The blood flow with heat transportation has prominent clinical importance during the levels where the blood flow needs to be checked (surgery) and the heat transportation rate must be controlled (therapy). This work presents an analysis of the melting heat transport of blood, which consists of iron nanoparticles along free convection with cross-model and solution of the partial differential equation (PDEs) are emerged by the mathematical model. Being the importance of iron oxide nanoparticles in applications of the biomedical field due to their intrinsic properties such as colloidal stability, surface engineering capability and low toxicity, this study has been launched. Furthermore, PDEs of the problem are converted into a set of nonlinear ordinary differential equations (ODEs) by proper transformations. The solution of this system of ODEs is calculated through RK 4 method and Keller–Box scheme. Some leading points and numerical results of this study of both types of presence and absence of meting effects are tabulated.

在需要检查（手术）血流量和必须控制（治疗）热量传输水平的过程中，带有热量传输的血流在临床上具有重要的临床意义。这项工作提供了对血液熔化传热的分析，该分析由铁纳米颗粒沿着自由对流组成，具有交叉模型，并且数学模型提出了偏微分方程（PDE）的解决方案。由于氧化铁纳米粒子的内在特性（例如胶体稳定性，表面工程能力和低毒性），在生物医学领域的应用中具有重要意义，因此这项研究已经启动。此外，通过适当的变换，可以将问题的PDE转换为一组非线性常微分方程（ODE）。该ODE系统的解决方案是通过RK 4方法和Keller-Box方案计算的。列出了存在和不存在相遇效应两种类型的这项研究的一些要点和数值结果。