Impact of magnetic-field on the dynamic of gas bubbles in N-dimensions of non-Newtonian hybrid nanofluid: analytical study

Abstract

Abstract 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.