OICC Press Mathematical Sciences 2251-7456 20 3 2026 06 30 Heat Transfer Investigation of Dissipative Couple Stress Rotating Fluid: Numerical and Theoretical Treatments 10.57647/mathsci.2026.2003.18 EN Mohamed M. Khader Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh, Saudi Arabia Mohamed Adel Department of Mathematics, Faculty of Science, Islamic University of Madinah, Medina, Saudi Arabia https://orcid.org/0000-0001-7069-697X Amel A. Alaidrous Department of Mathematics, Faculty of Sciences, Umm Al-Qura University, Makkah, Saudi Arabia Journal Article 2026 06 30 A comprehensive numerical study is presented to investigate heat transfer in the boundary layer flow of an incompressible fluid with a couple stress resulting from a permeable plate and linear extension. The model accounts for the combined influence of a transverse magnetic field and system rotation, where the inclusion of the Coriolis force introduces an additional rotational resistance that alters the flow structure. Fluid properties and wall permeability are systematically examined to assess their roles in shaping the thermal behavior. The thermal analysis is performed under a prescribed surface temperature condition, allowing for a clear eval-uation of heat transport mechanisms. Moreover, the formulation incorporates both viscous dissipation and energy due to couple stresses, which are essential in accurately capturing the physics of such fluids. These considerations are particularly relevant in processes associated with the manufacturing and handling of mag-netic materials, where rotational and electromagnetic effects coexist and significantly impact heat transfer characteristics. Similarity transformations create a nonlinear set of coupled ODEs with boundary conditions from the governing equations. The merged Fibonacci-Lucas polynomials (MFLPs) are used as part of the problem-solving strategy, along with the least-squares approximation technique, to simplify the equations that define the mathematical model into a nonlinear system of algebraic equations, then solved by Newton iteration approach. The research also includes examining the convergence and estimating the error of the proposed scheme. The results reveal that increasing the couple stress factor can slightly enhance skin fric-tion (3.5%) but significantly reduces heat transfer (26.7%), while increasing the magnetic field parameter markedly decreases both skin friction (50.4%) and heat transfer (23.9%). The discussion revolves around how relevant parameters affect the fluid’s temperature and velocity profiles. The technique’s effectiveness is shown through a table comparison, indicating good alignment with existing data and highlighting its accuracy.