Pollutant discharge concentration is essential to many industries and environmental management. Controlling and tracking water contamination is vital to preserving water supplies and upholding ecological regulations. Therefore, the objective of the present study is to examine the influences of waste discharge concentration, heat source/sink, inclined magnetic field, and thermophoretic particle deposition on Casson fluid flow via a flat plate with Blasius and Sakiadis flows. The system of PDEs (partial differential equations) is altered into ODEs (ordinary differential equations) by applying a suitable similarity transformation. The Runge-Kutta-Fehlberg-45 (RKF-45) order approach and shooting approach are applied to solve the resulting ODEs. A graphical representation will be utilized to demonstrate the consequences of several nondimensional constraints on their respective profiles. The key findings of this study demonstrate that the concentration profile will be improved by escalating the values of the external pollutant source and the external pollutant source variation constraints opposite trend is seen for the thermophoretic constraint. The Sherwood number declines by enhancing the magnetic parameters and the external pollution source variation. The minimum magnitude value of skin friction for the Casson parameter in Blasius flow is 0.3825. The maximum rate of heat and mass transfer values for Sakiadis flow is found to be 1.7180 and 2.5424 for heat source/sink and thermophoretic parameters, respectively.
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