Analytical Treatment of Unsteady Fluid Flow of Nonhomogeneous Nanofluids among Two Infinite Parallel Surfaces: Collocation Method-Based Study

Fluid flow and heat transfer of nanofluids have gained a lot of attention due to their wide application in industry. In this context, the appropriate solution to such phenomena is the study of this exciting and challenging field by the research community. This paper presents an extension of a well-known collocation method (CM) to investigate the accurate solutions to unsteady flow and heat transfer among two parallel plates. First, a mathematical model is developed for the discussed phenomena, then this model is converted into a non-dimensional form using viable similarity variables. In order to inspect the accurate solutions of the accomplished set of nonlinear ordinary differential equations, a collocation method is proposed and applied successfully. Various simulations are performed to analyze the behavior of non-dimensional velocity, temperature, and concentration profiles alongside the deviation of physical parameters present in the model, and then plotted graphically. It is important to mention that the velocity is enhanced due to the higher impact of the parameter Ha. The parameter N-t caused an efficient enhancement in the temperature distribution while the parameters N-t provided a drop in the temperature that actually affected the rate of heat transmission. Dual behavior of concentration is noted for parameter b, while it can be noted that mixed increasing behavior is available for the concentration against Le. The behavior of skin friction, the Nusselt number, and the Sherwood number were also investigated in addition to the physical parameters. It was observed that the Nusselt number increases with the enhancement of the effects of the magnetic field parameter and the Prandtl number. A comparative study shows that the proposed scheme is very effective and reliable in investigating the solutions of the discussed phenomena and can be extended to find the solutions to more nonlinear physical problems with complex geometry.

Automated summary

Fluid flow and heat transfer of nanofluids have been widely studied due to their applications in industry. This paper presents an extension of a well-known method to investigate the accurate solutions to unsteady flow and heat transfer among two parallel plates. The mathematical model is converted into a non-dimensional form and a collocation method is successfully applied to obtain the solutions to the nonlinear ordinary differential equations. Various simulations are performed to analyze the behavior of velocity, temperature, and concentration, as well as other physical parameters. The proposed scheme is shown to be effective and reliable for studying such phenomena.