This study presents a theoretical model to mimic heat transfer and nanoparticle transport through the tumour interstitium surrounding an inclined cylindrical blood vessel exposed to an alternating magnetic field. Using similarity transformations, we convert the governing equations (partial differential equations) into a system of ordinary differential equations, which we solve numerically with a MATLAB built-in solver (bvp4c). The convergence of the numerical solution is proved using the mesh convergence test. All parameters and their effects on fluid flow, heat, and mass transfer in the interstitium are studied and investigated. For instance, the nanoparticle penetration into the deep tissue can be enhanced by exposing the tumour to a magnetic field, increasing the tumour temperature and the nanoparticle Brownian motion, which is a consequence of increasing the tumour temperature. Moreover, we consider the case of non-Newtonian interstitial fluid in the tumour to mimic the nonlinearity of the fluid flow in the tumour tissue. The findings of this manuscript may optimise tumour ablation using hyperthermia by optimising nanoparticle delivery to deep tumour tissue and tumour temperature.