conductivity of the fluids through the mixing of nanoparticles in the ordinary base fluid. This approach makes things finer and quicker from the perspective of efficiency and structure. It has many applications in various domains especially in nano-medicines, chemotherapy, microprocessors, refrigeration, and biotechnology. In this work, nanofluid flow through a wavy cylinder is considered in the existence of thermal radiation, activation energy, and motile microorganisms. The physical model is computationally solved by developing a system of PDE's (partial differential equations) and then transformed into ODE's (ordinary differential equations) by the smooth implementation of similarity variables. The resultant ODE's numerically treated by the bvp4c built package of MATLAB and get the required results. These results are discussed and graphically visualized in the analysis section. For the validation of results, the statistical approach is implemented on the acquired results and shows the fitted model, contour plots, surface plots, residual plots, and streamlines of the involved parameters and their impacts on the model. The impact of involving physical quantities on flow velocity, thermal, concentration, and microorganism's density profiles also discussed. From the results, it is noted that the velocity profile increases by increasing the counts of mixed convection. Thermal distribution enhanced due to boosting the values of thermophoresis and Brownian motion. The concentration of nanoparticles increased by increasing the magnetic field strength. The larger values of peclet number minimize the density of microorganisms. Skin friction coefficient is increased by around 28% and mass transport going to be increased by 36% due to the existence of microorganisms. The analysis of variance shows that our model is significant and the fitted summary also shows the fitness of model.