Heat transfer is crucial in various biological applications, impacting physiological processes, medical treatments, and biotechnological innovations. We created a mathematical model for Sutterby nanofluid on the surface of an unexpended horizontal cylinder exposure to an external heat source and a magnetic field. This led to a nonlinear differential system, which we numerically solved using MATLAB's built-in solver (bvp4c). We explored the effects of Brownian motion, thermophoresis, interstitial fluid velocity, and tissue thermal absorption. Our findings reveal that increasing K enhances NP accumulation while raising interstitial fluid temperature. Conversely, higher R_d reduces NP concentration, potentially compromising treatment efficacy. The influence of thermophoresis and Brownian motion further underscores the importance of understanding particle behavior within the tumor microenvironment. The results demonstrate that higher thermophoresis parameters can increase NP concentration, while increased Brownian motion leads to a reduction in NP concentration. The magnetic field parameter was found to enhance both temperature and NP concentration, improving treatment efficiency. Overall, this study emphasizes the critical role of fluid dynamics and thermal properties in optimizing thermal therapy for cancer. The insights gained from this analysis can help in future research and clinical applications, guiding the development of more effective treatment strategies that leverage the unique properties of nanofluids. Future work should focus on further refining these models and exploring additional factors that may influence treatment efficacy.