This study delves into heat and mass transference in fluids with variable thermo-physical features, focusing on the Powell-Eyring fluid, a non-Newtonian substance with unique characteristics. Our aim is to understand the behaviour of this shear-thinning fluid when interacting with an exponentially stretchable surface, considering factors like mixed convection and thermal radiation. Our research endeavours to uncover novel findings in this intricate domain, with the primary objective of comprehending how this shear-thinning fluid behaves when it encounters an exponentially stretchable surface. To address the complexities, we employ the BVP4C technique in MATLAB, transforming governing equations into nonlinear partial differential equations (PDEs) based on mass, linear momentum, and energy conservation principles. The Homotopy method aids in navigating these equations, and numerical solutions are calculated using the powerful BVP4C technique for ordinary differential equations (odes). The research stands out for its comprehensive exploration of the interplay among diverse factors, including radiation, variable viscosity, mixed convection, and activation energy constraints. Findings are presented through tables and graphs, offering valuable insights into the intricate physical phenomena within this multifaceted field.
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