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One of the most pressing issues in contemporary applied mathematics is the regulation of energy transfer via the application of external forces. The processes of heat transfer are affected by magnetic force, which has many practical uses in industry, engineering, and medicine. This research explores the magnetohydrodynamics (MHD) three-dimensional stable axisymmetric boundary layer over a permeable moving plate, which consists of water as a base liquid and binary distinct nanoparticles to generate a hybrid nanofluid. In all of these, flow beyond the boundary layer area might be calculated by a small crosswise velocity. As a result of its high thermal conductivity, a pair of distinct kinds of nanoparticles have been considered, namely alumina and copper, which are integrated into the base water. The mathematical model is built within a boundary of specified geometry and then converted into a set of ordinary differential equations (ODEs). Resultant ODEs are solved numerically using the technique of three-stage Lobatto IIIa in bvp4c solver in 2017, MATLAB software. Results revealed that two branches exist in certain ranges of moving parameter. The impacts of an increasing physical parameter on profiles of velocities and temperature with skin friction as well as with heat transfer rate are represented in graphs. Furthermore, as the volume fraction of copper increases, so does the skin friction coefficient in the positive direction of λ. The effect of viscous dissipation on the temperature profile in the z-direction has the same rising results as observed in the x-direction. According to the results of the temporal stability analysis, the upper branch is realizable and stable.
Lund et al. (Sun,) studied this question.