Lie symmetry analysis on heat and mass transport aspects of rate type fluid flow with waste discharge concentration: Keller Box approach.

The present analysis examines the effect of thermal radiation on the stream of Maxwell liquid past a stretchy surface in the presence of a zero-mass flux condition. The effect of waste discharge concentration, thermophoresis-Brownian motion, and porous media on the fluid motion is also considered. Investigation of the liquid flow with waste discharge concentration in stretched sheets may lead to the growth of effective methods for disposing of waste and preventing pollution. Due to their extensive applicability, the mechanisms of flow and heat transmission in the context of thermal radiation play a crucial role in research and industry. This phenomenon often occurs in spacecraft, nuclear reactor cooling, power production, aerospace technologies, combustion applications, gas turbines, hypersonic flights, and high-temperature processes. The modelled governing partial differential equations (PDEs) are converted into dimensionless ordinary differential equations (ODEs) utilizing appropriate similarity variables. Further, the Keller-Box approach is utilized to solve the resultant ODEs numerically. The influence of several parameters on the temperature, concentration and velocity profiles is shown via graphic representations. The intensification in Deborah's number and porous parameter values declines the velocity profile. As the values of the radiation, thermophoresis, and Brownian motion parameters increase, the thermal profile increases. The concentration profile increases as the pollutant external source parameter value upsurges.