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ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik, vol.105, no.9, 2025 (SCI-Expanded)
In the current investigation, our work relying on 3-D Williamson fluid expanded in bidirectional past over a linear penetrating sheet. Firstly, magneto hydrodynamic effect is considered for both velocity profiles (i.e., x, y-axis) towards the momentum equation. As a second step, we have examined the influence of most efficient feature of today's research namely Cattaneo–Christov theory. Moreover, heat production/absorption, Joule heating and thermal radiation effects are opted whilst viscous dissipation impacts are also considered owing to its extremely significant effect on heat transmission. Lastly, energy optimization is conducted by letting entropy approach. The numerical solution of transformed equations has been attained by applying optimal homotopy technique. Moreover, the bearing of numerous influential parameters are varied to judge the behavior in the velocity and temperature profiles. Variation amongst the velocity profiles along (x, y-axis) are observed graphically under the varying values of magnetic parameter, Darcy number and also non-Newtonian Williamson parameter. Moreover, temperature difference parameter is also observed across the velocity profile along (y-axis). The outcomes reveals that velocity profile along (y-axis) is enhanced with higher estimations of (Formula presented.) parameter whilst both velocity trends along (x, y-axis) tends to be lowered with the rise in magnetic parameter, non-Newtonian Williamson parameter, and also Darcy number. Furthermore, Entropy generation remarkably enhanced for Brinkman number, magnetic parameter, radiation and temperature difference parameter, respectively. Moreover, in tabular form the governing parameters within the skin friction are also illustrated whilst the results appertain to involved parameter are validated and seen in total covenant with the earlier published literature by Malik et al. (2017).