This study presents a mathematical model and finite element simulations to investigate interstitial fluid flow and nanodrug transport in a solid tumor, incorporating transvascular exchange, convection-diffusion-reaction dynamics, and intratumoral injection mechanisms. Optimizing nanodrug distribution remains a critical challenge in cancer therapy. The proposed model advances nanomedicine by enhancing the mechanistic understanding of nanodrug transport in a solid tumor. Cancer, a global threat, often manifests as solid tumors driven by uncontrolled cell growth. The heterogeneous microenvironment, lymphatic drainage, nano-bio interactions, and elevated interstitial fluid pressure (IFP) hinder effective nanodrug delivery. Nanoparticle (NP)-based drug delivery systems offer a promising solution, with FES providing an effective approach to model and simulate the complex delivery process. The model considered a spherical and symmetrical tumor architecture comprising a central necrosis region, viable tumor, and surrounding healthy tissue with functional lymphatic dynamics. Substantial nanodrug carriers (dextran, liposomal, polyethylene glycol (PEG)-coated gold, and magnetic) and conventional doxorubicin are evaluated in the tumor. The governing fluid flow and solute transport equation along with the specified boundary conditions are solved using the finite element method through the Galerkin approach. Simulations show that IFP peaks in the necrotic core and sharply declines at the viable-healthy tissue interface. Both fluid pressure and velocity are sensitive when fluid flow resistance drops below 5. Necrotic core size influences IFP, and critical necrotic radius ( ) marks pressure stabilization and defines the threshold for effective nanodrug delivery. Vascular normalization and functional lymphatic dynamics show marginal impact. Smaller NPs (~10 nm) diffuse faster but undergo rapid degradation, while larger particles (>30 nm) exhibit prolonged retention at the injection site. Liposomal, PEG-coated gold, and magnetic variants demonstrate superior therapeutic action compared to conventional doxorubicin. The findings of the study highlight its strong potential for optimizing nanodrug delivery and design, as well as hyperthermia treatment, enhancing personalized cancer therapy.