Comparative study of radiation effect on titanium dioxide power-law nanofluid over a thin needle with cancer treatment applications: a quadratic regression model

Non-Newtonian fluids with nanomaterials are studied to improve industrial efficiency and production by enhancing thermal conductivity. In addition, the titanium dioxide nanoparticles can easily penetrate cells and tissues due to their small size. Its photocatalytic activities can also be utilized to produce reactive oxygen species, which have potential applications in cancer treatment. So, the present investigation intends to analyze the water-based titanium dioxide power-law nanofluid flow over a thin needle. Further, the thermal radiation was incorporated and analyzed as a complete case study for linear, nonlinear, and quadratic radiation. The governing equations are reformed into a dimensionless form using suitable similarity variables. Numerical solutions were found by implementing the Bvp4c technique. The major conclusion drawn from the present investigation reveals that the temperature is enhanced by the radiation, needle size, and titanium dioxide volume fraction. The nonlinear radiation case plays a dominant role compared to the other two radiation cases. In order to provide further insight into the engineering quantities, multiple quadratic regression models are utilized to predict skin friction and thermal transmission rate. The quadratic regression term of radiation and temperature ratio parameters has a negative influence on the heat transmission rate. The outcomes of this investigation may help to get a better theoretical understanding of various scientific research and biomedical applications, especially in the treatment of tumors, sterilization of medical instruments, drug delivery systems, and cancer treatment.