Investigation of heat and mass transfer performance in Casson fluid flow over nonlinear stretching sheet: Impact of novel similarity transformations

This article primarily aims to utilize novel similarity transformations that were created to overcome a limitation found in previous research. These similarity methods have proven to be effective in finding solutions to systems of partial differential equations. The study analyzed mass and heat transfer in a Casson fluid near a boundary on a stretchy, permeable surface, considering radiative heat transmission and non-homogeneous thermal effects. It focused on two heating methods: prescribed surface temperature (PST) and prescribed surface heat flux (PHF). Prior research involving stretchable surfaces has mostly used non-dimensional similarity metrics related to one variable that is not dependent on others (e.g., only or), which resulted in certain errors. To tackle this issue, we have introduced a novel set of similarity transformations that encompass all the independent variables in the equations. that are being studied (that is, x and y). This novel strategy seeks to significantly improve the accuracy of our results. The equations that dictate the behavior were transformed into nonlinear ordinary differential equations by employing specific similarity transformations. The Runge-Kutta-Fehlberg approach proved to be highly efficient in computing solutions, yielding fourth- and fifth-order approximations. The solutions were found to rely on various physical parameters, including the Casson fluid factor, Prandtl and Schmidt numbers, heat source and sink components, radiation parameters, and suction and injection factors. These parameters elucidate the behavior of velocity, concentration, and temperature profiles. When the Casson parameter increases by 212.5%, the temperature increases by 0.5270% for the PST case and by 1.4050% for the PHF case under suction conditions, and similarly, rises by 1.3238% for the PST case and by 5.7224% for the PHF case under blowing conditions.