We present an innovative, effective micro-macro numerical approach for modeling ferrofluids under the presence of a magnetic field and a driven-cavity flow. Our multi-model approach combines the localized use of a microscopic Smoluchowski equation solver and a continuous constitutive law coupled with the macroscopic flow and an externally applied magnetic field. The model is confirmed with a direct simulation and results are compared with the closure approximation proposed by Shen and Doi. We systematically study the change in viscosity by incrementally changing the numerical parameter settings. Indeed, "negative change" in viscosity is observed.