This article analyzes the growth of the vapor bubble in a novel model of power-law nanofluids (Al ₂ O ₃ /H ₂ O) under a new effect of variable surface tension. The governing equations of the rising vapor bubble flow model are formulated and converted to a single equation describing the bubble dynamics behavior. By employing the model of Plesset and Zwick method, we investigate a new model of equations within power-law nanofluids to examine the effect of different physical parameters such as initial superheating liquid, critical bubble radius, and thermal diffusivity on the vapor bubble formation. Furthermore, the effects of surface tension behavior with the initial bubble radius, time, and initial rate of bubble radius are examined. It is found that the growth of the vapor bubble radius increases with the increase of initial superheating liquid, critical bubble radius, and thermal diffusivity. In addition, the connection between shear stress and shear rate is analyzed in detail. Using appropriate values for the physical parameters, the behavior of solutions of the vapor bubble is discussed. Based on the conducted simulation analysis, the behavior of the solutions is found to be more accurate than those in the previous studies. Besides, the obtained results demonstrate that the vapor bubble in power-law nanofluids grows slower than in pure water.

The aim of this study is to focus mainly on the behavior of gas bubble growth under the effect of a magnetic field in N -dimensions of non-Newtonian hybrid nanomaterials. Many types of nanoparticles with base nanofluids have been used to study the problems that arise in the nanotechnology industrial processes. Considering these problems in nanomaterials, the effects of thermophysical parameters, such as nanoparticle size and type, nanoparticle volume fraction, N -dimensions, thermal diffusivity, and thermal conductivity are discussed. This investigation has demonstrated that the magnetic field B and electrical conductivity σ E have a significant impact on the dynamics of gas bubbles, showing that they play an important role in decreasing the growth processes. Furthermore, we examine the behavior of the gas bubble radius in the cases of pure water, mono nanoparticles, and hybrid nanofluid of nanomaterials (such as Cu − A l 2 O 3 / H 2 O , and Ti O 2 − A l 2 O 3 / H 2 O ) in N -dimensions of non-Newtonian fluid. Moreover, the relationship between shear stress and shear rate of non-Newtonian hybrid nanofluids is studied. The results are graphically represented to illustrate the behavior of solutions for the presented model. It is noted that the nanoparticles improve the thermophysical properties, which enhances the efficiency of the heat transfer rate of the nanofluids and decreases the behavior of the gas bubble radius. Based on the analysis of simulation procedures and system stability, we observe that the obtained results provide more accurate solutions and a greater reduction in the growth bubble process compared to previous models. Finally, we apply the phase plane approach to analyze the stability of the corresponding nonlinear system of the proposed model.