The lack of in vivo studies on the delivery of doxorubicin within human skin, especially the absence of data on the doxorubicin diffusion coefficient, has made understanding its transdermal delivery kinetics challenging. In this study, as a first step, governing equations and finite element methods were employed to reproduce Franz diffusion cell experiment in human cadaver skin. The application of this experiment representative model with a fitting method resulted in approximate values for the diffusivity of doxorubicin across various skin layers. The estimated values were used later to conduct a comprehensive examination of doxorubicin administration for breast tumor treatments. In a 2D axisymmetric model using Fick's Law and then a microneedles array 3D model, crucial parameters effects on delivery efficiency were examined, such as the microneedle tip diameter, tip-to-tip distance, and tumor depth. As highlighted by the findings of this study, these parameters have an impact on the effectiveness of doxorubicin delivery for treating breast tumors. The focus of this research is on the potential of numerical methods in biomedical engineering, which addresses the urgent need for data on doxorubicin diffusion in human skin and offers valuable insights into optimizing drug delivery strategies for enhanced therapeutic outcomes.