Solid cancer remains a serious threat to global health despite decades of progress. Traditional chemotherapy treatment has been used to curb the disease despite its inability to reach cancer cells at high enough quantities leading to adverse toxicity on healthy cells, producing severe side effects, and exacerbating patient suffering. Active targeted nano-drugs (ATNDs) acting as transporter systems have become a viable solution to this shortcoming, offering the possibility of more precise cancer targeting. Therefore, in the present study, we develop a numerical model of capturing ATNDs, incorporating movements within and outside the tumor spheroid and the magnetic forces guiding the nanoparticles. By combining a model of ATNDs transport with a tumor-effector dynamic model based on porous media phenomena, we demonstrate how the models may be combined to model drug-loaded nanoparticle transport in an external magnetic field. We analyze the controlled drug delivery against traditional chemotherapy based on the combined effect of immunotherapy and chemotherapy with the dispersion of nano-drugs to lead a solute cloud toward the tumor. We found that the amalgamation of immune and chemotherapy delivered by ATNDs enhances cancer therapy efficacy compared with conventional chemotherapy. Increased drug convection toward the tumor region presented by ascending values of the Peclet number inhibits the growth of tumor cells and prolongs progression-free survival. Increases in source term and vessel permeability also increase the likelihood of tumor suppression, while raising the hematocrit and magnetic number results in reduced tumor cell killing. Sensitivity analysis of the dynamic model parameters has been discussed. This work demonstrates that ATND-delivery systems can improve therapeutic agent delivery to the tumor tissue, and promote tumor cell killing.