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In this paper, pole placement-based design and analysis of a free piston Stirling engine (FPSE) is presented and compared to the well-defined Beale number design technique. First, dynamic and thermodynamic equations governing the engine system are extracted. Then, linear dynamics of the free piston Stirling engine are studied using dynamic systems theory tools such as root locus. Accordingly, the effects of variations of design parameters such as mass of pistons, stiffness of springs, and frictional damping on the locations of dominant closed-loop poles are investigated. The design procedure is thus conducted to place the dominant poles of the dynamic system at desired locations on the s-plane so that the unstable dynamics, which is the required criterion for energy generation, is achieved. Next, the closed-loop poles are selected based on a desired frequency so that a periodical system is found. Consequently, the design parameters, including mass and spring stiffness for both power and displacer pistons, are obtained. Finally, the engine power is calculated through the proposed control-based analysis and the result is compared to those of the experimental work and the Beale number approach. The outcomes of this work clearly reveal the effectiveness of the control-based design technique of FPSEs compared to the well-known approaches such as Beale number.

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In this paper, the steady-state natural convection in a square cavity filled with water–Al2O3 nanofluid in the presence of magnetic fields with variable inclination angles is investigated numerically. The enclosure is subjected to different side-wall temperatures while the top and bottom walls are assumed to be adiabatic. The thermal behavior of enclosure is assessed using a finite volume-based computer program. In order to ensure the accuracy of results, comparisons are also made with a previous published work. In this research, at constant magnetic field strengths, the effect of magnetic field inclination angle on the rate of heat transfer in the square cavity is investigated at the Rayleigh numbers of Ra = 103, 104, 105 and 106. In this work, the Hartmann number ranges from Ha = 0 to 120 and the solid volume fraction varies from φ = 0 to 0.06. Numerical results show that depending on the Rayleigh and Hartmann numbers, the maximum heat transfer rate may occur at magnetic field inclination angles of 45°, 60° or 90° and the effect of magnetic field inclination angle is significant at high values of Rayleigh and Hartmann numbers. It is found that addition of nano-sized solid particles causes higher heat transfer rate when Ra = 103, whereas at Rayleigh number of Ra = 106, a reverse behavior is observed. Results show that at Rayleigh numbers of Ra = 104 and 105, the effect of solid particles addition on the thermal performance of the enclosure depends on the Hartmann number. It is also shown that an increase in the inclination angle causes higher velocity within the enclosure and addition of solid particles leads to suppression of flow field.

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