This paper aims to analyze the second law of the thermodynamic for the non-Newtonian power-law nanofluids flow between inclined polygonal/polygonal or polygonal/cylinder shapes. Multi-wall carbon nanotubes are incorporated in the ethylene glycol as a base fluid to formulate the worked suspension. Electromagnetic forces together with the thermal radiation are taken into account. Unusually, the magnetic field is assumed to be horizontal while the flow domain is inclined and a semi implicit treatment is presented for the magnetic terms. The solution methodology is depending on the Galerkin finite element method (FEM) and the Characteristic-Based Split (CBS) scheme. Various designs for the considered models are considered based on the areas and shapes of the inner polygonal/cylinder. The main outcomes revealed that area of the flow and power-law index N control in the convective and heat transfer process. Also, the fluid friction irreversibility takes its maximum values at high values of the power-law index. Furthermore, ratios of the increase in values of the entropy tools (ST+,SF+,Stot+) due to the variations of γ take their maximum at γ=30 and low values of Ha.
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