| Summary: | Analytical techniques are used in this article to examine the forced flow and heat transfer in a non-Newtonian Reiner-Rivlin fluid between two infinitely revolving disks in a magnetic field. The partial differential equations (PDEs) emphasizing flow and heat transfer were transformed into a nonlinear ordinary differential equations (ODEs) system using the Von Karman similarity transformation. The system of nonlinear ODEs with boundary conditions was solved using the Homotopy Perturbation Method (HPM) and Akbari-Ganji's Method (AGM). The study assessed the effects of physical factors on temperature profiles and the radial, transverse, and axial velocity components, including the visco-inelastic parameter, Reynolds number, Prandtl number, forced parameter, and magnetic field. The Python programming language was used for symbolic and numeric calculations of velocity components and temperature profiles. The accuracy of the results obtained through the analytical approach validates the applicability and efficiency of the proposed approach for studying the forced flow and heat transfer in non-Newtonian fluids between rotating disks.
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