Subdomain method for unsteady flow of ZnO-SAE50 nano-lubricant through expanding/contracting walls in an asymmetric porous horizontal channel

The laminar time-dependent fluid flow of an engine oil (Zinc Oxide -Society of Automotive Engineers 50 alias ZnO -SAE50 nano-lubricant) through a rectangular channel is presented. The channel is made up of permeable walls that can expand or contract. It is also under the impact of thermal radiation and magnetic field is dominant enough to be ignored. The lower and upper walls of the channel bear different permeabilities and temperatures. Hence, a system of governing nonlinear partial differential equations is setup by means of conversation laws and aforementioned assumptions. By the implementation of suitable similarity transformations and conservation of mass, the equations for momentum, and energy are reduced to relatively simpler system of ordinary differential equations. The resulting system is solved by employing a semi analytical technique named as Subdomain Method (SDM). The results are further supported by another numerical scheme (a duos of shooting method along with Runge-Kutta-Fehlberg algorithm). The functioning of flow and temperature profiles under the variation in sig-nificant physical parameters is demonstrate upon the description of graphs and tables. Thorough discussions and concluding results are also presented at the end of the manuscript.

Automated summary

This paper presents the laminar time-dependent fluid flow of an engine oil (ZnO-SAE50 nano-lubricant) through a rectangular channel with permeable walls. The governing partial differential equations are simplified using similarity transformations and conservation of mass, and then solved using the Subdomain Method and another numerical scheme. The results show the variations of flow and temperature profiles under different physical parameters, and are supported by graphs and tables. The paper concludes with thorough discussions and concluding results.