In this article, the effects of swimming gyrotactic microorganisms for magnetohydrodynamics nanofluid using Darcy law are investigated. The numerical results of nonlinear coupled mathematical model are obtained by means of Successive Local Linearization Method. This technique is based on a simple notion of the decoupling systems of equations utilizing the linearization of the unknown functions sequentially according to the order of classifying the system of governing equations. The linearized equations, that developed a sequence of linear differential equations along with variable coefficients, were solved by employing the Chebyshev spectral collocation method. The convergence speed of the SLLM technique can be willingly upgraded by successive applying over relaxation method. The comparison of current study with available published literature has been made for the validation of obtained results. It is found that the reported numerical method is in perfect accord with the said similar methods. The results are displayed through tables and graphs.

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Summary Modeling with optimization has become a ubiquitous practice in the field of Stirling engine. A plethora of studies in the literature is dedicated in developing a feasible optimized model that can precisely predict the performance of Stirling engine. Hence, the purpose of this article is to compile and expansively review the thermodynamic models and optimization efforts made in pursuit of performance enhancement of the Stirling engine. An extensive range of models available in the literature is painstakingly discussed. Likewise, a wide variety of available optimization techniques spanning from conventional experimental and univariate methods to more complex multiobjective optimization approach are critically reviewed. A comparative analysis of the models is carried out based on the accuracy of their predictability of the performance of Stirling engines. Results obtained from the models are validated through the experimental data of the GPU‐3 Stirling engine prototype. Several optimization techniques are investigated based on the effective and efficient optimization of operating and geometric parameters of the Stirling engine. The review concluded that the Comprehensive Polytropic Model of Stirling engine (CPMS) demonstrated better accuracy in comparison with other models. In addition, the multiobjective particle swarm optimization (MOPSO) technique was found to be effective and computationally efficient.

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