The current research explores the thermal convection of magnetohydrodynamic flow in modified and constraint-based recto-triangular thermal systems (upper part rectangular and lower part triangular) filled with copper-oxide water nanofluid. The external uniform magnetic field is applied horizontally, while the magnetic field angle γ is varied systematically. The volume/area of thermal system cavities is maintained the same while their bottom triangular portions are adjusted considering various vertex angles (Θ) of 90–270°. The cooling and heating arrangements are provided for the same lengths using the top wall and the central portion of the bottom wall, respectively. The finite element method is used to discretize and solve the dimensionless governing transport equations. The thermal and flow analyses are conducted on the backdrop of constraint-based thermal systems for varying pertinent parameters like the Rayleigh number (Ra = 103–105), Hartmann number (Ha = 0–70), magnetic field angle (γ = 0–90°) and vertex angle (Θ = 90–270°). It is revealed that the flow structure becomes more complex and asymmetric in nature at high Ra and Ha. Furthermore, the average Nu is an increasing function of Ra and Θ, whereas it is a decreasing function of Ha. The entropy plots are also generated to study the entropy generation due to magnetohydrodynamic, viscous dissipation, and thermal effects that together constitute the total entropy of the system. The constraint-based system analysis could be very helpful for the design and identification of the most efficient system for the utilized same working fluid (volume).
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