The current work is categorized into the following format Background: Heat transfer controlling through therapy and blood flow has clinical importance in different levels of the human body. Biological faculties utilize blood in which iron oxide nanoparticles are incorporated for contrast agents and in the biomedical fields as they possess key and intrinsic characteristics, like low toxicity, capability of blood carrying nanoparticles, surface engineering and colloidal stability. This paper has a unique approach for analysis of blood flow containing nanoparticles with mathematical model of Carreau nanofluid. Furthermore, heat transport analysis has been provided by using the melting heat conditions and free convection. Carreau nanofluid for blood flow gives a set of partial differential equations (PDEs), which are handled by using the Keller Box scheme to obtain the numerical performances of the results. The obtained results are compared with Bvp4c, which is MATLAB built in program and found smooth agreement. The graphical plots and statistical tables have been provided for various dimensionless parameters to get the numerical simulations of the problem against velocity, temperature, and heat transfer Nusselt number. From the obtained results, the velocity and temperature of the fluid diminishes by the virtue of an amplification in unsteady parameter A. A positive variation in melting parameter M in the case of Prandtl number Pr and unsteady parameter A magnifies the heat transfer Nusselt number. This article shows the novelty in the sense that the effect of Tiwari and Das model accompanied with melting heat transfer phenomenon in the case of unsteady Carreau fluid has not investigated before in the available literature related to the Carreau fluid.