Bulirsch-Stoer computations for bioconvective magnetized nanomaterial flow subjected to convective thermal heating and Stefan blowing: a revised Buongiorno model for theranostic applications

Abstract

Theranostics is a novel procedure that integrates therapy and diagnosis in a single platform. For its application in theranostic and photothermal therapy for melanoma skin cancer, the hydromagnetic bioconvective flow of a nanomaterial over a lengthening surface is investigated. Realistic nanomaterial modeling is achieved by incorporating passive control of the nanoparticles at the boundary. The impact of the Newtonian heating and Stefan blowing constraints are also accounted. Apposite transformations are employed and then transmuted nonlinear ODEs are resolved using the Bulirsch-Stoer and Newton-Raphson methods. The influence of Stefan blowing parameter , the magnetic field parameter , and the Biot number on the heat transfer rate has been scrutinized and optimized utilizing the response surface methodology (RSM). The sensitivity of heat transport rate is computed. It is found that the Newtonian thermal condition intensifies the nanomaterial temperature that serves as a crucial role in the termination of cancerous cells or tumors. The maximum drag coefficient is experienced for the insignificant intensity of the magnetic field and Stefan blowing. Further, the heat transfer rate is maximum when the Stefan blowing and Biot numbers are at a high level and the Hartmann number is at a low level.