This study investigates the influence of a central conducting block embedded in fluid flow systems, mimicking thermal systems with obstructions. Numerical solutions of energy, momentum, and continuity equations are employed to analyze pure water-based magneto-thermal systems under classical differential heating. The impact of cavity inclination (φ) and solid-to-fluid conductivity ratios (Kr) is examined at different Rayleigh numbers (Ra) and Hartmann numbers (Ha), keeping block size fixed. Findings reveal higher φ and Ra increase heat transfer rates (average Nusselt number, Nu), irrespective of Kr and Ha values, while Nu decreases with rising Ha. The study establishes the need for both lower and higher thermal conductivities to achieve higher heat transfer rates across all system inclinations, crucial for practical applications. These insights facilitate material selection and inclination angle considerations, holding practical implications for designing and optimizing thermal systems.