Influence of Marangoni convection, solar radiation, and viscous dissipation on the bioconvection couple stress flow of the hybrid nanofluid over a shrinking surface

The heat transfer ratio plays an important role in the industrial and engineering sectors; in this model, the authors used the hybrid nanofluid because the heat transfer ratio of the hybrid nanofluid is more than that of the base fluid. The key objective of this research work is to boost up the heat transfer ratio, for example, not only the accomplishment of energy is enough but is also expected to regulate the feeding of energy, and this is possible only to approve the development of heat transmission liquids to the mechanism of the expenditures of energy and improvement. The current research study investigates the influence of Marangoni convection, solar radiation, and viscous dissipation on the bioconvection couple stress flow of the hybrid nanofluid over a shrinking surface. This type of flow has some important application in the industrial and engineering sectors for the purpose of cooling and heating effect. To transform the non-dimensionless form of the differential equation to the dimensionless form, the authors used the defined similarity transformation. The transformed dimensionless form of the differential equation is solved by the homotopic analysis method. The obtained important result is determined with the help of graphs which is obtained from velocity and temperature equations. The impression of different parameters such as couple stress parameter, Marangoni convection parameter, nanoparticle volume fraction, solar radiation parameter, magnetic field parameter, thermophoresis parameter, Eckert number, and Prandtl number is taken over graphs. The skin friction coefficient and Nusselt number are described in the form of tables.